The Thermal Transport Properties of Helium, Helium-Air

ORNL/TM-4931

The Thermal Transport Properties of Helium, Helium-Air Mixtures, Water, and Tubing

Steel Used in the CACHE Program to Compute HTGR Auxiliary Heat

Exchanger Performance

J. R. Tallackson

^ f H O I I C E Vv,

PORTIONS OF T H I S REPORT ARB I L L E G I B L E . I I has been reproduced from th-3 bent available copy to por-jit the broadest possible avail-ability.

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This report was prepared as an account of work sponsored by the United States Government. Neither the United States nor the Energy Research anc! Development Administration, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe privately owned rights.

O R S L / T M - 4 9 3 1

Contract !?c. W-7k05-eng-26

R e a c t o r D i v i s i o n

THE THERMAL TRANSPORT PROPERTIES OF HELIUM, HELIUM-AIR MIXTURES, WATER, AIID TU3I1JG JTEEL USED III TI'IE CACHE

PROGRAM TO COMPUTE HTGR AUXILIARY HEAT EXCHANGER PERFORMANCE

J* R. Tallackcon

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FEBRUARY 1976

^ B O T I C E x

£PBJXQ.^s_QFJjjIS_REPORT APE - t. hr;" ToDror.ucr-d i'ron the t c c t w i * ccpy to permit the broadest possible a v i -ability.

N O T I C E : T h i s d o c u m e n t c o n t a i n s i n f o r m a t i o n o f a p r e l i m i n a r y n a t u r e a n d w a s p r e p a r e d p r i m a r i l y f c r i n t e r n a l u s e a t t h e O a k R i d g e N a t i o n a l L a b o r a t o r y . I t i s s u b j e c t t o r e v i s i o n o r c o r -r e c t i o n a n d t h e r e f o r e d o e s n o t x * e p r e s e n t a f i n a l r e p o r t .

OAK RIDGE NATIONAL LABORATORY Oak Ridge, Tennessee 37330

operated by UNION CARBIDE CORPORATION

for the U. S. ENERGY RESEARCH AND DEVELOIMENT ADMINISTRATION

iii

CONTENTS

Abstract 1 INTRODUCTION 1 I. THE THERMAL TRANSPORT PRO PERT XL'S Or FUSE HELIUM 3

A. Thennal Conductivity 3 3. Viscosity 4 C. Specific Heat 4

II. THE THERMAL TRANSPORT PROPERTIES 0? WATER 5

A. Therr.al Conductivity cf Water 5 3. Viscosity of Water 7 C. Specific Heat of Liquid Water 7

III. THE THERMAL CONDUCTIVITY OF STEEL TUSTKG 9 IV. THE THERMAL TRANSPORT PROPERTIES OF H-.LIUM DILUTED

WITH OXYGEN, NITROGEN AND CARBON MONÎDE 12 A. The Thercol Conductivity cf Heiiuir. Diluted with

Nitrogen, Oxygen, and Carbon Monoxide 17 3. The Viscosity of Helium Diluted with Nitrogen,

Oxygen, and Carbon Konoxidt . 21 C. The Specific Heat of Helium-Air Gas Mixtures 27

APPENDIX A. EQUATIONS AND TABULATIONS FOR THE THERMAL CONDUCTIVITY OF PURE HELIUM 30 Summary of Equations Developed for Evaluating the Thennal Conductivity of Helium 83

AFPENDIX 3. THERMAL CONDUCTIVITY OF HELIUM-NITROGEN MIXTURES 88

APPENDIX C. THE VISCOSITY OF HELIUM 93 The Viscosity of Pure Helium 93

APPENDIX D. THE SPECIFIC HEAT OF HELIUM-AIR MIXTURES 100 REFERENCES 106

THE T:-IERMAL TRANSPORT PROPERTIES OF HELIUM, HELIUM-AIR MDITUREoj WATER, Alffi TU3IKG STEEL USED IK THE CACHE

?R:GRAM TO CD.'-TUTE HTGR AUXILIARY HEAT EXCHANGER PERFORMANCE

J. R. Tallachsor.

Abstract

This ropcrt presents, quantitatively, the thermal trans-port properties cf the materials involved in digital computer calculation:; zC heat transfer rates by the Core Auxiliary ••cat Exchangers in large HTGR nuclear .-tear, supply systems. Tr.cr.c- :::ato rials arc euro helium, mixtures of helium with com-mon rones having molecular '.'eights in the range of 28 to 32, alloy .;teel tubing, and water.

For use in programmed computations the viscosity, thermal conductivity, and specific heat, arc represented primarily by equations augmented by curves and tabulations. Materials supporting the development and selection of the property e-quatier.s is included.

Keywords: Helium, carbon monoxide, nitrogen, heat trans-fer, thermal conductivity, oxygen, chrome — molybdenum steels, air, heat capacity, viscosity, gases.

MTSOD'UCTIOH

ORNL has been producing independent calculations of the afterheat removal capability of HTGR emergency cooling systems undergoing licens-ing review. Afterheat is transferred from the reactor core by auxiliary loops which circulate core coolant gas to Core Auxiliary Heat Exchangers (CAIffis). Heat removed by a CAHE is dumped, externally, by a water-tc-air heat exchanger.

Adequate performance by the CAHE is vital to HTGR safety} therefore, it is essential that all computations of CAHE heat transfer rates be con-ducted with more than ordinary care.

2h

CAHE p e r f o r m a n c e i s s t r o n g l y i n f l u e n c e d "by t h e t r a n s p o r t p r o p e r t i e s

o f t h e c o r e c o o l a n t g a s e s , a n d t o a m u c h l e s s e r e x t e n t , b y t h e p r o p e r t i e s

o f t h e t u b i n g s t e e l a n d w a t e r . I n n o r m a l c i r c u m s t a n c e s HTGR a f t e r h e a t i s

r e m o v e d f r o m t h e c o r e b y c i r c u l a t i n g p r e s s u r i z e d h e l i u m t h r o u g h t h e s t e a m

g e n e r a t o r s . D u r i n g r e f u e l i n g o r u n d e r e m e r g e n c y c o n d i t i o n s t h e c o o l a n t

g a s i s c i r c u l a t e d t h r u g h t h e a u x i l i a r y l o o p s . T h e t r a n s p o r t p r o p e r t i e s

o f c o n c e r n j t h e r m a l c o n d u c t i v i t y , v i s c o s i t y , a n d s p e c i f i c h e a t , o f h e l i u m ,

s t e e l , a n d w a t e r a r e w e l l d o c u m e n t e d a n d r e a d i l y a v a i l a b l e . U n c e r t a i n t i e s

i n p e r f o r m a n c e c o m p u t a t i o n s a s s o c i a t e d w i t h t h e s e m a t e r i a l s a r e s m a l l .

T h e l i m i t i n g s i t u a t i o n a r i s e s d u r i n g a D e s i g n B a s i s D e p r e s s u r i z a t i o n

A c c i d e n t (BBDA) f o l l o w e d b y a Lc-ss o f M a i n L o o p C o o l i n g ( K > M L C ) . I n t h e

r e m o t e e v e n t t h a t a n HTGR e x p e r i e n c e s a DBDA p l u s LOMLC, t h e h e l i u m r e -

m a i n i n g i n t h e r e a c t o r v e s s e l w i l l b e c o m e d i l u t e d b y t h e i n g r e s s o f a i r

f r o m t h e c o n t a i n m e n t b u i l d i n g . T h e o x y g e n i n t h e a i r w i l l r e a c t w i t h

t h e g r a p h i t e i n t h e c o r e a n d c a r b o n m o n o x i d e w i l l b e p r o d u c e d . T h e c o r e

c o o l a n t g a s i s , t h e n , a m i x t u r e c o n s i s t i n g p r i n c i p a l l y o f h e l i u m , n i t r o g e n ,

a n d c a r b o n m o n o x i d e . M i x t u r e c o m p o s i t i o n v a r i e s w i t h e l a p s e d t i m e a f t e r

t h e a c c i d e n t a n d t h e p r o p e r t i e s o f t h e m i x t u r e , d e p e n d e n t o n c o m p o s i t i o n ,

s t r o n g l y i n f l u e n c e t h e p e r f o r m a n c e o f t h e C A H E s .

T h e t h e r m a l t r a n s p o r t p r o p e r t i e s o f g a s m i x t u r e s a r e , i n g e n e r a l ,

n o t w e l l e s t a b l i s h e d b y e x p e r i m e n t . T h e o r e t i c a l c a l c u l a t i o n s o f t e n l e a v e

much t o b e d e s i r e d . F o r t u n a t e l y , a s m a l l a m o u n t o f d a t a o n t h e t h e r m a l

c o n d u c t i v i t y a n d v i s c o s i t y o f m i x t u r e s o f h e l i u m w i t h o x y g e n a n d n i t r o g e n

i s a v a i l a b l e . H i s r e p o r t d e s c r i b e s how t h e s e d a t a w e r e u s e d t o d e v e l o p

e q u a t i o n s t o d e s c r i b e t h e p r o p e r t i e s o f t h e c o r e c o o l a n t g a s f o l l o w i n g a

DBDA.. T h e e x p e r i m e n t a l d a t a a n d s u p p o r t i n g i n f o r m a t i o n a r e i n c l u d e d .

B e c a u s e d i g i t a l c o m p u t e r c a l c u l a t i o n s a r e f a c i l i t a t e d b y u s i n g

e q u a t i o n s r u t h e r t h a n t a b u l a t i o n s bo d e s c r i b e v a r i a b l e p a r a m e t e r s , a l l

p r o p e r t y d f . t a a r e s p e c i f i e d w i t h eq. r c i o n s f o r u s e i n t h e C o r e A u x i l i a r y

C o o l i n g H e a t E x c h a n g e r (CACHE) p r o g r a m u s e d t o d e t e r m i n e CAHE p e r f o r m a n c e .

D u r i n g t h e c o u r s e o f d e v e l o p i n g t h e g a s p r o p e r t y d a t a u s e d f o r t h e

c o m p u t a t i o n s a l a r g e a m o u n t o f r e l a t e d s u p p o r t i v e i n f o r m a t i o n w a s p r o d u c e d .

T h e s e d a t a , w h i l e n o t u s e d d i r e c t l y f o r t h e HTGR c o m p u t a t i o n s , a r e i n c l u d e d

w i t h t h e t h o u g h t t h a t t h e y may b e c o n v e n i e n t a n d u s e f u l f o r f u r t h e r r e l a t e d

s t u d y .

^ A c r o n y m f o r C o r e A u x i l i a r y C o o l i n g H e a t E x c h a n g e r

3

I. THE THERMAL TRANSPORT PROPERTIES OF PURE HELIUM

The thermal transport properties of helium have been thoroughly ^ rvc* st^ at^d ard v^ll d3^'.JLr"» R-'^^^^rc^s 1 t rcu-"** 1 Q b^^n

reviewed for the purpose of selecting suitable methods to evaluate these properties in programs used to calculate heat transfer to or from helium. The formulas reported by Petersen1 were selected for use in the CACHE program. They were chosen chieCly because they are simple in format} not necessarily because it was assumed they were the most pre-cise. It is shown in Appendix A that if the helium property data derived from different sources are compared within the applicable temperature range, the differences, reflected by CAHE heat transfer computations, are i ns i gni f i c ant.

A. Thermal Conductivity

In Ref. 1, the thermal conductivity, r:y Is given by this equation: k = (2.682 x 10~3 )(l.O + 1.323 X 1o- 3p)r 3- 7 l ( l-°- 0 0 0 2 P) (i.Al)

k = w/'(irf* K/m) T = absolute temperature, K P = barj (bar = lO If/n? = O . 9 8 6 9 phys. atm)

Petersen1 states: "The standard deviation, cr, is about ZS at 273 K and Gf> at liOO K, i.e.; o = 0.0035

Within the pressure range from 15 psia to 7 5 0 psia the effect of pressure on the conductivity is less than 1.0$. For example:

k at 1 atm (-15 psia), 1000°F = 0.1802 (Btu/hr)/(ft2-°F/ft), k at 51 atm (~750 psia), 1000°F = O . I 8 1 5 (Btu/hr)/(ft2-°F/ft). For this reason the effect of pressure was ignored for use in the

CACHE program and Eq. I.Al above was simplified, thus: k = 2 . 6 8 5 T 0' 7 1 w/(ms K/m) (l.A2)

and in English units k = (1.0221 X IO" 3)T 0 , 7 1 0 (I.A3)

at P = 1 atm = l';-. Y psia k = ( I . O 8 U 9 x I 0- 3)T° , 7° 3 (I.AU)

at P = 51 atm = 750 psia k = (Btu/hr)/(ft2-°F/ft); T = °Pankine

It

Equation I.A3 "was chosen to evaluate helium thermal conductivity "because, compared with several other equations in recent or current use, it is the simplest in format and easily programmed.

In Appendix A five other equations for thermal conductivity are listed and helium conductivity computed vith Eq. I.A! and also with these five additional equations is tabulated in Tables A.l and A.7. These tables are for pressures of 1 atm, 100 psia, 500 psia, 7 5 0 psia, 1000 psia, 1500 psia and 2000 psia and for temperatures from 50°F to 2000°F. Typical calculations of heat exchange rates with pressurized helium in HTGR Core Auxiliary Heat Exchangers involve helium film temperatures in the range 300°F to 1000°F. Within this range all tabulated conductivities agree within 3.0$.

B. Viscosity

As with thermal conductivity, there is no dearth of data sources for the viscosity of helium. The equation for viscosity which is incorporated in the CACHE program is from Ref. 1 and is a version of

VL = (3.67^ X 10-7) if3'70, kg/(m sec). (i.Bl) T = K

For the CACHE programs this equation was recast, thu ': » = (5.89 x 10-4) T 0' 7 0, lbm/(ft-hr) (I.B2)

T = °Rankine The author, Petersen,1 states, "The standard deviation, o, is about at 273 K and 2.7$ at 1800 K, i.e., cr = 0.001?

Appendix B contains other equations in recent or current use for computing helium viscosity. Figure 11 in section IV shows a curve of helium viscosity calculated with Eq. I.B2.

C. Specific Heat

All the authorities reviewed agree that within the ranges of temper-ature and pressure in typical HTGR systems that the specific heat of helium is essentially constant and cite values from 1.2^0 to l,2b2 Btu/lbjn-°F. The higher value is used in the CACHE programs.

5

II. THE THERMAL TRANSPORT PROPERTIES OF WATER

A. Thermal Conductivity of Water

Within the CACHE program the thermal conductivity of vater is evaluated by the equation

> = 0.310^ + (6.910 X 10~4)T-(l.^32 X lO-5)!2 (II.Al)

+ (5.255 x i o " 1 0 ) r

k = (Btu/hr)/' (ft2 -°F/ ft)

T = °Fj 32°F s I < U50°F

This equation is a least squares fit11 to data obtained by interpo-lation at 6 7 0 psia from tabulated data.12 The equation for thermal conductivity in this reference is unnecessarily complex for use in CACHE. A second data source, Touloukian10 et. al. was reviewed for purposes of comparison but was not used to develop Eq. II.Al above. Table 1 provides a comparison of tabulated end computed thermal con-ductivities of waterj these data are plotted on Fig. 1.

The effect of pressure on thermal conductivity was ignored. If the pressure of liquid water at 300°F is increased from 75 psia to 1000 psia, the conductivity is increased by 0.6$.

Table 1. The thermal conductivity, k, of liquid water

Temperature Thermal conductivity, k, (°F) (Btu/hr)/(ftg-°F/ft)

k from k from Error Per cent Ref. 22 Eq. II.Al error

32 0.3308 0.3310 +0.0002 +0.06 50 0 . 3 ^ 0.3^13 -0.0001 -0.03

100 0.3655 0.3652 -0 .0003 - 0 . 0 8 150 0.3826 0.3825 -0 .0001 +0.03 200 0.3935 0.3935 0.000 0.00 250 0.3985 0.3988 +0.0003 -0.08 300 0 .3980 0.3985 +0.0005 , 0 . 1 3 350 0.3938 0.3933 -0.0005 -0.13 boo 0 . 3 8 3 6 0.3833 -0.0003 - 0 . 0 8 ^50 0 .3689 0.3692 +0.0003 - 0 . 0 8

6

ORNL—DWG 76-2158 Toptrnture, °C

0 in 200 300 ItOO 500 Tenp?rature•

Vig. 1- The thermal conductivity of liquid water O Data from Ref. 12; V Data from Ref. 10.

?.. Viscosity cf Water

Water vise;city in t:.e CACHE program is evaluated with the

. = 275.4 T"1'151, ( I I* 3 1)

T = °Fj I00°F = T S 500°F

This equation is a least squares fit11 to tabulated12 viscosity data for liquid water at 1000 psia. Table Z and Fig. 2 show viscosity as a function of temperature from the- tabulation and from Eq. 11.31. For the- purposes of heat transfer computation::, the effect of pressure or. viscosity may be penorod. For example, at 300°F, increasing the pressjre from rsia to ICCO psâ increaser the v^scccitv bv ~ .I/-;.

Table 2. The viscosity of liquid water at 1000 psia

Temp Viscosity, Error Per cent (° F) lbr/(ft-hr) e rror

From Ref. 22 From Eq. II.B1

100 1.65 1.64 - 0 . 0 1 0 -0.6 150 1 . 0 3 1.02 -0.010 -1.0 200 0.729 0.725 -0.004 - 0 . 5 250 0.551 0.557 -0.003 - 0 . 5 300 0.445 0.44o -0.004 - 0 . 9 350 0.372 0,375 -0.003 -r-0.6 l-oo 0 .320 0.320 0.000 0.0 450 0.230 O .27S -0.002 - 0 . 7 500 0.250 0.246 -0.004 -1.6

C. Specific Heat of Liquid Water

The equation in CACFE for the specific heat of pressurized water is.

C = 1.035 - (k,55 X 10"4) T + (1.38 X 10~6) T3, (II.01) P C = Etu/(lb -°F)j T = °F, 100°F 400°F. p ^ % m '7 '

8

ORNL- DWG 76-2171

T e m p e r a t u r e , ° C

F i g . 2 . T h e v i s c o s i t y o f l i q u i d w a t e r . B a s e d o n d a t a f r o m R e f . 1 2 .

9

Equation II.CI is a least squares fit11 to data obtained, by inspection, from a curve of l/C^ versus T at 1000 psia in Fig. 6, page 293 in Ref. 12. It is obvious from this curve, that within the pressure range 0 to 1000 psia, the effect of pressure on specific heat is negligible. Table 3 and Fig. 3 show values of C from Ref. 12 and those calculated from Eq. II.CI. P

Table 3. Specific heat of liquid water at 1000 psia

Temperature Specific heat, Cp Difference Per cent (°F) Btu/(lb-°F) error

Ref. 12. Eq. II.CI

i o o 0 .996 1.00U +0.008 +0.80 150 0.996 0.997 +0.001 - 0 . 1 0 200 1.000 0.999 -0.001 -0.10 250 1.010 1.007 -0.003 -0.30 300 1.020 1.022 +0.002 +0.20 350 1.0^2 1.09^ +0.002 +0.19 U00 1.075 1.073 +0.002 +0.19

III. THE THERMAL CONDUCTIVITY OF STEEL TUBING

The tubing material currently specified for the cooler 75$ of the core auxiliary heat exchangers is a low alloy, 1/2$ Cr-l/2$ Mo, steel. Data for the thermal conductivity of this steel were obtained from Refs. 13 and and, for the CACHE program, tube wall conductivity is described by a first degree, least squares fit.11 The equation is:

k = 22.2 - 0.00276T (iII.Al) k = (Btu/hr)/(ft2-°F/ft)j T =

in metric units

k = 38.28 - 0.008597T (III.A2) k = watts/(m2 °C/m)j T = °C

The data and Eq. III.A1 are shown in Fig. The tubing in the hot end, the lower 25$, is specified to be

Cr - 1$ Mo steel. Steels of this type with chromium and molybdenum as the principal alloying agents and having a total alloy content, Cr + Mo, from 2$ to 5$ will have almost constant thermal conductivity

O R N L - D W G 76-2160

Temperature, °C 50 100 150 200

100 150 200 250 300 350 l»00 Temperature, °F

Fig. 3. The specific heat, Cp, of liquid water. Data based on Figure 6 in Ref. 12.

VI 0\ Conductivity, k, (Btu/hr)/(ft -°F/ft)

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s o

s o

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M IO N fO IM U) *R \JI -

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it 1 I / o I ) j 4 i 4 1 / rv> I —a 11 r CT\ i

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II

12

from room temperature to 1500°F. From the curves, Fig. 5, and by interpo-lation of the tabulated data in Ref. 14, the thermal conductivity of this alloy was established to be constant at l6.J (Btu/hr)/(fts-°F/ft).

IV. THE THERMAL TRANSPORT PROPERTIES OF HELIUM DILUTED WITH OXYGEN, NITROGEN AND CARBON MDNOXIDE

In an HTGR, the Design Basis Depressurization Accident (DBDA) coupled with a Loss of Main Loop Cooling (LOMLC) involves heat transfer by the CAHE from mixtures of helium with air and the reaction products formed by air in contact with high temperature graphite. It is, there-fore, necessary to have good information as to the thermal transport properties of these gas mixtures if leliable computations of afterheat removal rates are required. If the mixture composition is established and if the specific heats of the components therein are known, it is a simple matter to evaluate the specific heat, Cp, of the mixture. A similar statement does not apply to thermal conductivity and viscosity. There are, apparently, no simple theoretical expressions which describe the conductivity and viscosity of gas mixtures in terms of mole fractions, molecular weights, or weight fractions of the components of the mixture and the transport properties of the pure components. This is particularly true when the mixture consists of a monatomic gas and multi-component gas molecules of widely disparate weights) helium and air, for example.

This unfortunate situation is illustrated by quotations from Refs. 15 and 16.

From Reid and Sherwood15 pages 199 and 201: 6-8. Estimation of the Viscosity of A Gas Mixture

"The extension of the modern molecular theory to describe the viscosity of a nonpolar gas mixture at low pressure has been summarized by Hirschfelder et al. (32,177)* The relations obtained are quite complicated, and less complex, though less accurate, relations are given by Wilke (4-72) and Johnson.

With regard to the problem of estimating viscosities of gas mixtures at elevated pressures, only a small amount of experimental data is available, and proposed estimation methods have not been fully tested."

13

ORNL—DWG 76-2162

F i g . 5 - T h e t h e r m a l c o n d u c t i v i t y * o f c h r o m e - m o l y b d e n u m a l l o y s t e e l s .

^ U n i t e d S t a t e s S t e e l C o . d a t a . T h i s f i g u r e i s a r e p r o d u c e d c o p y o f d a t a i n R e f . I k .

14

and from page 24Q: 7 - 7 . Thermal Conductivity of Gas Mixtures

"The thermal conductivity of a gas mixture is not generally a linear function of the composition of the mixture and may "be greater or less than that for any of the pure constituents.

Application of the modern kinetic theory to the problem of predicting the thermal conductivities of nonreacting mixtures is quite complicated and gives only fair predictions even for monatomic-gas mixtures. Various semiempirical relations have been developed, however, the best of these being due to Lindsay and Bromley (235) and to Brokaw (40)." Brokaw1® states:

"When the experimental thermal conductivities of binary mixtures of hydrogen or helium with heavier gases (mixtures in which thermal conductivity varies over a wide range) are examined the experimental conductivity is lower than that predicted by simple molar mixing, that is:

\n < X S M = X1*1 + (iV.Al)

But measured values are larger than those calculated from a reciprocal mixing rule: "

* > T — = + (IV.A2) m RM' \a

mole fraction

thermal conductivities

SM simple mixing

RM reciprocal mixing

m mixture

It is oven more unfortunate that published experimental data on mixture properties are relatively scarce and do not span the range of compositions and temperatures involved in CAHE performance computations.

15

In summary: There exist small amounts of published experimental data on the viscosity and thermal conductivity of mixtures. Theoretical methods to estimate these properties are available but, as indicated above, they are of uncertain accuracy. In addition, the user will re-quire a more than passing familiarity with statistical and quantum mechanics if these theoretical estimates are to be used with confidence.

It was decided to use such experimental data as are available to develop the temperature and composition dependent relations used to com-pute viscosity and thermal conductivity of mixtures in the CACHE pro-grams.

Two publications served as sources for the thermal conductivity and viscosity of mixtures of helium diluted with nitrogen and oxygen. The monumental work of Touloukian^ Liley and Saxena10 contains thermal conductivity data-curves and tabulations. A report by Johnson17 presents experimentally determined viscosities. Neither publication contains ranges required to evaluate, properly and completely, the afterheat re-moval capability of an HTGR after a DBDA and LOMLC.

It is not possible to determine to a high degree of precision the conditions expected to exist in an HTGR reactor vessel after the extremely unlikely occurrence of a sudden depressurization. The atmos-phere in the reactor vessel will be a time varying mixture consisting principally of helium diluted by nitrogen, oxygen and carbon monoxide.

Estimates of conditions in an HTGR after a DBDA + LOMLC have been 18

made • Figure 6 shows the results of a typical set of calculated post-BBDA conditions which have been used as the basis for CAHE heat trans-fer computations. Note that the constituents of the gas mixture are not explicitly stated; the variation of mixture composition is stated only in terms of molecular weight. This is reasonable since the diluent gases, nitrogen, oxygen and carbon monoxide, are all non-polar and all have similar (28 to 32) molecular weights.

16

ORNL- DWG 76-2171

F i g , 6 . " E x p e c t e d " a n d " c o n s e r v a t i v e " CAHE i n l e t g a s c o n d i t i o n s u s e d t o a n a l y z e t h e p e r f o r m a n c e o f t h e CAHE a f t e r a D e s i g n B a s i s D e -p r e s s u r i z a t i o n A c c i d e n t ( D B D A ) .

T h e s e d a t a f r o m T a b l e s Q . 6 . 3 - 1 7 . 2 a n d Q 6 . 3 - 1 7 . 3 , c h . 2 3 , F e b . 1 9 7 5 , i n t h e F u l t o n G e n e r a t i n g S t a t i o n P S A R . 1 8 " E x p e c t e d " c o n d i t i o n s a r e i n T a b l e Q 6 . 3 - 1 7 . 2 .

17

A. The Thermal Conductivity of Helium Diluted with Nitrogen, Oxygen, and Carbon Monoxide

The thermal conductivities of the pure diluent gases and of air are net dissimilar. This is evident from Fig. 7' These curves are based on conductivity tabulations in Ref. 10. In Fig. 8 the thermal conductivities of helium-nitrogen mixtures are shown. The solid line curves represent graphically smoothed experimental data from Table 85b in Ref. 10. The dashed lines are calculated conductivities developed by an equation, IV.A3, shown in the next paragraph.

Experimental data10 for the helium-nitrogen system and the helium-oxygen system at 113°F, Fig. 9, are nearly identical and tend to support the assumption inat the conductivities of helium with any air-like gas with a molecular weight of 28 to 32 are quite similar. The tabulations for the helium-nitrogen system, spanning a wider temperature range, were used to develop the equations used to evaluate the thermal conductivity of the HTGR core coolant gas after a DBDA. The graphical smoothing pro-cedure used to develop these tables10 produced a recognizable asymptotic error in the 601°F dataj i.e., when the mole fraction of nitrogen is zero the tabulated thermal conductivity of pure helium is 0.135 (Btu/hr)/ (fts-°F/ft). A more correct value, Eq. I.Al, is O.lUk. The tabulation of helium-nitrogen system thermal conductivity at 601°F (589K) with the substitution of the higher and correct value of conductivity, when the mole fraction of nitrogen is zero, was used as baseline data to develop the mixture conductivity equation used in HTGR Core Auxiliary Heat Ex-changer heat transfer computations after a depressurization accident. The equation arrived at is:

k = j ^ g y y ^ p ~ .003196 + .07011+F - .15767**- + .086321*1 (T/106l),6S

(IV.A3) k = mixture thermal conductivity (Btu/hr)/(ft2-°F/ft) F = mole fraction of nitrogen (or oxygen or carbon monoxide) T = absolute temperature, °R

The bracketed polynomial is an equation developed to fit the nelium-nitrogen data at 601°F (l06l°R). The term in parentheses approximates the variation of conductivity with temperature.

18

O R N L - D W G 7 6 - 2 1 M

TC»«Ptll*TU*f» Efn r

Fig. 7- The thermal conductivities of common gases having molecular weights from 28 to kk.

19

ORNL- DWG 76-2171

Fig. 8. Thermal conductivity of helium-nitrogen mixtures. aSolid line curves at 601°F, 219.4°F, and 113.2°F are experimentally

based data from Ref. 10. ^Dashed line curves are calculated with Eq.(lV.A3).

20

ORNL-DWG 76-2166

Mole fraction of N2 or 02

Fig. 9' Thermal conductivity of helium-nitrogem and helium-oxygen mixtures. (Data from Ref. 10).

21

Figure 10 snows additional curves of thermal conductivity as a function of molecular weight evaluated with Eq. IV.A3. For comparison, the conductivities of pure helium and pure nitrogen are included. The applicable temperature rai.ge for typical HTGR computations, based on mean gas film temperatures, is from 3C0°F to I000°F. The anticipated mixture molecular weights are not expected to exceed 20. Additional data and discussion of the procedure used to develop Eq. IV.A3 is in Appendix B.

B. The Viscosity of Helium Diluted with Nitrogen, Oxygen, and Carbon Monoxide

The viscosity of helium mixed -with oxygen, nitrogen, and carbon monoxide has been estimated by using experimental data published by Johnson.17 This report contains experimental curves of viscosity versus temperature for three mixtures of oxygen and helium. The oxygen mole fractions in the mixtures were 0.28, 0.53* an<? 0.72 corresponding to mixture molecular weights of 11.8, 18.8, and 2b.2. Garber^ developed three equations to fit Johnson's data. These are:

A. Mole fraction 0 2 = 0.28 n = (5-9^2 X 10"4)T'71 (IV.B1)

B. Mole fraction Cfe = 0.53 H = (7*216 X 10"4)T,68S (IV.B2)

C. Mole fraction Os = 0.72 H = (10.50 X 10"4)T'639 (IV.B3)

)_L = viscosity, lbm/ft-hr T = absolute temperature, °Rankine

Figure 11 shows the experimental viscosity data from Johnson's report, a gas mixture viscosity curve calculated with Eq. IV.B1, and the viscosity of pure helium calculated with Eq. I.B2. Unlike the thermal conductivity of similar gas mixtures, the addition of oxygen to helium

P. Garber, ORNL summer participant (student) sponsored and funded by Oak Ridge Associated Universities.

22

Temperature, °F x 10 2 ORNL DWG 76 2167

Temperature, R x 10

Tig. 10. The thermal conductivity of helium-nitrogen gas mixtures from Eq. IV. A3 and the thermal conductivities of pure helium1 and pure nitrogen.10

23

ORr. 'L-DWG 76-2168 Temperature, °F

lUo 2l»0 3Uc UUo 5^0 6h0 TUo 81*0

Temperature °R

Fig. 11. The viscosity of helium and helium—oxygen mixtures. *Experimental data O 28 mole$ 0 £

• 53 mole$ 72 mole$ 0 2

*C. A. Johnson; SURI Rept. Che. E. 273-566 F3, 1956.

2h

does not produce drastic changes in the viscosity of the resulting mix-ture if compared with the viscosity of pure helium. The data also show that when the mole fraction of oxygen in the mixture exceeds 0.28 that oxygen additions to the mixture have little or no effect on viscosity. This aspect of mixture "behavior is well illustrated by Fig. 12 also de-rived from Johnson's work. The continuous curves are theoretical calcu-lations by Johnson17 of viscosity as a function of composition. The results of two theoretical methods are shown. The three discrete points are experimental values. The agreement of theory and these experiments is adequate from the standpoint of use in heat transfer computations and tends to contradict the general statements by Reid and Sherwood and by Brokaw cited earlier in this report. Additional experimental evidence is a prerequisite to firm conclusions regarding such agreement.

By inspection of Fig. 11 it is apparent that Eq. IV.B1 is a suf-ficiently good fit to the data for mixtures containing oxygen mole fractions of 0.28, and 0.53. This equation currently is used to specify mixture viscosity in CAHE heat transfer calculations when the gas mixture molecular weight is above 11.0.

When the molecular weight of the gas mixture is less than 11.0, equivalent to an air mole fraction of 0.28, mixture viscosity is speci-fied by a simple linear interpolation between the viscosity of gas mix-ture with oxygen mole fraction of 0.28 and the viscosity of pure helium. The interpolating equation used in the CACHE heat exchange program is:

|im = (Fd/'28> ^.28^ + [ ( 0' 2 8 •

F^ = mole fraction of diluent gas or gases (nitrogen, oxygen, carbon monoxide); 0.0 < 0.28

^ 28 ~ viscosity of helium-air mixture containing 0.28 mole fraction of oxygen, evaluated with Eq. IV.Bl; lbm/ft-hr

(j,, = viscosity of pure helium evaluated with Eq. I.B2, lbm/ft-hr

^ = gas mixture viscosity, lbm/ft-hr.

Figure 13 shows viscosity versus mixture composition for the temper-ature range applicable to post-DBM calculations of CAHE performance.

25

O R N L - D W G 7 6 - 2 1 6 9

Molecular weight of gas mixture 9 14 19 24 29

0.09

a

-P •r) W O V W •H >

0.03:

0.07

i - i

J ! ; ' i L ; T j ;•

. . .

Ifli-i

j i i i

• 1

i t f

M n ftT-r 7 t-ri { r f

i j - n u i t !

- *

: • • ry,: r]

• f i - i - ^ U i 1; : : : ;,.!" . i-. i

~ jv - T i m

1

i'i i i ItT-i !-i i : lit""

~ jv - T i m

1 - f - f t t ' ' M !

H-i4- 1 . i , i

I .LLl.i.I ill ' l-J- 1 -J .! '

~ jv - T i m

1 - f - f t t ' ' M ! F F M i l

rzhLt

' i + r

• i T i i i + i ^ p ; n • • ! 1 . b p n . q i f r j

i i ' 1 1 ' "ill"":' •p i! * r i

0.5 0.4 0.6 0.8 Mole fraction of diluent gas, (O2)

1.0

Fig. 12. Viscosity of helium-oxygen gas mixtures at 571°F (1031°R) based on data in Ref. 17-NOTE: (l) The continuous curves are theoretical values.

(2) The molecular weight scale is based on the assumption that oxygen and air are equivalent.

26

ORNL-DWG 76-2170

Fig. 13. Viscosity of the gas mixtures used to calculate Core Auxiliary Heat Exchanger (CAHE) performance after a Design Basis De-pressurization Accident (DBDA).

^ h e gas mixture is assumed to consist of helium diluted with

nitrogen, carbon monoxide, and oxygen.

27

Use cf this method of specifying viscosity contains these implicit t>; sumptions:

(1) The viscosity of mixtures of helium with carbon monoxide and/or nitrogen behave similarly to helium-oxygor. viscosities and ore numerically similar. In this connection it. is noted that the molecular weights of these- diluent gases are equal or nearly equal and that the viscosities of the pure diluent gases are not far apart. Appendix C contains viscosity data for pure nitrogen, oxygen, carbon monoxide and air to illustrate this similarity.

(2) That Eq. J' .Bl is a good approximation to csixture viscosities at gas temperatures not included in Johnson's experiments. This is not unreasonable since, very generally, gas viscosity tends to vary with absolute temperature raised to a fractional exponent at temperatures encompassing CAHE computational requirements.

It is, perhaps, fortunate that small percentage changes or errors in specifying gas viscosity are reflected as considerably smaller changes in the gas film heat transfer coefficient.19 In a typical CAHE heat exchange computation involving gas mixtures, a 1053 error in speci-fying mixture viscosity will alter the computed gas film coefficient by approximately 3"/J. From Fig. 11 it is seen that, from temperatures of

to 930°F, the viscosity increases produced by adding oxygen to helium are about 10$} i.e., if helium viscosity were specified, regard-less of the gas composition, the calculated CAHE performance would be increased approximately 3$.

C. The Specific Heat of Helium-Air Gas Mixtures

The specific heat of a gas mixture is obtained by summing the products of the specific heats of the component gases and their weight fractions in the mixture. In a mixture of N different gases the mixture specific heat is

<CP>mixt " ^ V 1 + + " + V C P > N ( I V ' C 1 )

(C_) . , = mixture specific heat, Btu/lb-°F

28

(Cp)ij (Cp)2 ^p)^ = heats of the component gases in the mixture

Ya " Yjt = weight fractions of the component gases in the mixture

For HTGR computations it has been assumed that the specific heat of air is representative of the specific heats of the gases that dilute the helium after a DBDA. The specific heat of air has been -well estab-lished; therefore, it is considered to be a single component gas of molecular weight 29 for purposes of determining post-DBDA. gas mixture specific heat. For helium-air mixtures IV.CI becomes

<CpW = W h + ^V^Va' Btu/lb"°F

Y^ = weight fraction of helium in the mixture

(C = specific heat of helium

(C ) h = 1.242 Btu/lb-°F

(C ) v p'a = specific heat of air, Btu/lb-°F

(C ) = 0.2304 + ( 3 . 7 6 7 2 x 10~5) T - (4.860 x 10~9JT2 P a (IV.C3)

T = °F

Figure 14 shows the specific heats of air-helium mixtures at 300°F and 1000°F as a function of the molecular weight of the mixture. Weight and mole fractions of the air in the mixture are included in Fig. 14.

Appendix D contains equations for computing weight fractions and mole fractions from the molecular weight of the mixture. This appendix also contains tabulations, and on Fig. D.2 ,curves of the specific heats of air, oxygen, nitrogen, and carbon monoxide. These are the gases which are predicted to exist in the primary containment in the unlikely event of a DBDA. It can be noted from Fig. 0.2 that, as should be ex-pected from the similarity of their molecular weights, the specific heats of nitrogen, carbon monoxide and oxygen are not far apart. The data for air is compared with calculated values from Eq. IV.C3, the least squares fit to the data.

29

ORNL- DWG 7 6 - 2 1 7 1

1.0

3.6 "

10 15 20 Moleculer weight of eir-heliura mixture

Fig. lU. The specific heat and fractional compositior of air-helium mixtures.

30

Appendix A

Equations and Tabulations far the Thermal Conductivity of Pure Helium

During and after establishing the programs to calculate HTGR heat exchanger performance , it became evident that persons currently investi-gating heat transfer by helium are not using the same equations to evaluate the viscosity and thermal conductivity of helium. Because the results of the computations are likely to receive careful scrutiny, it was deemed appropriate to investigate the vaiiations in computed proper-ties obtained by choices of the thermal conductivity equation used in the heat transfer programs. The effect on computed heat transfer rates was then estimated.

Since the information has been gathered and is available, it is in-corporated in this appendix with the thought that others may find the data useful.

Six equations for thermal conductivity are listed. * No attempt to evaluate them on a comparative basis was made and none should be inferred. Figures Al and A2 show maximum and minimum curves of conductivity at two pressures. These curves are envelopes and, between them, enclose all values of conductivity computed from the six equations listed. Typical calculations of Core Auxiliary Heat Exchanger (CAHE) performance in-volve helium film temperatures from 300°F to 1000°F with average film temperatures in the 600°F — 700°F region. At 750 psia and 650°F the maximum and minimum values of calculated conductivity are 0.151 and 0.lk6 (Btu/hr)/(ft3-°F/ft). In CAHE performance calculations the gas side film coefficient of heat transfer is evaluated with equations having the general form:

N (A.1A)

or

(A.IB)

*(Refs. 1, 2, 8, 20, 21, 22, 23, 2b)

31

ORNL DWG 7E r.JL3

Fig. A.l. The range, maximum and minimum values, of helium thermal conductivity at lU.7 psia from the computed values in Table A.l.

32

ORNL DWG lb 9954

Fig. A.2. The range, maximum and minimum values, of helium thermal conductivity at 750 psia from the computed values in Table A.h.

33

in which

h = film coefficient of heat transfer, (Btu/hr)/(ft5-°F) r. = thc-mal conductivity of the gas evaluated at the mean film

temperature, (Btu/hr )/( ft*-°F/'ft) ^ = viscosity of the gas evaluated at the near, film temperature,

lb/ft-hr D = equivalent diameter (tube dia.), ft G = mass flow rate of gas, lb/(fta-hr) C^ = specific heat, at constant pressure, of the gas, Btu/(lb-°F)

C = constant o

It is easy to show that the effect (the fractional change in the film coefficient, h) produced by incremental differences, Ak and Au, in thermal conductivity and viscosity is given by:

f = (i - y) f - (x - y ) ^ (A.2A)

Typical values of the exponents x and y will be 0.60 and 0.33 , re-spectively. The above equation then becomes

0.67 ££ - 0.27 ^ (A.2B) n k n

In Fig. A.2 the maximum and minimum values of k at 650°F are 0.151 and 0.1^6} using their difference as Ak in Eq. A.2B:

ffU0.67 0.022 h 0.151

It can be concluded that, for CAHE performance calculations, if helium conductivity is evaluated with any of the listed equations, the results will be uniform within about 2 f>.

Tables A.l through A.7 are helium conductivities calculated using the equations A.3 through A.8 in the following section. Conductivities are in English and metric units. It should be mentioned that: (l) Equation A.3 (Ref. l), used in the CACHE programs* to compute CAHE performance during operation with pressurized helium gives values on or near the maximum curves on Figs. A.l and A.2.

R. Tallackson, CACHE-An Extended Basic Program which Computes the Performance of Shell and Tube Heat Exchangers. ORNL-TM-i+952 , 1975-

2h

Table A.l

THERMAL CONDUCTIVITY OF HELIUM AT 14.696 PSIA

T H E R M A L C O N D U C T I V I T Y OK H E L I U M C O M P U T E D W I T H D I F F E R E N T E Q U A T I O N S

R E F E R E N C E L I S T :

I U J R I S O R E P T 2 2 4 . K2J GA C O . K 3 ; J . P . S A N D E R S , O R N L . K 4 J D . L • MC E L R O Y , O R N L K 5 ; J U L I C H , R E P T X F A - I R E - 1 7 / 7 2 . K 6 J A S H R A E , T H E R M O P H Y S . P R O P . , 1 9 7 3 .

P R E S S U R E = 1 4 . 6 9 6 P 3 I A = 1 A T M = 1 . 3 1 3 2 7 3 A R

T E M P E R A T U R E T H E R M A L C O N D U C T I V I T Y

DEG F DE3 R U N I T S OF K

K1 K 4

IC2 K 5

K 3 K 6

DEG C DEG iC U N I T S OF ;{

5 0 . 0 0 5 0 9 . 7 0 B T U / C H R - F T - F )

0 . 0 3 5 4 0.0862 0 . 0 3 4 5

3 . 0 8 5 9 0 . 0 8 4 3

1 0 . 0 1 2 3 3 . 1 7 tfATT/CMETER-X)

0 . 1 4 7 8 0 . 1 4 9 1 0 . 1 4 6 3

0 . 1 4 8 6 0 . 1 4 5 9

1 0 0 . 0 0 5 5 9 . 7 0 B T U / C H R - F T - F )

0 . 0 9 1 2 3 . 0 9 1 6 0 . 0 9 3 5

0 . 0 9 0 8 0 . 0 9 0 1

3 7 . 7 8 3 1 0 . 9 4 ' J A T T / C M E T S R - K )

0 . 1 5 7 9 a . 1 5 8 8 0 . 1 5 6 7

0 . 1 5 7 2 0 . 1 5 5 9

1 5 0 . 0 0 6 0 9 . 7 0 B T U / C H R - F T - F )

0 . 0 9 6 9 0 . 0 9 7 2 0 . > 5 9 6 3

0 . 0 9 5 7 0 . 0 9 5 7

6 5 . 5 6 3 3 8 . 7 2 " A T T / C M E T E R - K )

3 . 1 6 7 8 3 . 1 6 8 3 id. 1 6 6 8

0 . 1 6 5 6 0 . 1 6 5 7

2 3 0 . 0 0 6 5 9 . 7 3 B T U / C H R - F T - F )

0 . 1 0 2 5 0 . 1 6 2 5 0 . 1 0 2 0

0 . 1 0 0 5 0 . 1 0 1 3

9 3 . 3 4 3 6 6 . '• 'ATT / C M E T E R - K )

0 . 1 7 7 5 •i:1 . 1 7 7 4 S . 1 7 6 6

0 . 1 7 3 9 3 . 1 7 5 4

2 5 0 . 3 0 7 0 9 . 7 ' : ! 3 T U / C H H - F T - F )

3 .10.33 :•) . 1 0 7 7 f) . 1 ' 1 7 6

. 1 0 5 2 3 . 1 0 6 9

l a i . 12 3 9 4 , • r A T T / C M E T E R - X )

0.1869 8 . 1 >64 0 .13 f,o

0 . 1 3 2 1 0 . 1 <3 50

35

Table A.l (Continued)

THERI1AL CONDUCTIVITY OF HELIU:i COMPUTED Ml TH DIFFERENT EQUATIONS

P R E S S U R E = IA.69 6 P S I A = 1 A T M = 1 . 0 1 3 2 7 B A R

T E M P E R A T U R E THSRtlAL C O U D U C T I VI T Y

D E G F D E 3 R U N I T S O F it

K1 K2 K 5

::3 K 6

DEG C DEG K U N I T S O F K

3 0 0 . 0 0 7 5 9 . 7 0 3 T U / C H R - F T - F )

1 4 3 . 9 0 4 2 2 . 0 6 '?ATT/<METER-K>

0.1 133

0 . 1 9 6 1

V, . 1 123 0 . 1 134}

0 . 19 52 C . 1 9 5 6

0 . 1 0 9 9 0 . 1 1 2 3

0 . 1 9 0 2 0 . 1 9 4 4

3 5 0 . 3 3 3 0 9 . 7 3 B T U / C H R - F T - F >

0. 1 186 3 . 1 1 7 7 0 . 1 184

0 . 1 145 0 . 1 1 7 7

1 7 6 . 6 7 4 4 9 . 3 3 U A T T / t M E T E R - K )

0 . 2 0 5 2 3 . 2 2 37 0 . 2 0 4 9

f). 1953 0 . 2 0 3 7

4 0 0 . 0 3 8 5 9 . 7 0 B T U / C H R - F T - F 5

0 . 1 2 3 7 0 . 1 2 2 6 0 . 1 2 3 6

2 . 1 1 9 1 0 . 1 2 3 0

2 3 4 . 4 5 4 7 7 . 6 1 VTATT / ( M E T E R - K >

0 . 2 1 4 1 3 . 2 1 2 1 0 . 2 1 4 0

0.20 62 0 . 2 1 2 9

4 5 0 . 0 0 9 0 9 . 7 0 B T U / C H R - F T - F )

0 . 1 2 8 8 0 . 1 3 0 6

0 . 1 2 7 3 0 . 1 2 8 8

0 . 1 2 3 7 0. 1282

2 3 2 . 2 3 5 0 5 . 3 9 '.TATT/CMETER-K)

0 . 2 2 2 9 0 . 2 2 6 3

0 . 2 2 0 4 0 . 2 2 2 9

0 . 2 1 4 0 0 . 2 2 1 9

5 0 0 . 0 0 9 5 9 . 7 0 B T U / C H R - F T - F )

0 . 1 3 3 8 0 . 1 3 5 3

0 . 1 3 2 0 0 . 1 3 3 9

0 . 1 2 8 1 0 . 1 3 3 4

2 6 0 . 0 1 5 3 3 . 1 7 I T A T T / t M i T E R - K )

0 . 2 3 1 5 0 . 2 3 4 2

0 . 2 2 8 4 0 . 2 3 1 7

3 . 2 2 1 8 0 . 2 3 0 8

5 5 0 . 0 0 1 0 0 9 . 7 0 B T U / C H R - F T - F )

0 . 1 3 8 7 0 . 1 3 9 8

3 . 1 3 6 6 0 . 1 3 3 9

0 . 1 3 2 6 0 . 1 3 3 4

2 3 7 . 7 3 5 6 0 . 9 4 U A T T / C M Z T S R - X )

0 . 2 4 0 0 lu .2420

3 . 2 3 6 4 S . 2 4 3 3

0 . 2 2 9 4 0 .2396

36

Table A. 7 (Continued)

THERMAL CONDUCTIVITY OF HELIUM COMPUTED UITH DIFFERENT E Q U A T I O N S

P R E S S U R E = 14.696 PSIA = 1 ATM = 1.01327 BAR

T E M P E R A T U R E THERMAL CONDUCTIVITY

DEG F DEG H UNITS OF K

Kl K4

K2 K5

K 3 K 6

DEG C DEG K UNITS OF K

600.00 1059*70 3TU/CHR-FT-F5

0 = 1 4 3 5 0 . 1 4 4 3

0.1411 3.1438

0.1369 0.1433

315.56 558.72 UATT/CMSTER-KJ

0 *24S4 0.2498

0.2442 0.2489

0.2370 0.2481

650.00 £ 109.70 3TU/<HR-FT-FJ

0.1483 1488

0.1456 0.148 6

0.1412 0.1482

343.34 616.50 U A T T / C M E T E R - K )

0 . 2 5 6 7 0 .2575

0.2519 0.2572

0.2444 0.2564

700.00 1159.70 3TU/(HR-FT-F3

0.1530 0.1532

0. 1500 0.1534

0. 1455 0.1529

371.12 644.28 ,;ATT/<MSTE°.-K)

0.2648 0.2651

0.2595 0.2655

0.2518 0.2646

750.00 1209.70 BTU/(HR-FT-F>

0.1577 0.1575

0.1543 0 . 1 58 1

0.149 7 0.1575

398.90 672.06 U A T T / < M E T E R - K )

0.2729 0 .2726

0.2670 0.2737

0.2591 0.2 72 6

800.00 1259.70 BTU/<HR-FT-F>

0.1623 0 . 1 6 1 8

0.1586 0.1627

0.1538 3.1620

426.67 699.83 •?ATT/(METER-K)

0.2809 0.2301

0.2744 3.2317

0.2662 0.2804

850.00 1309.73 3TU/(HR-FT-F>

0.1663 0 . 1 6 6 1

•3 . 1 628 . 1 673

0.1579 0.1665

454.45 727.61 '/ATT/CMETER-K)

0.283 7 3.2875

0.2817 0 .239 6

0.2733 0 . 2 8 8 1

37


THERI1AL CONDUCTIVITY OF HELIU:i COMPUTED Ml TH DIFFERENT EQUATIONS

PRESSURE = 14.69 6 PS IA = 1 ATM = 1.01327 3AR

TEMPERATURE THERMAL CONDUCTIVITY

DEI F DEG R UNITS OF K

K 1 K4

K 2 K 5

K3 K6

DEG C DEG X UNITS OF X

900.00 1359.70 BTU/<HR-FT-F>

0 . 1 7 1 3 0 . 1 7 3 4

0.1669 0.1718

0.1619 0.1708

482.23 755.39 WATT/CMETER-K)

0.2965 0.2949

0.2839 0.2973

0 .2303 0.2956

950.00 1409.73 BTIJ/(HR- FT-F)

0•1758 0.1740

0.1710 0. 1762

0.1659 0.1751

510.01 783.17 UATT/<METER-K>

0.3042 0.3022

0.29 60 0.3050

0.23 72 0.3030

1000.00 1459.70 BTU/<HR-FT-F>

0 . 1802 0.1768

0.1751 0. 1805

0.1699 0.1793

537.78 810.94 UATT/CMETER-IO

0.3118 0.3094

0.3031 0.3125

0.2940 0.3103

1050.00 1509.70 BTU/CHR-FT-F)

0.1345 0.1829

0.1791 0.1348

0.1737 0.1834

565.56 838.72 WATT/<METER-K>

3.3194 0.3165

0.3100 0.3198

0 .3007 0.3174

1100.00 1559.70 BTU/(HR-FT-F)

0.1388 0. 1370

0.1831 0 .1839

0.1775 0. 1875

593.34 866.50 VATT/(METER-X )

0.3268 0.3236

•3.3169 0.3270

0.30 73 0.3244

1150.00 1609.70 BTU/(HR-FT-F)

0.1931 0.1910

0. 18 70 0. 1930

£ . 1 8 1 3 0.1914

621.12 394.28 UATT/(METER-K)

0.3343 0.3306

0.3237 0.3341

0.313S 0.3313

38


T H E R M A L C O N D U C T I V I T Y OF H E L I U M C O M P U T E D U I T H D I F F E R E N T E Q U A T I O N S

P R E S S U R E = 1 4 . 6 9 6 P S I A = 1 A T M = 1 . 0 1 3 2 7 BAR


DEG F DEG R U N I T S OF K

K1 K 4

K 2 K5

K 3 5C6

DEG C DEG K U N I T S OF K

1 2 0 0 . 0 0 1 6 5 9 . 7 0 B T U / C H R - F T - F )

0 . 1 9 7 4 0 . 1 9 5 1

0 . 1 9 0 9 0 . 1 9 7 0

0 . 1 8 5 0 0 . 1 9 5 4

6 4 8 . 9 0 9 2 2 . 0 6 U A T T / C METER-1C )

0 . 3 4 1 6 0 . 3 3 7 6

0 . 3 3 0 5 0 . 3 4 1 0

0 > 3 2 0 2 0 . 3 3 8 1

1 2 5 0 . 0 0 1 7 0 9 . 7 0 B T U / C H R - F T - F )

0.2016 0 . 1 9 9 0

0 . I 9 4 3 0 . 2 0 0 9

0 . 1886 0 . 1 9 9 2

6 7 6 . 6 7 9 4 9 . 8 3 U A T T / C M E T E R - K )

0 . 3 4 8 9 0 . 3 4 4 5

0 . 3 3 7 1 0 . 3 4 7 7

0 . 3 2 6 5 0 . 3 4 4 8

1 3 0 0 . 0 0 1 7 5 9 . 7 0 B T U / C H R - F T - F )

0 . 2 0 5 7 0 . 2 0 3 0

0 . 1 9 8 6 0 . 2 0 4 7

0 . 1 9 2 2 0 . 2 0 3 0

7 0 4 . 4 5 9 7 7 . 6 1 U A T T / C M E T E R - K )

0 . 3 5 6 1 0 . 3 5 1 3

0 . 3 4 3 8 0 . 3 5 4 3

0 . 3 3 2 7 0 . 3 5 1 4

1 3 5 0 . 0 0 1 8 0 9 . 7 0 B T U / C H R - F T - F ) "

0 . 2 0 9 9 0 . 2 0 6 9

0 . 2 0 2 4 0 . 2 0 8 5

0 . 1 9 5 8 0.2068

7 3 2 . 2 3 1 0 0 5 . 3 9 U A T T / C M E T E P . - i C )

0 . 3 6 3 2 0 . 3 5 8 1

0 . 3 5 0 3 0 » 3 6 0 8

0 . 3 3 8 S 0 . 3 5 7 8

1 4 0 0 . 0 0 1 8 5 9 . 7 0 B T U / C H R - F T - F )

0 . 2 1 4 0 0 .2108

0.2062 0.2122

0 . 1 9 9 3 0 . 2 1 0 4

7 6 0 . 0 1 1 0 3 3 . 1 7 V A T T / O I S T S R - K )

0 . 3 7 0 3 0 . 3 6 4 8

3 . 3 5 6 8 3 . 3 6 7 2

0 . 3 4 4 9 0 . 3 6 4 2

1450.30 1909.70 BTU/CHR-FT-F)

0 . 2 1 8 3 0 . 2 1 4 6

• 3 . 2 2 9 9 0 . 2 1 5 8

0 . 2 0 2 7 0 . 2 1 4 1

7 3 7 . 7 3 1 0 6 0 . 9 4 • / A T T / C J E T E R - K )

0 . 3 7 7 4 0 . 3 7 1 4

• 3 . 3 6 3 2 0 . 3 7 3 4

0 . 3 5 0 8 0 . 3 7 0 5

39


THERMAL CONDUCTIVITY OF HELI'JM COMPUTED UITH DIFFERSMT EQUATIONS

PRESSURE = 1/4.69 6 PS IA = 1 ATM = 1 .01327 BAR

TEMPERATURE THERMAL COMDTJCTIVI TY

DEG F DEG UNITS OF K

R IC1 K4

::2 K 5

K 3 :c6

DEG C DEG UNITS OF K

1500.00 1959. BTU/CHR-FT-F)

70 0.2221 0.2164

0 . 2 1 3 5 0.2193

I3.2061 G.2177

815.56 1083, VATT/(METER-K)

72 0.3843 0.3779

3.3696 0.3796

0.3566 0.3767

1550.00 2009, BTU/CHR-FT-F)

70 0.2261 0.2221

0.2172 0.2228

0.2094 0.2212

343.34 1116. 'FATT/<MET ER-K>

50 0.3913 0.3844

0.3760 0.3856

0.3 624 0.3828

1600.00 2059, BTU/<HR-FT-F)

70 0.2301 0.2258

0.2203 0.2263

0.2126 0.2247

871.12 1144. WATT/C METER-K)

28 0.3982 0.3909

3.3322 0.3916

0.3 680 0.3889

1650.00 2109, BTU/CHR-FT-F)

73 0.2340 0.2295

0.2244 0.2297

0.2159 3.2231

398.90 1172, 'JATT/CMSTEP.-IO

06 0 .4k55k) 0.3972

0.33S 5 0.3975

0.3 736 0.3949

1700.00 2159 3TU/CHR-FT-F)

.70 0.2379 2 .2332

0.2280 0.2331

0 .21914 0.2315

926.67 1199, UATT/CMETER-K)

83 0.4118 2.4035

0•394 6 3.40 34

0.3 791 0.4007

17 50.00 2209, BTU/CHR-FT-F)

70 0.2418 3.23 68

0.2316 0.2364

0.2221 0.2349

954.45 1227 '•J ATT / ( MET ER -K )

.61 0 . 4 1 8 5 0.4098

0.4008 0.4092

0.3844 0.4065

bo


THERMAL CONDUCTIVITY OF HELIUM COMPUTED UITH DIFFERENT EQUATIONS

PRESSURE 14.69 6 .JSIA = 1 ATM = 1.01327 3AR


DEG F DEG R UNITS OF K

K1 K4

::2 X 5

K3 K 6

DEG C DEG :C UNITS OF 3{

1800.00 2259.70 BTU/CHR-FT-F)

0.2457 0.2403

0.2351 0.2398

0.2252 0.2382

982.23 1255-39 UATT/CMETER-K)

0.4252 0.4159

0.4069 0.4150

0.389 7 0.4123

1850.00 2309.70 BTU/CHR-FT-F)

0.2495 0.2438

0.238C 0.2431

0.2281 0.2415

1010.01 1283.17 UATT/CMETSR-K)

0.4319 0.4220

0.4129 0.4208

0.3949 0.4180

1900.00 2359 O70 BTU/CHR-FT-F)

0.2534 0.2473

0.2420 0.2464

0.2311 0.2447

1037.78 1310.94 WATT/(MET ER-X)

0.4385 0.4280

0.4189 0.4265

0.3999 0.4236

1950.00 2409.70 BTU/CHR-FT-F)

0.2572 0.2503

0.2455 0.249 7

0.2340 0.24 79

1065.56 1338.72 UATT/CMETER-JC)

0.4451 0.4340

0.4249 0.4322

0 . 4 0 4 9 0 . 4 2 9 1

2000.00 2459.70 BTU/CHR-FT-F)

0.2609 0.2542

0.2489 0 .2530

0.2368 0.2511

1093.34 1366.50 UATT/C METER-K)

0.4516 0.4399

0.4308 0.4379

0.4098 0.4346

Ul

Table A.2 THERMAL CONDUCTIVITY OF HELIUM AT 100 PSIA

T H E R M A L CONDUCTIVITY OF HELIUM COMPUTED WITH DIFFERENT EQUATIONS

R E F E R E N C E LIST:

KI; R I S O R E P T 224. :<2; GA CO. K3; J . P . SANDERS.. ORNL. X4J D.L. MC ELROY,ORNL K5; JUL I CHJ REPT XFA-IP.E- 1 7/72 . K6J ASHPAEJ THERMOPHYS • P R O P . , 1 9 7 3 .

P R E S S U R E = 100 PSIA = 6.30457 ATM = 6.3949 BAR

T E M P E R A T U R E T H E R M A L COFJDUCTI VI TY

DEG F DEG R UNITS OF K


50.00 509.70 B T U Z ( H R - F T - F )

X 4

0.0355

:c2 K 5

0.0890 0.0846

K3 K 6

0.0885 0.0843

10.01 283.17 W A T T / C M E T E R - K )

100.00 559.70 B T U / < H R - F T - F )

37.78 310.94 WATT/CMETER-JO

150.00 609.73 B T U / C H R - F T - F )

65.56 333.72 '•7 ATT / (METEP.-K)

0.1480

09 14

0.1582

0.0971

0 . 1 68 1

0.1540 0. 1463

0.094 6 0.09155

0. 1637 0. 156 7

0 . 1 Ufc) 1 0.0963

<1. 1 732 .1663

0.1532 0.1459

0.0935 0.0901

A.1613 0.1559

0 . 0 9 3 4 0.0957

0.1702 3.1657

200 • £10 659 .70 3TU/< H R - F T - F )

0.1027 0 . 11? 54 0. 1020

3. 1032 0.1013

93.34 366.5J '•'ATT/C METER-.-O

250.00 709.70 B T U Z ( H R - F T - F )

. 1 777

0. 1082

0 . 1 ••>23 . 1 766

:.) . 1 1 C 5 !<376

3. 1786 0.1754

0.103 3 " 0.10 69

121.12 394. '-IH 'RATT/<MSTE',.-:0

0 . 1 9 1 3 0 . 13 62

0 . 18 69 J . 13 5*

1*2

Table A.2 (Continued)

THERMAL CONDUCTIVITY O?' HELIUM COMPUTED 71TH DIFFERENT EQUATIONS

P R E S S U R E = 1 0 3 P S I A = 6 . 3 0 4 5 7 AT.-i = 6 . 3 9 4 9 BAR

T E M P E R A T U R E THERMAL CJ-JDUCTI v i T Y

D E ' j F DEG R U N I T S OF K

III K4

AC :c5

K3

DEG C DEG X U N I T S OF K

3 3 0 . 0 3 7 5 9 . 7 0 B T ' J / C H R - F T - F )

0 . 1135 0 . 1 1 5 6 0 . I 1 3 0

0 . 1 1 2 7 0 . 1 1 2 3

1 4 3 . 9 0 4 2 2 . 0 6 7 A T T / C M E T E R - K )

3 . 1 9 6 4 0 . 2 0 0 1 0 . 1 9 5 6

0 . 1 9 5 1 id . I 9 4 4

3 5 0 . 0 0 8 0 9 . 7 0 B T U / C H R - F T - F )

0 . 1 l a y 0 . 1 2 0 5 C . 1 1 8 4

0.1174 0.1177

1 7 6 . 6 7 4 4 9 . 8 3 7 A T T / C M E T E R - K )

a . 2 3 5 5 0 . 2 0 8 6 0 . 2 0 4 9

0 . 2 0 3 2 0 . 2 0 3 7

4 0 0 . 0 0 8 5 9 . 7 0 B T U / C H R - F T - F )

0 . 1 2 3 9 3 . 1 2 5 4 0 . 1 2 3 6

0 . 1220 0 . 1 2 3 3

2 0 4 . 4 5 4 7 7 . 6 1 W A T T / ( M E T E R - K )

0 . 2 1 4 5 0 . 2 1 7 0 0 . 2 1 4 0

0.2112 3 . 2 1 2 9

4 5 0 . 0 0 9 0 9 . 7 0 B T U / C H R - F T - F )

0 . 1 2 9 0 0 . 1 3 0 3

3 . 1 3 B 1 0 . 1 2 3 8

0 . 1 2 6 6 0 . 1 2 3 2

2 3 2 . 2 3 5 3 5 . 3 = ) 7 A T T / C M E T E R - K )

0 . 2 2 3 2 3 . 2 2 6 4

0 . 2 2 5 3 3 . 2 2 2 9

0 . 2 1 9 1 0 . 2 2 1 9

5 0 0 . 0 0 9 5 9 . 7 0 3 T U / C H R - F T - F )

0 . 1 3 4 0 0 . 1 3 5 4

0 . 1 3 4 8 0 . 1 3 3 9

0 . 1 3 1 1 0 . 1 3 3 4

2 6 0 . 0 1 5 3 3 . 1 7 H A T T / C M E T E R - i O

0 . 2 3 1 9 ?• . 2 3 4 3

0 . 2 3 3 3 0 . 2 3 1 7

0 . 2 2 6 9 0 . 2 3 0 8

5 5 0 . 0 0 1 0 0 9 . 7 0 • 3 T U / C H R - F T - F )

9 . 1 3 8 9 0 . 1 3 9 9

0 . 1 3 9 4 0 . 1 3 5 5 3 . 1 3 8 4

2 8 7 . 7 8 5 6 0 . 9 4 7 A T T / C M E T E R - i ( )

0 . 2 4 0 4 ( i . 2 4 2 1

0 . 2 4 1 3 3 . 2 4 0 3

0 . 2 3 4 6 • 3 . 2 3 9 6

k3


THERMAL CONDUCTIVITY OF HELIUM COMPUTED VITH DIFFERENT EQUATIONS

P R E S S U R E = 1 0 0 P S I A = 6 . 8 0 4 5 7 A T M = 6 . 3 9 4 9 3 A R


DEG F DEC U N I T S OF K

R iCl K 4

K 2 K 5

K 3 K 6

DEG C DEG U N I T S OF K

6 0 0 . 0 0 1 0 5 9 , B T ' J / C H P . - F T - F )

7 0 0 . 1 4 3 7 0 . 1 4 4 4

3 . 1 4 3 9 0 . 1 4 3 8

0 . 1 3 9 9 0 . 1 4 3 3

3 1 5 . 5 6 5 8 8 , W A T T / C M E T E P . - K )

7 2 0 . 2 4 3 7 0 . 2 4 9 9

0 . 2 4 9 1 0 . 2 4 3 9

0 . 2 4 2 1 0 . 2 4 3 1

6 5 0 . 0 0 1 1 0 9 , B T U / C H R - F T - F )

7 0 0 . 1 4 8 5 0 . 1 4 8 8

0 . 1 4 S 4 0 . 1 4 3 6

0 . 1 4 4 2 0 . 1 4 8 2

3 4 3 . 3 4 6 1 6 . ' J A T T / C M E T E R - K )

5 0 0 . 2 5 7 0 0 . 2 5 7 5

0 . 2 5 6 8 0 . 2 5 7 2

0 . 2 4 9 6 0 . 2 5 6 4

7 0 0 . 0 0 1 1 5 9 , B T U / C H R - F T - F )

7 0 0 . 1 5 3 2 0 . 1 5 3 2

0 . 1 5 2 S 0 . 1 5 3 4

0 . 1 4 8 5 0 . 1 5 2 9

3 7 1 . 1 2 6 4 4 . T A T T / C M E T E R - K )

28 0 . 2 6 5 2 0 . 2 6 5 1

0 . 2 6 4 4 0 . 2 6 5 5

0 . 2 5 7 0 0 . 2 6 4 6

7 5 0 . 0 0 1 2 0 9 , B T U / C H R - F T - F )

70 3 . 1 5 7 9 0 . 1 5 7 6

0 . 1 5 7 1 0 . 1 53 1

0 . 1 5 2 7 0 . 1 5 7 5

3 9 8 . 9 0 6 7 2 , V A T T / C M E T E R - K )

06 0 . 2 7 3 2 0 . 2 7 2 7

0 . 2 7 1 9 • : i . 2 7 3 7

0 . 2 6 4 3 0 . 2 7 2 6

8 0 0 . 0 0 1 2 5 9 , B T U / C H H - F T - F )

7 0 0 . 1 n 2 5 0 . 1 6 1 9

0.1614 1 <: 2 B

0 . 1 5 6 9 0 . 1 6 2 0

4 2 6 . 6 7 6 9 9 . T A T T / C M E T E P . - K )

8 3 0 . 2 3 1 2 i? . 2 S d 2

0 . 2 7 9 3 « . 2 8 1 7

0 . 2 7 1 6 3 . 2 8 3 4

3 5 0 . 0 0 1 3 0 9 , B T U / C H R - F T - F )

0 . 1 6 7 S 0 . 1 6 52

J • 1 6 5 c o . 1 6 7 3

J . 1 6 1 J 0 . 11>6 5

4 5 4 . 4 5 7 2 7 . 6 1 \ ' A T T / C M " T E R - : 0

0 .2.=I90 0 . 2 5 7 6

.1 .11366 0 . 2 o 9 6

.-:•. V. 7 7 S . J i i M


THERMAL CO:JDUCTI VITY OF HELIUM COMPUTED T.:ITH DIFFERENT EQUATIONS

PRESSURE = 1(30 PSIA = 6.30457 RTTM = 6.S949 3AH

T E M P E R A T U R E

DEG F DEG UNITS OF ;C

DEG R, DEG UNITS OF

R :C 1 K4

T H E R M A L CONDUCTIVITY

i I5 :C3 IC6

900.30 1359.70 S T U/<HR-FT-F)

432.23 755.39 VATT/CMETER-IO

950.00 1439.70 3 T U / C H R - F T - F )

510.01 753.17 ^ A T T / C M E T E R - K )

1000.00 1459.70 B T U / ( H R - F T - F )

537.78 810.94 ,TA?T/( METER-iO

1050.00 1509.70 B T U / < H R - F T - F )

565.56 838.72 r .'ATT /< M ST ER-K)

1 100.00 1 559.70 B T U Z ( H R - F T - F )

59 3.34 3 66.50 UATT/c:i2TS'.'.-:c)

1 150.00 1609.73 B T U / ( H R - F T - F )

•4.1715 I 7<J4

0 . 29 6C5 0 . 2 9 4 -.>

C . 1759 0 . 174 6

0.304 5 5 .3222

0.1803 0 .178 3

0.3121 3.3094

2 .1847 A.1829

Y . 31 9 7 0.3166

0. 1896 0.1370

0.3272 Z .3237

R-. 1933 0.1911

3.1698 0.1713

1.2938 0.2973

<J. 1 739 0.1762

0.3009 0.3050

0.1779 0 . 1 8 0 5

0.3030 0 . 3 1 2 5

J•1520 J.1848

0.3149 3.3193

0.1859 0.138 9

0.3213 F>.32 7(J

0. 1 O99 0. 1930

0. 1651 io. 1 7td8

0.23 57 0.2956

0. 1690 0.1751

0.2926 0.3030

0.1730 C.1793

0.2994 0.3103

0.1769 0.1334

J?.3061 0.3174

U . 1 oil 1 0.1875

0.3127 0.3244

0.1644 0.1914

6 2 1 . 1 2 3 9 / 1 . 2 8 •A » 3346 ."3 . 3 3 J 7

3.3286 3.3341

0.3192 0.3313


THERMAL CONDUCTIVITY OF HELIUM COMPUTED 'IITH DIFFERENT EQUATIONS

PRESSURE = 100 PSIA = 6.80457 ATM = 6.8949 BAR


DEG F DEG R UNITS DF K

K1 K4

K2 :-C3 X 6


1200.00 1659.70 BTU/CHR-FT-F)

0 .1975 0 .1951

3.1938 1972

C. 1381 E.1934

648.90 922.06 WATT /C MET ER-SO

0.3419 3.3377

3.3354 3.3413

0.3256 0.3381

1250.00 1709.70 BTU/CHR-FT-F)

0.2017 0.1991

0.1976 3.2339

0.1918 0. 1992

676.67 949.83 WATT/CMETER-K)

0 . 3 4 9 2 0 . 3 4 4 5

3.3420 0.3477

0.3320 0.3443

1300.00 1759.70 BTU/CHR-FT-F)

0 .2059 0.2030

0.2314 0 .2124 7

0. 1954 0.2030

704.45 977.61 '.•JATT/CMSTER-K)

0.35 64 3.3514

0. 343 7 3.3543

0.3382 0.3514

1350.00 1809.70 BTU/CHR-FT-F)

0.2100 0 .20 69

3.2052 3 . 2 0 0 5

3.19S9 0.2063

732.23 1005.39 UATT/CMETER-K)

0 .3635 0.3581

0.3552 3.360S

0.3443 0.3578

1400.03 1359.70 BTU/CHR-FT-F)

0.2141 3.2103

3 • 2I39 3 0.2122

0.2024 0 .2124

760.01 1033.17 UATT/CMETER-K)

0 .373 6 I). 3 64 3

3« 3617 0.3572

0.35C3 0.3542

1450.00 1939.73 BTU/CHR-FT-F)

0 . 2 1 8 2 0 . 2 1 4 6

•3.2127 3.2153

3.2353 3.2141

787.73 1063.94 "RATT/C METER-K)

3.37 76 3.371 ••'!

'3. 363 1 3734

T;. 3 5 62 0.3 70 5

U6


THERMAL CO.'JD'JCTI VITY OF HELI'IM COMPUTED "ITil DIFFERENT "TJATI ONS

PRESSURE = u r psit\ = 6.5^457 ATM = 6.3^49 J.^M

TEMPERATU-*. THERMAL CONDUCTI VI TY

D E G F D E G R

U T F L T S O F K K1 K4

iC2 K5

!C3 K6

D E ' J C D E G K

U N I T S O F :C

1 5 0 0 . 0 3 1 9 5 9 . 7 0

M T U / < H R - F T - F ) 0.2222 0 . 2 1 3 4

0.2164 I ) . 2 1 9 3

0 . 2 0 9 2 !i . 217 7

S I 5 . 5 6 1 0 3 3 . 7 2 U A T T / C M E T E R - X )

0 . 3 3 4 6 0 . 3 7 6 0

0 . 3 7 4 5 ^ . 3 7 9 6

0 . 3 6 2 1 0 . 3 7 6 7

1 5 5 0 . 0 0 2 0 0 9 . 7 0 3 T U / C H R - F T - F )

J . 2 2 6 2 0 . 2 2 2 1

•I . 2 2 . 4 1 ' . 2 2 2 3

0 . 2 1 2 5 0.2212

S 4 3 . 3 4 1 1 1 6 . 5 0 ' ' A T T / C M E T E R - K >

0 . 3 9 ! 6 0 . 3 3 4 5

•J • 3 3 U > I 0 . 3 3 5 6

0 . 3 6 7 3 0 . 3 8 2 3

1 6 0 3 . 0 0 2 0 5 9 . 7 0 3 T U / ( H R - F T - F >

0 . 2 3 0 2 0 . 2 2 5 9

0 . 2 2 3 7 • 3 . 2 2 6 3

0 . 2 1 5 3 Z . 2 2 4 7

8 7 1 . 1 2 1 1 4 4 . 2 3 U A T T / C M E T E R - K )

0 . 3 9 3 4 0 . 3 9 0 9

0 . 3 3 7 1 0 . 3 9 1 B

0 . 3 7 3 4 0 . 3 8 8 9

1 6 5 0 . 0 0 2 1 0 9 . 7 3

3 T U / ( H R - F T - F ) 0 . 2 3 4 2 0 . 2 2 9 5

0 . 2 2 7 3 J . 2 2 9 7

0 . 2 1 9 0 0 . 2 2 3 1

3 9 8 . 9 0 1 1 7 2 . 0 6 U A T T / C M E T E R - K )

0 . 4 0 5 3 0 . 3 9 7 3

0 . 3 9 3 4 3 . 3 9 7 5

0 . 3 7 9 0 0 . 3 9 4 9

1 7 3 0 . 0 0 2 1 5 9 . 7 0

B T T J / ( H R - F T - F ) 0 . 2 3 8 1 0 . 2 3 3 2

0 . 2 3 0 8 0 . 2 3 3 1

0 . 2 2 2 1 0 . 2 3 1 5

9 2 6 . 6 7 1 1 9 9 . 3 3

U A T T / ( M E T E R - ; O C . 4 1 2 1 O .4036

0 . 3 9 9 5 0 . 4 J 3 4

Z . 3 3 4 4 0 . 4 0 3 7

1 7 5 0 . 0 0 2 2 0 9 . 7'.)

3 T U / C H R - F T - F ) G . 2 4 2 3 0 . 2 3 6 3

3 . 2 3 4 4 3 . 2 3 6 4

3 . 2 2 5 2

0 . 2 3 4 9

9 5 4 . 4 5 1 2 2 7 . 6 1 \ ' A T T / ( M E ^ E R - S O

3.41 US . 4 ' O 9 3

3 . 4 2 5 7 A . 4 3 9 2

0.33 9 7 0 . 4 0 6 5

U7


THERMAL CONDUCTIVITY OF HELIU.I COMPUTED '71TH DIFFERENT EQUATIONS


TEMPERATURE T H E R M A L C O N O ' J C T I V I T Y

DEG F DE3 R UNITS OF IT

:ci >C4

X2 K 5

K 3 it 6

DEG C DEG U N I T S OF iC

1300.00 2259.70 BTU/CHR-FT-F)

0.2459 0 .2403

0.2379 0.2393

0.2232 0.2332

982.23 1255.39 WATT/CMETER-K)

0.4255 0.4160

0.4118 3 . 4 1 5 0

0.3950 0.4123

1850.00 2309.70 BTU/(HR-FT-F>

3.2497 0.2439

0.2414 3.2431

0.2312 0.2415

1010.01 1283.17 U A T T / C M E T E R - X )

0.4322 0.4220

3.4178 J.4233

0.4001 0.4130

1900.00 2359.73 BTU/CHR-FT-F)

3.2535 0.2473

0.2449 0.2464

0.2341 0.2447

1037.78 1313.94 U A T T / C M E T E R - K )

0.4383 0.4281

0.4233 3.4265

0.4051 0.4236

1950.00 2409.70 BTU/C HR-FT-F)

J .2573 0.2508

0.2483 0.2497

3.2369 0.2479

1065.56 1333.72 UATT/CMETER-IO

0.4U53 0 .4340

0.4293 O.4322

0.4101 0.4291

2000.00 2459.70 STU/CHR-FT-F)

0.2611 C.2542

? .251 7 0 .253IN

3.2397 0.2511

1093.34 1366.50 IJATT/CMETER-X)

0.4519 0 .4399

0.4357 0.4379

0.4149 3 .4346

U8

T a b l e A . 3

THERMAL CONDUCTIVITY OF HELIUM AT 500 PSIA

T H E R M A L COMDUCTI VITY OK HELIUM C O M P U T E D VIITH DIFFERENT E Q U A T I O N S

R E F E R E N C E LIST:

RISO REPT 224. X2J GA CO. ;C3J J . P . SANDERS,ORML. -C4J D.L. MC SLROY, ORML K5; J U L I C H , REPT XFA-1 R E - 1 7 / 7 5 . K6J A S H R A E , T H E R M O P H Y S . P R O P . , 1 9 7 3 .

P R E S S U R E = 5H0 PSIA = 34.U229 ATIL = 34.4745 BAP.


DEG F DSG R UNITS OF K

DEG C DEG K UNITS OF : c

1(4 .-C3 K 6

50.00 509 B T U / C H R - F T - F )

70

10.01 233.17 UA'I.T/CMETER-LO

103.33 559.70 3TU/CMF.-FT-F)

I . 0 S 6 2

O .1492

0.0921

3 .0903 3 .13346

3.1571 U . 1 463

w .t'964 U .'J9 3 5

0.0698 0.0843

3. 1554 0.1459

E.B948 3.0931

37.73 310 <JATT/CMETE.:-.-O

9 4 0 . 1 59 4 •j . 1 66J . 1 5 6 7

0 . 1 6 4 J 0.1559

1 5 0 . 0 0 6 3 9 , BTIJ/CHR-FT-F)

7:i 0.09 7O tf . 1 e> 1 o 3 . v) 9 64

3 . 0 9 9 7 3 • j 9 5 7

65.56 333 VATT/CMETSR-IO

72 • 1 69 3 0.1762 •:> .166-3

0.1725 0.1657

230.00 659 BT'J/CHH-FT-F)

7 P r.. 1034 3 . 1 J*. 71 0 . 1020

0. 1045 0.1013

9 3.34 3 66, UAT?/C;IETEV:-K)

53 . 1 792 3.13 54 •1 . 1 766

0. 1809 0.1754

2 5 0 . 1 7 0 ? B T'! / C LIR* - FT - F )

.79 J . 1 '33? 0. 1 123 •3.1076

0. 109 3 3.13 69

12 1.1? 394 RATT/Ci-lETE?-:;)

C . 18 b 5 w . 1 j . I;; ? 2

y . 1 o 9 2 3. 13 5G

1*9


THER.IAL CONDUCTIVITY OF HELIUM COMPUTED *TITH a) I r FERENT EuUATIOMS



DEG F DEG R UNITS OF IC

K 1 IC4

K 2 IC 5

K3 K 6


300.03 759.70 BTU/CHR-FT-F)

0.1 143 0. 1 1 74 9.1130

0.1141 0. 1 123

148.90 422.06 UATT/CMETER-;C)

0.1977 3.2031 0 . 1956

0. 1974 0. 1944

350.00 809.70 BTU/CHR-FT-F)

0. 1 195 3.1223 3.1 184

3.1 188 0. 1 177

176.67 449.83 WATT/CMETER-K)

400.00 859.73 BTU/CHR-FT-F)

0 .23 65

0 . 1247

0.2117 0 .2TO49

3.1272 0. 1236

0.2055 0.2037

0.1234 3.1232

204.45 477.61 UATT / C MET ER -IC )

U.2153 0.2231 0.2140

0.2135 0.2129

450.00 909.70 BTU/CHR-FT-F)

0.1297 0.1312

•3.1319 3.1283

0.1279 0.1232

232.23 505.39 UATT/CMETER-K)

0.2245 0 .2271

0 .2283 0.2229

0.2214 0.2219

500.00 959.70 BTU/CHR-FT-F)

3.1347 3.1357

0.1366 0 . 1339

0. 1 325 0.1334

260.01 533.17 "ATT/CMETER-K)

0.2332 0.2349

3.2364 0.2317

0.2292 0.2333

550.00 1009.75 BTU/CHP.-FT-F)

3.139 6 '3 . 1 402

0.1412 3.1339

0.1369 3. 1384

237.73 563.94 MATT/CMETER-K)

'3 .2417 0 .2427

3.2444 3.240 3

0.2369 0.239 6

50


T H E R M A L C O N D U C T I V I T Y OF H E L I U M COMPUTED U l TH D I F F E R E N T E Q U A T I O N S

P R E S S U R E = 5 0 0 P S I A = 3 4 . 0 2 2 9 A T M = 3 4 . 4 7 4 5 OAR

T E M P E R A T U R E . T H E R M A L C O N D U C T I V I T Y

DE'1 F DEG P. U N I T S OF K

X I X 4

X2 X 5

X 3 X 6


6 0 0 . 0 0 1 0 5 9 . 7 0 B T U / C H R - F T - F )

0 . 1 4 4 5 0 . 1 4 4 7

y . 1 4 5 7 3 . 1 4 3 3

. 1 4 1 3 0 . 1 4 3 3

3 1 5 . 5 6 5 8 3 . 7 2 V A T T / C M E T E R - X )

0 . 2 5 3 1 0 . 2 5 0 4

'.^.2522 0 . 2 4 3 9

0 . 2 4 4 5 3 . 2 4 3 I

6 5 0 . 0 0 1 109.7'-"? B T U / C H R - F T - F )

0 . 1 4 9 3 0 . 1 4 9 1

9 . 1 5 0 2 •3 • 1 4 3 6

0 . 1 4 5 6 0 . 1 4 3 2

3 4 3 . 3 4 6 1 6 . 5 3 U A T T / C M E T E R - X )

0 . 2 5 3 3 0 . 2 5 8 0

0 . 2 5 9 9 0 . 2 5 7 3

0 . 2 5 2 0 0 . 2 5 6 4

7 0 0 . 0 0 1 1 5 9 . 7 0 B T U / C H R - F T - F )

0 . 1 54-3 0 . 1 5 3 5

0 . 1 5 4 6 0 . 1 5 3 4

0 . 1 4 9 9 0 . 1 5 2 9

3 7 1 . 1 2 6 4 4 . 2 3 ' • / A T T / C M E T E R - X >

0 . 2 6 6 5 0 . 2 6 5 6

0 . 2 6 7 5 0 . 2 6 5 5

0 . 2 5 9 4 0 . 2 6 4 6

7 5 2 . 0 2 1 2 3 9 . 7 0 BT'J / < H P.- F T - F )

0 . 1 5 3 6 0.1573

0 . 1 5 3 9 3 . 1 5 3 1

0 . 1 5 4 1 J . 1 5 7 5

3 9 8 . 9 3 6 7 2 . 0 6 U A T T / C M S T i ^ - i O

3 . 2 7 4 5 0 . 2 7 3 1

3 . 2 7 5 0 0 . 2 7 3 7

0 . 2 6 6 7 0 . 2 7 2 6

3 0 3 . ( 5 0 1 2 5 9 . 1 Z B T U / C H R - F T - F )

M . 1 6 3 2 0 . 1 62 1

0 . 1 6 3 2 0 . 1 6 2 3

0 . 1 5 3 3 0 . 1 6 2 3

4 2 6 . 6 7 6 9 9 . 3 3 i / A T T / C M E T E I - j o

0 . 2 3 2 5 0 . 2 3 0 6

0 . 2 3 2 4 0 . 2 3 1 7

0 . 2 7 3 9 0 . 2 3 0 4

3 5 0 . 0 3 1 3 3 9 . 7 0 B T U / < H R - F T - F >

A . 1 67 O 0.16C4

0 . 1 6 7 4 • J . 1 6 7 3

0 . 1 6 2 4 . 1 6 6 5

4 5 4 . 4 5 7 2 7 . 6 1 ' r A T T / C MET EP.- X ) 0 . 2 3 3 3

3 . 2 3 9 7 O . 2 3 9 6

U . 2 D 1 C 0 . 2 8 3 1

51


T H E R M A L CONDUCTIVITY OF HELIUM COUP') M O VI-TH DIFFERENT EQUATIONS

P R E S S U R E = 500 PSIA = 34.0229 ATM = 34.4745 3ii.\

T E M P E R A T U R E :HZRMAL CONDUCTIVITY

DEG F DEG R U N I T S OF IC

:ci K 4

.12

.(5 K 3 jC6

DEG C DEG IC UNITS OF K

900.00 1359.70 B T U / C H R - F T - F )

0.1722 0 . 1 7 0 6

0.1715 0.1713

3.1 664 3.1703

4S2.23 755.39 MATT/CMETER-;O

0.2931 0.2953

3.2969 0.29 73

0.2S80 0.2956

950.00 1409.70 B T U / C H R - F T - F )

0 . 1 7 6 7 0 . 1 7 4 3

0 . 1 7 5 6 0.1762

3.1704 0.1751

510.01 7 8 3 . 1 7 U A T T / C M E T E R - K )

0.3058 0.3026

3.3040 0.3350

0.2949 0 .3030

1000.00 1459.70 B T U / C H R - F T - F )

0.1811 0.1790

0.179 7 0.1805

0.I 743 0.1793

537.73 8 1 0 . 9 4 UATT/CMSTER-IC)

0.3134 0 .3098

0.3110 3 . 3 1 2 5

0 . 3 0 1 7 0.3103

1050.00 1509.70 B T U / C H R - F T - F )

0.18 54 3.1331

G. 1337 3.1848

3.1732 3 . 1834

565.56 8 3 8 . 7 2 '.JATT/CMETER-K)

0.3209 0.31 69

0.3180 3.3198

0.3084 E . 3 1 74

1100.00 1559.70 B T U / C H R - F T - F )

0 . 1 8 9 7 <3 .1372

3. 1877 3. 133 9

0.1323 0.1875

59 3.34 8 66.50 U A T T / C M E T E R - K )

0.3234 0.3240

0.3249 3.32 73

3 . 3 1 4 9 2 . 3 2 4 4

1150.00 1609.73 B T U / C H R - F T - F )

0.1940 0.1913

•3.1916 0.1930

3.1357 0.1914

62 1.12 894.23 U A T T / C M E T E R - K )

0.3353 0.3315

0 . 3 3 1 7 0 . 3 3 4 1

0 . 3 2 1 4 3.3313

52


T H E R M A L C O N D U C T I V I T Y OF H E L I U M COMPUTE] ) I ' I TH D I F F E R E N T E Q U A T I O N S

P R E S S U R E = 3 ^ 0 P S I A = 3 / 1 . 0 2 2 9 A T M = 3 4 . 4 7 4 5 BAR

T E M P E R A T U R E T H E R M A L C O N D U C T ! V I T Y


K1 ;<4

::2 .£5

.-C3 :c6

DEG C DEG K U N I T S OF

1 2 0 0 . 0 0 1 6 5 9 . 7 0 B T U Z ( H R - F T - F )

S . l 9 3 2 0 . 1 9 5 3

0 . 1 9 5 5 0 . 1 9 7 0

0 . 1 8 9 4 M . 1 9 5 4

6 4 8 . 9 0 9 2 2 . 0 6 U A T T / C M 2 T S P . - K )

0 . 3 4 3 1 0 . 3 3 8 0

0 . 3 3 8 4 3 . 3 4 1 0

0 . 3 2 7 8 0 . 3 3 3 1

1 2 5 0 . 0 0 1 7 0 9 . 7 0 3 T U > C H R - F T - F )

G . 2 0 2 4 0 . 1 9 9 2

3 . 1 9 9 4 3 . 2 0 3 9

0 . 1 9 3 0 3 . 1 9 9 2

6 7 6 . 6 7 9 4 9 . 8 3 V A T T / C M E T E R - K )

0 . 3 5 0 4 d . 3 4 4 8

0 . 3 4 5 1 . 3 . 3 4 7 7

£>.3341 0 . 3 4 4 3

1 3 0 0 . 0 0 1 7 5 9 . 7 0 3 T U / C M R - F T - F )

0 n 0 . 2 3 3 2

J . 2 J 3 2 O . 2 3 4 7

3 . 1 9 6 6 Z » 2 O 3 0

7 0 4 . 4 5 9 7 7 . 6 1 U A T T / ( M E T E R - r £ )

0 . 3 5 7 5 0 . 3 5 1 6

0 . 3 5 1 7 2 . 3 5 4 4

' ) . 3 4 0 3 0 . 3 5 1 4

1 3 5 0 . 0 0 1 8 0 9 . 7 0 3 T U / C H R - F T - F J

0 . 2 1 0 7 0 . 2 0 7 1

3 . 2 3 7 C 0 . 2 0 8 5

0 . 2 3 E 1 & . 2 0 6 3

7 3 2 . 2 3 1 3 3 5 . 3 9 V A T T / C METER- . ' £>

0 . 3 6 4 7 0 . 3 5 3 4

v). 3 5 6 3 3 . 3 6 £ 3

H . 3 4 6 4 3 . 3 5 7 a

1 4 P 0 . 0 0 1 8 5 9 . 7 0 3 T U / C H R - F T - F )

3 . 2 1 4 o 0 . 2 1 0 9

0 . 2 133 0 . 2 1 2 2

. 2 0 3 6 V . 2 1

7 6 3 . ' J 1 1 0 3 3 . 1 7 T A T T / C l E T E . ' i - . O

0 . 3 7 1 3 i> . 3 6 5 1

" . 3 6 4 i . 3 6 7 2

0 . 3 5 2 3 . 3 6 4 2

14 5 0 . ^ 0 1 9 t ' 9 . 7 0 3 T u / < H : _ , - F T - F )

"..21 . y l 43

J . 2 1 '15 .?•. 11 3:"'.

Z . 2<S 7£' •1 . *?. 1 4 1

7 3 7 . 7 3 1 J 6 U . 9 4 ''ATT/CiCTE::-"-:)

* .37";.3 •J. 37 17

) . 3 7 1 2 " . 3 7 3 4

j . 3 5 r ' 2 'v • 3 Ik ' O

53


THERMAL CONDUCTIVITY OF HELIUM COMPjTEO •JITII DIFFERENT E'.lUATl 0.J3

P K E S S U > . E ^ 5 PS I A = 3 4 . 3 2 2 9 A T . i = 3 4 . 4 7 4 5 3 / \ R


DEG F U N I T S OF ;c

.CI K 4

iC2 K 5

;c3 /16

DEG C DEG K U N I T S OF X

1 5 0 0 . 0 0 1 9 5 9 . 7 0 3 T U / C H R - F T - F )

0 . ^ 2 2 9 0 . 2 1 8 5

0 . 2 1 3 2 3 . 2 1 9 3

0 . 2 1 0 3 0 . 2 1 7 7

8 1 5 . 5 6 1 0 8 8 . 7 2 U A T T / C M E T E R - i O

0 . 3 3 5 7 0 . 3 7 8 2

0 . 3 7 7 6 0 . 3 7 9 6

0 . 3 6 4 0 0 . 3 7 6 7

1 5 5 0 . 0 0 2 0 0 9 . 7 0 B T U / C H R - F T - F )

0 . 2 2 69 0 . 2 2 2 3

3 . 2 2 1 3 0 . 2 2 2 3

3 . 2 1 3 6 0 . 2 2 1 2

8 4 3 . 3 4 1 1 1 6 . 5 3 U A T T / C M E T E R - K )

0 . 3 9 2 7 0 . 3 8 4 7

0 • 3 8 3 9 0 . 3 3 5 6

0 . 3 6 9 7 0 . 3 8 2 3

1 6 0 0 . 0 0 2 0 5 9 . 7 0 B T U / C H R - F T - F )

0 . 2 3 0 8 0.226W

3 . 2 2 5 5 3 . 2 2 6 3

0 . 2 1 6 8 0 . 2 2 4 7

8 7 1 . 1 2 1 1 4 4 . 2 8 W A T T / C M E T E R - K )

0 . 3 9 9 5 0 . 3 9 1 1

3 . 3 9 0 2 0 . 3 9 1 6

0 . 3 7 5 3 0 . 3 8 8 9

1 6 5 0 . 0 0 2 1 0 9 . 7 0 B T U / C H R - F T - F )

3 . 2 3 4 8 0 . 2 2 9 7

0 . 2 2 9 1 0 . 2 2 9 7

0.2200 0 . 2 2 3 1

8 9 8 . 9 0 1 1 7 2 . 0 6 U A T T / C M E T E R - K )

0 . 4 0 6 3 0 . 3 9 7 5

0 . 3 9 6 4 0 . 3 9 7 5

3 . 3 8 0 7 0 . 3 9 4 9

1 7 0 0 . 0 0 2 1 5 9 . 7 0 B T U / C H R - F T - F )

0 . 2 3 8 7 3 . 2 3 3 3

fl < . 2 3 2 6 3 . 2 3 3 1

0 . 2 2 3 1 0 . 2 3 1 5

9 2 6 . 6 7 1 1 9 9 . 8 3 U A T T / C M E T E R - ' O

0 . 4 1 3 1 0 . 4 3 3 8

3 . 4 3 2 6 3 . 4 0 3 4

Z.33 61 0 . 4 0 0 7

1 7 5 0 . 0 0 2 2 0 9 . 7 0 B T U / C H R - F T - F )

0 . 2 4 2 6 0 . 2 3 6 9

0 . 2 3 6 2 0 . 2 3 6 4

0.2261 0 . 2 3 4 9

9 5 4 . 4 5 1 2 2 7 . 6 1 U A T T / C M E T E R - r C )

0 . 4 1 9 3 0 . 4 1 3 0

3 . 4 0 3 7 0 . 4 3 9 2

0 . 3 9 1 4 0 . 4 0 6 5

5h


T H E R M A L C O N D U C T I V I T Y OF H E L I U M CO I P U T E J •-TI T . I D I F F E R E N T E Q U A T I O N S

P R E S S U R E = 5 0 2 P S I A = 3 4 . 3 2 2 9 ATM - 3 4 . 4 7 4 5 BAR


DEG F DEG U N I T S O F X

x i X 4

X 2 X 5

X 3 •f ft

D E G C D E G U N I T S OF X

1 8 0 0 . 0 0 2 2 5 9 , B T U / C H R - F T - F )

7 3 0 . 2 4 6 4 0 . 2 4 0 5

0 . 2 3 9 7 3 . ' 2 3 9 3

3 . 2 2 9 1 • 2 3 o 2

9 3 2 . 2 3 1 2 5 5 . ' T A T T / C M E T E R - K )

3 9 3 . 4 2 6 5 Z . 4 1 6 2

6 . 4 1 4 3 0 . 4 1 5 0

3 . 3 9 6 5 3 . 4 1 2 3

1 3 5 0 . 0 0 2 3 0 9 , 3 T U / C H R - F T - F )

7 0 & • 2 5 0 3 Q . 2 4 4 0

3 . 2 4 3 2 . 1 . 2 4 3 1

3 . 2 3 2 1 0 . 2 4 1 5

1 3 1 3 . 0 1 1 2 8 3 , V A T T / C M S T E R - ' O

17 3 . 4 3 3 1 f i . 4 2 3 9 / ': . «»203

3 . 4v' 1 6 2 . 4 1 8 0

1 9 0 0 . 0 0 2 3 5 9 , B T U / C H R - F T - F )

7 3 3 . 2 5 4 1 0 . 2 4 7 5

3 . 2 4 6 6 0 . 2 4 6 4

0 . 2 3 4 9 3 . 2 4 4 7

1 0 3 7 . 7 3 1 3 1 0 V A T T / C M E T Z R - . : )

9 4 3 . 4 3 9 7 0 . 4 2 3 3

5 . 4 2 O 9 3 . 4 3 6 6 0 . 4 2 3 6

1 9 5 0 . ( 1 0 24" ' 1 9, 3 T U / C H R - F T - F )

7 ? 2" .2 579 3 . 2 5 0 9

0 . 2 531 0 . 1 4 9 7

^ . 2 3 7 7 . 2 4 7 9

1 0 6 5 . 5 6 1 3 3 3 "ATT/(M-:TSP.-X>

72 5 . 4 4 6 3 0 . 4 3 4 2

0 . 4 3 2 3 • • 3 . 4 3 2 2

0 . 4 1 1 5 3 . 4 2 9 1

2 - 2 3 2 . J3 2 4 5 9 :JTU/CH~--F7-F>

.7.3 . 2 'J 1 S 0 . 2 5 4 3

0 • 2 5 3 j C . 2 4 0 5 } . 2 5 1 1

1 ^ 9 3 . 3 4 ''ATT/C IE

w . 4 5;j.< 3 .44." 1

.; . 1 3 3 .5 J . 4 3 7 9

< . 4 1 6 2 A.434o

55

Table A.A THERMAL CONDUCTIVITY OF HELIUM AT 750 PSIA

T M E R M A L CONDUCTIVITY OH HEUIUM COMP'JTSJ "ITH OIFFIRZ.JT E'LUAT 10.J3

REL-ERZMCE LIST:

! C I ; R I 3 0 R E P T 2 2 4 . . C 2 ; 3 A 0 0 .

. C 3 ; J . P . S A N D E R S , O R N L . A'ii D . L . MC I L R O Y j O R . J L ( 5 ; < J " L I C H / P . E P T ; I F A - I " Z - 1 7 / 7 2 . :;6; AS.-IRA THERMOPHYS . PROP.., 1973.

PRESSURE = 75,5 PS IH = 51.3343 ATM = 51.7117 3AII

TZ 1PZRATMRZ T HERMAL COM'J'ICTI "I TY

DEI F DEI R UNITS OF

•<1 i<4 ,„5

-C3 ,C6

DEI C D -C "MI TS OF "C

50.0* 539.70 .3TM/CMR-FT-F)

3 .38 66 3 . 3 9 1 3 a .id 346

^.3936 3.3343

13.31 253.17 "A^T/CMZTZR-.O

3 . 1 4 "5 9 3 . 1 5:51 3.1463

U.1563 3.14 59

13N.3? 539.70 •ST'L/CHR-FT-F)

3 .3925 3 .3969 3.3 9 3 5 3•39 5 1

37. 313.94 MATT/C METER

3 . 1 Se1 3.1573 3.156 7

3 . 165 5 3.1559

150.3C 6P9.73 3T'J/CHR-FT-F)

3 .39 33 A . 1324 3 .3964

3. 1 03 5 VI. 093 7

6 5 . 5 6 3 3 3 . 7 2 "A^T/C METER-.I)

3.1701 3.177£ A • 1 6 6 3

3.1743 3.1657

2P0.iV 65^.711 dT'J/( H R - F T - F )

1339 3 . 1377 / . 1

3. 13 54 3 • 1 3 1 J

O.? . 34 366. 1 •','XTT/CM IT?...-.-*)

3 . 1 7 J 7 3 . 1 i 6 'J . 1 7 66

•3.1 -4 3.1754

.-ITM/CM ~>-7T-F) . 1 <? 9 3 3.1 I 2

/i . If 7ft t). 1 l/!i /) . 1 O ?

1?1 .12 3 3 J. •'ATT/C R.T^R-.O

•3 . 1 iS9'2 . I 9 5 '1 / . 1 3i '-j

1 9 3 7 :. 1 5 i

56


T H E R M A L CO.JLIMCTI'FLTY 'JF '-{EL IM 0 1 !T :!.> "'IT4 DI I F -:R':MT E T U T I O.CO

?H-:SS'JRE = 75.1 PSlM = 51 ..'313 ->TM = 51.7117

TEM?-:RAT'JRE T H E R M A L CJJ:J JCTI VITY

DEj F 0Z3 R MÔITS OF

DE3 C 'JOI 'J:jits JF ii

KI -C5

,C3 .C6

333 IF3 7 59.7I* BT'J/( HR-F""-F)

14O.93 422.. • 'ATT/( METER-.O

350.^3 329.70 •JTM/CHR-F^-F)

"ATT/C.IZTSR-RO

430. 3'3 359.7,! !3T!J/(HR-FT-F>

3.1147

3.1935

i) . I I 9 9

3 .2 -3 7 6

3. 1231

3 . 1 1 7 9 3.1 133

3.2041 3 . 1 957

3. 122; 3.1134

3.2127 3.2049

3.1277 3. 1236

3.M 149 J. 1 123

3. 1939 3. 1944

3.1 196 3.1177

3.2370 3.2337

3.1242 3.1233

234.4 5 47 7.61 'FATT/CMETER-IO

450.00 ^09.7? 3T'J/(HR-FT-F >

232.2 3 535.J9 '.'ATT/CMETE?.-;:)

3.2165

3 . 1 302 3.1314

3 .2253 ?.227 5

3.2211 3.2140

d . 1325 3.1283

3.2293 3.2220

0.2150 3.2129

3. 1233 3.1282

3.222 9 3.22 19

5 310.3-3 959.70 3 T M / C H R - F T - F )

3.1351 3.13 63

3.1372 3.1339

3.1333 3.1334

263.31 533.17 "ATT/C1T"—!-'-":)

3.2339 3 .2353

3.2 37 4 3.2317

3.230 7 3.23^8

550.'TI? 13^9.7^1 .3T'J / (MR - FT-F >

.1 .113 1 3 • 1404

3.1413 3.I 339

3.13 73 3.1334

7.7-j 56" . 3 'l r. . 2 4 2 'i 3 . 2 4 3 1

j.2454 0.243 3

3.2334 0.2396

57


T4ERMAL CONDUCTI VITY OF HELIU.-L C O M P U T E D "I TH DI F F ERENT EQUATIONS

PRZSS'IKZ = 750 PSIA = 51.0343 AT.L = 51.7117 JAR

T E M P E R A T U R E T H E R M A L C DMDUCT1"ITY

DE3 F DEI R UNITS OF :C

K 1 K4 IV o

.C3

.Co

DEI C DEG A UNITS OF ::

60C-.03 10 59.70 B T U / C H R - F T - F )

A.1449 0.1449

0.1453 3.1433

3.1422 0.1433

315.56 538.72 " A T T / C M E T E R - K )

C.2333 0 .2538

0.2532 3.2439

3.2463 3.2431

650.00 1109.7/1 3 T U / C H R - F T - F )

•3. 1497 0 . 1433

3 . 1 53 7 3.143 6

3 . 146 5 3. 1432

343.34 616.53 VATT/C-1ST £P.-K)

3 .2593 0.2534

3.2639 3.2 573

FL.253 5 0.2564

700 .03 L 1 59 • ZITU/CHR-FT-F)

3.1544 3.1537

3.1551 3.1534

'3. 1 537 3.1529

371.12 644.23 '.'ATT/C M E T E R - / )

3 .2 '>72 3 .2 66.1

3 .268 5 3 .2655

3.260} 3.2646

7 50.00 1200.7 0 "3TU/CHR-FT-F )

3 . 1593 3.1530

3 . 1 59 5 3 • 1 58 1

3. I 550 3.1575

39-3.O0 672.36 'JATT / C M E T EP - )

0 .il^'l 3 .2735

'3 .27 63 3.2737

3.2632 3.2 7,26

3 0 3 . 3 0 1259.73 3 T U / C H R - F T - F )

3 . 163 6 3 . 1 62 3

3.1637 3 . I 6.2 3

3.1591 3.1623

426.67 699.3 3 U A T T / C N S T IP-:C)

3 .2332 3 .23.-J

• 2 3 <4 •/! - 2 S 1 7

3.2754 3 . 2 <I V) 4

353.33 1339.73 3TU/CM '.-Fi'-f }

•3 . I EV-J I 0 . 1 •io

I). 1 67'J 3.1 J 7 J

3.1632 1665

45'1.45 727 .61 ''ATT/CMET IR--:)

el . 2 9 1H J . 2 o y 6

3 .2325 ..'. '2 -J j 1

58


T H E R M A L C O . J D U C T I V I T Y A? JJ.;.' ' . ' I T i l D I F F E R E N T i - l ' J . k T I ^ . ; . ;

P R E S S U R E = 7 5 3 P o l A = 5 1 . •••) 3 '1 J A T I = 5 1 - 7 1 1 7 2 u R

T E M P E R A T T T:-I E K: I „ L CO.I J'JJ TI '.'I TY

D E G F D E 3 U N I T S OF<?;C

•a X 4

V -

.-Cb C 3 -C 6

D E 3 C D E I U N I T S OF K

9 0 0 . 0 3 1 3 5 9 . 7 0 B T U / C H R - F T - F )

3 . 1 7 2 6 0 . 1 7 3 J

•J • 1 7 2 1 / . 1 7 1 3

3 . 1 6 7 2 0. 1 70-3

4 3 2 . 2 3 7 5 5 . 3 9 U A T T / C N E T E R - . - : )

0 • 2 9 r5.-. 3 . 2 9 5 6

3 . J 7 3 < 3 . 2 ) 7 3

3 . 2 3 9 4 3 . 2 9 5 6

9 5 0 . 0 0 1 4 3 9 . 7 3 B T U / C H R - F T - F )

3 . 1 7 7 1 0 . 1 7 5 0

3 . 1 7 6 2 3 . 1 7 6 2

0 . 1 7 1 2 3 . 1 7 5 1

5 1 0 . 0 1 7 3 3 . 1 7 V A T T / O l E T S R - i O

3 . 3 3 6 5 3 . 3 3 2 9

3 . 3 3 5 3 3 . 3 3 5 3

3 . 2 9 6 3 3 . 3 3 3 0

1 0 0 0 . 0 0 1 4 5 9 . 7 0 B T U / C H R - F T - F )

3 . 1 3 1 3 3 . 1 7 9 1

3 . I 3 3 3 <j » 1 i v5 3

J . 1 7 o l 3 . 1 7 9 3

5 3 7 . 7 3 3 1 3 . 9 4 ' . ' A T T / C M E T E R - K )

0 . 3 1 4 3 3 . 3 1 0 1

3 . 3 1 2 3 3 . 3 1 2 - 5

3 . 3 3 3 1 3 . 3 lt?3

1 0 5 3 . 0 0 1 5 0 9 . 7 0 13TU/C H R - F T - F )

0 . 1 3 5 3 3 . 1 3 3 3

3 . 1 3 4 3 0 . 1 3 4 3

3 . 1 7 9 3 it . 1 3 3 4

5 6 5 . 5 6 8 3 3 . 7 2 U A T T / C M E T E R - X )

^ . 3 2 1 6 3 . 3 1 7 2

•3 . 3 1 9 3 3 . 3 1 9 3

3 . 3 3 9 3 3 . 3 1 7 4

1 1 0 0 . 0 0 1 5 5 9 . 7 3 B T U / C H R - F T - F )

3 . 1 9 3 1 3 . 1 3 7 3

3 . 1 3 3 3 3 . 1 3 3 9

3.1 323 3 . 1 ^ 7 5

59 3 . 3 4 3 6 6 . 5 v ? U A T T / C M E T E R - Z v )

?. . 3 2 9 3 3 . 3 2 4 2

, 1 . 3 2 5 9 0 . 3 2 7 3

3 . 3 1 6 3 3 . 3 2 4 4

1 1 5 0 . 0 0 1 6 0 9 . 7 3 B T U / C H P . - F T - F )

3 . 1 9 4 I 3 . 1 9 1 4

3 . 1 9 2 2 3 . 1 9 3 3

3 . 1 3 6 3 3 . 1 9 1 4

6 2 1 . 1 2 3 9 4 . 2 3 " A T T / C M E T E R - X >

. 3 3 6 4 3 . 3 3 1 ?

J . 3 3 2 7 3 . 3 3 4 1

3 . 3 : ^ 1 0 . 3 3 13

59


T H E R M A L C O N D U C T I V I T Y OF H E L I U M C O M P U T E D W I T H D I F F E R E N T E Q U A T I O N S

P R E S S U R E = 7 5 0 P S I A = 5 1 . 0 3 4 3 A T M = 5 1 . 7 1 1 7 3 A R

TEMPERATURE T H E R M A L C O N D U C T I V I T Y

D E I F DEG R U N I T S OF I t

it 1 K 4

li 2 :<5

K 3 .t6

DEG C DEG it U N I T S OF :t

1 2 0 0 . 0 0 1 6 5 9 . 7 0 B T U / C H R - F T - F )

0 . 1 9 S 6 0 . 1 9 5 4

0 . 1 9 6 1 0 . 1 9 7 0

0 . 1 9 0 2 0 . 1 9 5 4

6 4 8 . 9 0 9 2 2 . 0 6 V A T T / C M E T E R - K )

0 . 3 4 3 7 0 . 3 3 3 2

0 . 3 3 9 4 0 . 3 4 1 0

0 . 3 2 9 2 0 . 3 3 3 1

1 2 5 0 . 0 0 1 7 0 9 . 7 0 B T U / C H R - F T - F )

0 . 2 0 2 3 0 . 1 9 9 4

3 . 2 0 0 0 0 . 2 0 0 9

0 . 1 9 3 8 0 . 1 9 9 2

6 7 6 . 6 7 9 4 9 . 8 3 U A T T / C M E T E R - K )

0 . 3 5 0 9 0 . 3 4 5 1

0 . 3 4 6 1 3 . 3 4 7 7

0 . 3 3 5 4 0 . 3 4 4 8

1 3 0 0 . 0 0 1 7 5 9 . 7 0 B T U / C H R - F T - F )

3 . 2 0 6 9 0 . 2 3 3 3

0 . 2 0 3 3 3 . 2 0 4 7

0 . 1 9 7 4 0 . 2 0 3 0

7 3 4 . 4 5 9 7 7 . 6 1 U A T T / C M S T E R - K )

0 . 3 5 3 1 3 . 3 5 1 9

0 . 3 5 2 7 3 . 3 5 4 4

0 . 3 4 1 6 0 . 3 5 1 4

1 3 5 0 . 0 0 1 3 0 9 . 7 0 B T ' J / C H R - F T - F )

0.2110 0 . 2 3 7 2

3 . 2 0 7 6 3 . 2 0 8 5

0 . 2 0 0 9 0 . 2 0 6 3

7 3 2 . 2 3 1 0 3 5 . 3 9 U A T T / C M E T E R - i O

3 . 3 6 5 2 3 . 35.-.6

3 . 3 5 9 3 3 . 3 6 3 3

0 . 3 4 7 6 0 . 3 5 7 3

1 4 0 0 . 0 0 1 3 5 9 . 7 0 B T U / C H R - F T - F )

0 . 2 1 5 1 0.2110

3 . 2 1 1 3 3 . 2 1 2 2

0 . 2 0 4 3 3 . 2 1 0 4

7 6 0 . 0 1 1 0 3 3 . 1 7 U A T T / C M E T E R - K )

0 . 3 7 2 3 0 . 3 6 5 3

0 . 3 6 5 8 0 . 3 6 7 2

3 . 3 5 3 6 0 . 3 6 4 2

1 4 5 0 . 3 0 1 9 0 9 . 7 0 B T W / C H R - F T - F )

3 . 2 1 9 2 0 . 2 1 4 9

0 . 2 1 5 0 0 . 2 1 5 6

0 . 2 0 7 7 0 . 2 1 4 1

7 3 7 . 7 8 1 3 6 0 . 9 4 " A T T / ( : i ZTER-.-C)

v i . 3 7 9 3 0 . 3 7 1 9

' 3 . 3 7 2 2 0 . 3 7 3 4

0 . 3 5 9 5 3 . 3 7 0 5

60


THERMAL CONDUCTIVITY OF HELIUM OO.LP JTFC: J UITH DIFFERENT EQUATIONS

PRESSURE = 7 50 PSIA = 51.0343 HTM = 51.7117 .JAR

T E M P E R A T U R E THERMAL C O N D U C T I V I T Y

DEG F DEC U N I T S OF X

.CI :C4

X2 ::5

X 3 ;c6

DE3 C DEI U N I T S OF X

1 5 0 C . 3 3 19 5 9 • D T U / C H R - F T - F )

7 0 0 . 2 2 3 2 0 . - 2 1 3 7

0 . 2 1 8 7 T) • 2 1 93

0.2110 0.2177

8 1 5 . 5 6 1 0 8 8 , 'TATT/CMETER-X)

7 2 0 . 3 3 6 3 0 . 3 7 3 4

0 . 3 7 8 6 0 . 3 7 9 6

a . 3 6 5 2 0 . 3 7 6 7

1 5 5 0 * 0 0 2 0 0 9 . 7 0 B T U / C K R - F T - F )

8 4 3 . 3 4 1116.50 U A T T / C M E T E R - X )

1 6 3 0 . 3 0 2 0 5 9 . 7 0 B T U / C H R - F T - F )

0 . 2 2 7 2 0 . 2 2 2 4

0 . 3 9 3 2 0 . 3 8 4 9

0 . 2 3 1 1 0.2261

0 . 2 2 2 4 S .2228 0 . 3 3 4 9 0 . 3 3 5 6

0 . 2 2 6 0 0 . 2 2 6 3

0 . 2 1 4 3 0 . 2 2 1 2

0 . 3 7 0 8 3 . 3 3 2 3

0 . 2 . 1 7 5 0 . 2 2 4 7

8 7 1 . 1 2 1 1 4 4 . V A T T / C M E T E R - X )

2 3 0 . 4 3 0 2 0 . 3 9 1 3

0 . 3 9 1 2 3 . 3 9 1 6

0 . 3 7 6 4 3 . 3 3 3 9

1 6 5 3 . 0 0 2 1 0 9 B T U / C H R - F T - F )

. 7 3 0 » 2 3 5 1 0 . 2 2 9 3

0 . 2 2 9 6 3 . 2 2 9 7

3 . 2 2 0 6 3 . 2 2 o l

8 9 8 . 9 3 1 1 7 2 . M A T T / ( M E T E R - X )

06 0 . 4 0 6 8 0 . 3 9 7 7

3 . 3 9 7 4 3 . 3 9 7 5

0 . 3 6 1 6 • 3 . 3 9 4 9

1 7 0 0 . 0 0 2 1 5 9 , B T U / C H R - F T - F )

70 3 . 2 3 9 0 3 . 2 3 3 4

0 . 2 3 3 2 0 . 2 3 3 1

0 . 2 2 3 7 0 . 2 3 1 5

9 2 6 . 6 7 1 1 9 9 , U A T T / C M E T E R - X )

3 3 0 . 4 1 3 6 3 . 4 0 4 0

0 . 4 3 3 6 3 . 4 3 3 4

0 . 3 8 7 2 0 . 4 0 3 7

1 7 5 0 . 0 0 2 2 0 9 B T U / C H R - F T - F )

. 7 0 0 . 2 4 2 6 0 . 2 3 7 3

3 . 2 3 6 7 3 . 2 3 6 4

0 . 2 2 6 7 0 . 2 3 4 9

9 5 4 . 4 5 1 2 2 7 , U A T T / C M E T E R - X )

SI 3 . 4 2 8 3 0 . 4 1 3 2

0 . 4 0 9 7 3 . 4 0 9 2

3 . 3 9 2 4 3 . 4 3 6 5

61


THERMAL CONDUCTIVITY JF HELIUM COMPUTED WITH DIFFERENT EQUATIONS

PRESSURE = 750 PSIA = 51.0343 ATM = 51.7117 JAR


DEG F DEG R UNITS OF X

XI .C4

(? .C 5

X3 :C6

DEG C DE3 K UNITS OF

1300.03 2259.70 BTU/CHR-FT-F)

3 .2467 3 .2435

3.2 43 3 0.2393

3.229 7 3.2332

982.23 1255.39 "ATT/CMETER-X)

0.42 69 0 .4163

0.4153 0.4150

0. 3975 3.4123

18 5-3.00 2 309.7? 9T'J/< HR-FT-F)

0.2535 0 .2441

3.2437 3.2431

0.2326 3.24 1 5

1010.01 1283.17 VATT/CMETER-K)

0 .4335 0.4224

3.4219 3.4233

0.4326 0.4130

1903.00 2359.70 3TV/CHR-FT-F)

0.2543 0 .2475

3.2472 3 .2464

3.2354 0.2447

1037.78 1310.94 V'ATT/CMETER-X)

0 .4431 3.4234

3.4279 3.4265

3 . 43 7 5 0.4236

19 50.00 2409.70 BTU/CHR-FT-F)

0.2531 0.2510

3 .2507 3.2497

3.2332 0.2'I79

1065.56 1333.72 •JATT/C METER-K>

0 .4466 0 .4344

3.433 3 3.4322

3.4123 3.4291

2K?23.00 2459.70 BTU/CHR-FT-F)

0 . 2 6 1 3 0.2544

3 .2541 3.2533

0.2410 0.2511

1093.34 1366.50 UATT/CMETER-K)

0.4531 0.4403

3 .4393 0.4379

3.4171 3.4346

62

Table A.5 THEKIAL CONDUCTIVITY OF HELIUM AT 1 0 0 0 PS IA

T H E R M A L C O M D ' J C T I V I TY OF H E L I ! ' 1 0 JMHU FED V I T H D I F F E R E N T E Q U A T I O N S

R E F E R E N C E L I S T :

K I ; R I S O R E P T 2 2 4 . .;A C O . K 3 ; j . r . S A N D S ^ S * 0 I M L . K 4 ; D . L . MC E L R J Y . , O R M L •-C5J J ' J L I C H , K E P T X F A - I R E - 1 7 / 7 2 . K 6 ; A S H R A E * T H E r t n O P K Y S . r T i O r 1 . j i 9 7 J .

P R E S S U R E = 1 0 0 3 P S I A = 6 3 . 0 4 5 7 A T M = 6 3 . 9 4 9 BA 1


DEG F DEG R U N I T S O F K

K1 rC4 K 5

K 3 x{6

DEG C DEG K U N I T S OK K

5 0 . 0 0 5 0 9 . 7 0 B T U / ( H R - F T - F )

• 3 . 0 3 7 3 3 .3913 0 . 0 3 4 6

0 . 0 9 1 4 0 . 0 3 4 3

1 0 . 0 1 2 8 3 . 1 7 ' J A T T / C M E T E R - K )

0 . 1 5 0 6 0 . 1 5 3 8 0 . 1 4 6 4

0 . 1 5 3 2 0 . 1 4 5 9

1 0 0 . 0 0 5 5 9 . 7 3 3 T U / C H R - F T - F )

2 . 0 9 2 9 0 . 0 9 7 4 0 . 3 9 3 5

0 . C 9 6 4 0 . 0 9 0 1

3 7 . 7 8 3 1 0 . 9 4 T7ATT/C M E T E R - K )

0.1 68 6 0 . 1 5 6 7

0 . 1 6 6 9 0 . 1 5 5 9

1 5 0 . 0 0 6 0 9 . 751 B T U / C H R - F T - F )

3 . 0 9 8 6 (>« 1 0 2 3 0 . 0 9 6 4

0 . 1 0 1 3 0 . 0 9 5 7

6 5 . 5 6 3 3 8 . 7 2 t f A T T / C M E T S R - K )

0 . 1 7 0 7 3 . 1 7 3 0 0.1668

0 . 1 7 5 4 0 . 1 6 5 7

2 0 0 . 0 0 6 5 9 . 7 0 B T U / C H R - F T - F )

3 . 1 0 4 2 3 . 1 0 3 1 0 . 1 0 2 0

0 .10 62 0 . 1 0 1 3

9 3 . 3 4 3 6 6 . 5 0 W T T / C M E T E R - X )

0 . 1 8 3 4 0 . 1 8 7 2 0 . 1 7 6 6

0 . 1 8 3 8 0 . 1 7 5 4

2 5 0 . 0 0 7 0 9 . 7 0 B T ' J / C H R - F T - F )

0 . 1 0 9 7 0 . I 1 3 3 3 . 1 0 7 6

3 . 1 1 1 0 0 . 1 3 6 9

1 2 1 . 1 2 3 9 4 . 2 3 M A T T / C M E T E R - K )

U . 1 3 9 9 3 . 1 9 0 1 3 . 1 3 6 2

: • . 1 9 2 2 0 . 1 3 5 0

63


T H E R M A L C D I . T / J C T I V I T Y OF H E L I U l l COMMUTED u i T : - ; D I F F E ' T M T E T J A T I D

PRESSURE = 1330 ^SIA = 60'157 ATI = 3 3.741? EAT

T E M P E R A T U R E THiRlirtL CQ::J';CTI VI TY

DEG F DEG P. UNITS OF

Kl ;<4

::2 .i5

Ij .16

DEG C DEG K UNITS OF X

3 0 0 . 3 0 7 5 9 . 7 0 B T U / C H R - F T - F )

0 . 1 1 5 1 0 . 1 1 3 4 C . 1 1 3 3

3 . 1 1 5 6 0 . 1 1 2 3

1 4 3 . 9 0 4 2 2 . 0 6 U A T T / C M E T E R - K )

3 . 1 9 9 1 3 . 2 3 4 9 3 . 1 9 5 7

0 . 2 0 0 4 Z.1944

3 5 0 . 0 3 3 0 9 . 7 0 B T U / C H R - F T - F )

3 . 1 2 3 3 0 . 1 2 3 3 0 . 1 1 5 4

3 . 1 2 0 5 3 . 1 1 7 7

1 7 6 . 6 7 4 4 9 . 3 3 UATT/C METER-::)

0 . 2 0 3 2 3 . 2 1 3 4 T . 2 0 4 9

3 . 2 2 3 5 3 . 2 3 3 7

4 0 0 . 0 0 3 5 9 . 7 i ? " 3 T U / C H R - F T - F )

3 . 1 2 5 5 •3. 1 2 8 2 3. 1*36

D . 1 2 5 1 0 . 1 2 3 0

2 0 4 . 4 5 4 7 7 . 6 1 W A T T / C M E T E R - K )

1 . 2 1 7 2 3 . 2 2 1 o 3 . 2 1 4 3

3 . 2 1 6 5 0 . 2 1 2 9

4 5 0 . 0 0 9 0 9 . 7 3 B T U / C H R - F T - F )

3 . 1 3 0 5 3 . 1 3 1 7

Z . 1 3 2 9 3 . 1 2 3 3

3 . 1 2 9 7 3 . 1 2 3 2

2 3 2 . 2 3 5 * 5 . 3 9 ^ A T T / C . M T - . n - K )

0 . 2 2 5 9 ' .2 23/)

3 . 2 3 3 1 i.222 9

0 . 2 2 4 4 a . 2 2 1 9

5 M 0 . 0 0 9 5 9 . 7 - ? B T U / O i R - F T - F )

P . 1 3 5 5 : . 1 3 6 2

'. 1 WK- 1 . 1 3 4 2 133- ' .

2 6 0 . 3 1 5 3 3 . I - 7

"ATT/C METER-:-:) 3 . 2 3 4 5 3 . 2 3 5 3

3. 233 2 J-2317 3 . 2 3 0 3

5 5 R . 3 0 1 0 0 9 . 7 1 3 3 T U / C F T - F )

• 3 . 1 4 3 4 0 . 1 4 3 7

ri • 1 4 2 2 3 . 1 0 0 9

I . 1 3 3 6 ; . 1 3 6 4

2 3 7 . 7 3 5 6 C . 9 4 U A T T / C M . : T E : : - . C )

C . E 4 3 o i <. 4 3 5

W • 2 4 6 1 . 2 '13 3

.2399

6k


J ..JI/JC ri vi" .' F -IEI-IVM

IS-j'll.S = 10'V? *>:;ia .</•*; 5 / .Yi 1 = i . J ?

rZi-i.'Er.ATu'::- r . ' j . > C T I I- ' ITY

DEG F D E I n t j i T S K 9 F .v /<. i;

:ci YM

DEG C DE ' l U N I T S OF X

6 0 P . 0 3 i e . 5 9 . 7 0 3 T ' i / ( H R - F T - F )

t) . 1 •'15 3 3.1451

J . 1 «'i o 7 3 . 1 4 3 3

3 . 1 4 3 C 3 . 1 4 3 3

3 1 5 . 5 3 5 3 3 . 7 2 V A T T / < M E T E R - X )

0.2JI 4 3 . 2 5 1 1

3 . 2 5 3 9 J . 2 4 3 9

3 . 2 4 7 5 0 . 2 4 8 1

6 5 0 . 0 3 1 1 3 9 . 7 0 ! 3 T U / ( M P - - F T - F )

0 . 1 5 3 3 3 . 1 4 9 5

0 . 1 5 1 2 3 . 1 4 3 6

0 . 1 4 7 3 3 . 1 4 3 2

3 4 3 . 3 4 6 1 6 . 5 0 U A T T / ( M E T E R - ; 0

13 . 2 5 9 6 3 • 2 5 8 8

3 . 2 6 1 7 (•J . 2 5 7 3

1L . 2 5 5 0 ^ . 2 5 6 4

7 0 0 . 3 0 1 1 5 9 . 7 3 3 T M / C H R - F T - F )

0 . 1 5 4 7 • J . 1 5 3 9

3 . 1 5 5 6 0 . 1 5 3 4

e ) . 1 5 1 6 0 . 1 5 2 9

3 7 1 . 1 2 • 6 4 4 . 2 3 1 'AT T / ( ; 1 E T E R - X )

0 . 2 6 7 3 0 . 2 6 6 3

C . 2 6 9 2 3 . 2 6 5 5

0 . 2 6 2 4 0 . 2 6 4 6

7 5 0 . 0 0 1 2 3 9 . 7 0 H T U / C H R - F T - F )

0 . 1594 •3.1532

Z . 1 5 9 9 0.1501

0 . 1 5 5 3 0 . 1 5 7 5

3 9 8 . 9 0 6 7 2 . 0 . " A T T / C M Z T Z R - X )

3 . 2 7 5 8 2 . 2 7 3 d

• 3 . 2 7 6 7 G . 2 7 3 7

2 . 2 6 9 7 0 . 2 7 2 6

3 0 0 . 0 0 1 2 5 9 . 7 0 B T U / ( H R - F T - F )

3 . 1 6 3 9 0 . 1 6 2 5

3 . 1 6 4 2 3 . 1 3 2 3

W . 1 6 3 3 0 . 1 62 .3

4 2 6 . 6 7 6 9 9 . 3 3 7 A T T / { M E T E R - K )

3 . 2 3 3 3 •3 . 2 3 1 2

0 . 2 3 4 1 0.26 1 7

3 . 2 7 6 9 3 . 2 3 3 4

8 5 0 . 0 0 1 3 t n . 7 U 3 T U / C H R - F T - F )

3 . 1 6 3 5 '3 . 1 6 6 7

•3 . 1 6 8 4 •3 . 1 6 7 3

0 . 1 6 4 3 3 . 1 6 6 5

4 5 4 . 4 5 7 2 7 . 6 1 ' ' A T T / ( M ET E\ i - K >

3 . 2 9 1 6 0 . 2iib 6

0 . 2 9 1 4 3 . 2 3 9 6

L i . 2 3 3 9 0 . 2 8 3 1

65


T H E R M A L C O N D U C T I V I T Y OF H E L I U M C O M P U T E D U l T H D I F F E R E N T E Q U A T I O N S

P R E S S U R E = 1 0 0 0 P S I A = 6 3 . 3 4 5 7 A T M = 6 8 - 9 4 9 3A»

T E M P E R A T U R E T H E R M A L COU J ' . 'CT I V I T Y

DEG F DEG R U N I T S OF X

1U K 4 X 5

K 3 X 6

DEG C U N I T S OF

DEG :I

9 0 0 . 0 0 1 3 5 9 . 7 3 B T U / C H R - F T - F )

0 . 1 7 3 0 0 . 1 7 1 0

3 . 1 7 2 5 0 . 1 7 1 3

0 . 1 6 3 1 0 . 1 7 0 3

4 8 2 . 2 3 7 5 5 . 3 9 U A T T / C M E T E R - K )

3 . 2 9 9 3 0 . 2 9 5 9

0 . 2 9 3 6 0 . 2 9 7 3

0 . 2 9 0 9 0 . 2 9 5 6

9 5 0 . 0 0 1 4 0 9 . 7 0 B T U / C H R - F T - F )

0 . 1 7 7 4 0 . 1 7 5 2

0 . 1 7 6 7 0 . 1 7 6 2

0 . 1 7 2 3 0 . 1 7 5 1

5 1 0 . 0 1 7 8 3 . 1 7 U A T T / C M E T E R - K )

0 . 3 3 7 0 0 . 3 0 3 1

0 . 3 ® 5 7 3 . 3 0 5 3

0 . 2 9 7 8 0 . 3 3 3 0

1 0 0 0 . 0 0 1 4 5 9 . 7 0 3 T U / C H R - F T - F )

0 . 1 3 1 3 3 . 1 7 9 3

3 . 1 8 0 7 0 . 1 3 0 5

0 . 1 7 5 9 3 . 1 7 9 3

5 3 7 . 7 8 8 1 0 . 9 4 U A T T / C M E T E R - X )

0 . 3 1 4 6 3 . 3 1 0 3

3 . 3 1 2 3 •3.3125

3 . 3 0 4 5 3 . 3 1 0 3

1 0 5 0 . 0 0 1 5 3 9 . 7 0 B T U / C H R - F T - F )

0 . 1 3 6 1 3 . 1 3 3 4

3 . 1 8 4 7 .? . 13 4 3

0 . 1 7 9 8 3 . 1 3 3 4

5 6 5 . 5 6 3 3 3 . 7 2 U A T T / C M E T E R - X )

3 . 3 2 2 1 0 . 3 1 7 4

•3.3197 3 . 3 1 9 3

3 . 3 1 1 2 0 . 3 1 7 4

1 1 0 0 . 0 0 1 5 5 9 . 7 3 BTU/ 'C W R - F T - F )

i ) . 1 9 3 4 3 . 1 3 7 5 0 . 1 3 3 9

0 . 1 3 3 6 3 . 18 7 5

5 9 3 . 3 4 j m o . 5 ; T A T T / C M E T E R - X )

fi.3295 0 . 3 2 4 5

w . 32 6.'i 0 . 3 2 7;*/

0 . 3 1 7 7 0 . 3 2 4 4

1 1 5 0 . 0 0 1 6 3 9 . 7 i-i 3 T U / C H R - F T - F )

0 . 1 9 4 7 0 . 1 9 1 5

3 . 1 9 2 7 1 9 3w

. 1 3 7 3 tf . 1 ? 1 4

6 ^ 1 . I f ! 3 9 4 . 2 3 U A T T / C i E T E R - X )

0 . 3 3 6 9 0 . 3 3 1 5

3 . 3 3 3 4 3 . 3 3 4 1

. 3 2 4 2 < 5 . 3 3 1 3

66


THI:::.:.\L C T J D O C T I V N - R OF H E L I U M CO.!.,,.,TEO • '1 TH DI F F E R E N ? E- i ' JAT I 0 J '"">

= 1 -J 3 J P S I r i = 6 3 . . : '15 7 . i T . l - O > ' .

TEiiPs.iATa.'i: THi . - ; . lAL C 0 . i i) JU r i VI TY

D E I F DEG U N I T S OF :C ;;4

:-:3

DE'-l C DEO U N I T S OF :C

1 2 0 3 . 0 0 1 6 5 9 . 7 3 B T U / C H R - F T - F )

3 . 1 9 3 9 0 . 1 9 5 5

.j . 1 9 6 6 ' 0 . 1 9 7 0

0 . 1 9 1 3 O . 1 9 5 4

6 4 8 . 9 0 9 2 2 . 0 6 uATT/criETEP.-;:)

0 . 3 4 4 2 0 . 3 3 3 4

3 . 3 4 0 2 0 . 3 4 1 0

0 . 3 3 0 5 Z . 3 3 8 I

1 2 5 0 . 0 0 1 7 0 9 . 7 0 B T U / C H R - F T - F )

3 . 2 0 3 3 0 . 1 9 9 5

3 . 2 3 0 4 a . 2 0 0 9

0 . 1 9 4 6 0 . 1 9 9 2

6 7 6 . 6 7 9 4 9 . B 3 V A T T / C M E T E R - K )

0 . 3 5 1 4 3 . 3 4 5 3

3 . 3 4 q 9 3 . 3 4 7 7

3 . 3 3 6 3 3 . 3 4 4 3

1 3 6 ) 3 . 0 3 1 7 5 9 . 7 0 B T U / C H R - F T - F )

3 . 2 0 7 2 0 . 2 3 3 4

•j . 2 3 4 2 0 . 2 3 4 7

0 . 1 9 3 1 0 . 2 0 3 0

7 0 4 . 4 5 9 7 7 . 6 1 U A T T / C . ' I E T E K - K )

0 . 3 5 3 6 0.3521

0 . 3 5 3 5 3 . 3 5 4 4

0 . 3 4 2 9 0 . 3 5 1 4

1 3 5 0 . 0 0 1 8 0 9 . 7 0 B T U / C H R - F T - F )

3 . 2 1 1 3 0 . 2 0 7 3

0 . 2 0 8 0 J . 2 3 J 5

• 3 . 2 3 1 6 0 . 2 0 6 3

7 3 2 . 2 3 1 0 0 5 . 3 9 ' . . 'ATT/CMETER-: -C)

3 . 3 6 5 7 •3 . 3 5 8 8

0 . 3 6 3 0 3 . 3 6 0 3

0 . 3 4 3 9 0 . 3 5 7 3

1 4 0 0 . 0 0 1 8 5 9 . 7 0 3 T U / C H R - F T - F )

0 . 2 1 5 4 0.21 12

3 . 2 1 1 3 0.2122

3 . 2 2 5 0 0 . 2 1 0 4

7 6 0 . 0 1 1 0 3 3 . 1 7 T A T T / C I I E T E R - X )

0 . 3 7 2 7 0 . 3 6 5 5

3 . 3 6 6 5 3 . 3 6 7 2

0 . 3 5 4 9 0 . 3 6 4 2

1 4 5 0 . 0 0 1 9 0 9 . 7 0 B T U / C H R - F T - F )

? . 21 9 'l 3 . 2 1 5 5 3 . 2 1 5 3

0 . 2 3 8 4 0 . 2 1 4 1

7 8 7 . 7 S 1 0 6 3 . 9 4 t r A T T / C H Z T E : ! - ! ' )

PI. 3 7 9 7 3 . 3 7 2 1

3 . 3 7 3 3 0 . 3 7 3 4

0 . 3 6 0 7 0 . 3 7 a 5

67


THERMAL CONDUCTIVITY OF HZLI JM COMMUTED "ITH DIFFERENT EQUATIONS

PRESSURE = 1 300 PSIA = 53.0457 AT."! = 63.949 JAM

TEMPERATURE THERMAL COL'DUCTI VI TY

DEG F DEG UNITS OF

R lil iC4

i \ 2 5

!'3 :i6

DEG C DEG UNITS OF

1500.00 1959 BTU/CHR-FT-F)

70 0.2234 0 .2188

0.2192 0.2193

0.2117 0.2177

815.56 1088 I UATT/C METER-ID

S.3867 0.3786

0.3 793 3.3796

0.3664 3.3767

1550.00 2009.70 BTU/CHR-FT-F)

0.2274 0.2225

0.2223 0.2228

0.2149 0.2212

843.34 1116. 'ATT/CMETER-K)

50 3.3935 0.3351

0.3857 0.3356

3.3720 3.3828

1600.00 20 59 , DTU/CHR-FT-F)

70 0.2313 0 . 2 2 6 2

3.2265 0.2263

3.2181 0.2247

871.12 1144.28 VATT/CMETER-JO

1650.00 2109.70 BTU/CHR-FT-F)

0.4304 0.3915

3.2352 0.2299

0.3919 0.3916

3.2301 0.2297

3.3775 0.3339

0.2213 0 . 2 2 8 1

393.9? 1172 "ATT/CMETER-IC )

.06 0.407 1 0.3973

•*.39>32 ?.39 75

0.3329 3.3949

1700.00 2159. BTU/CHR-FT-F)

70 3.2 35 1 ?.2335

0 .2336 3 . 2 3 3 1

3.2243 ".2313

926.67 1199 UATT/CMETER-K)

3 0.4139 3 . 4fc>4 1

.4344 0 . 4 0 34

3.333 2 B .43 R> 7

17 50.03 2209 J T ' J / C F T - F )

.7 0 3.243 : 3.2 371

•:) . 2 3 7 2 3. r.36

II. 227 3 U.2349

954.45 1227 "ATT/CM :T".R- ,C)

.2399 41 >3

3 . 4 1 r. 5 . - . 4 3 . 1 P

LI. 3934 •. 65

68


7HZ. "1"»L . C i J i i : ) t I C . T I " , : l T Y i ^ i ' ! : ' J ) ! 3 !

" I T - r - I r r ERUMT v " v i

P R E S S U R E = l o u e P S I A = 6 3 . 3 4 5 7 A T : ; = 6C. . 9 4 9 i

TEMP ZRATURE T H E R M A L C O N D U C T I V I T Y

DEG F DEG UNITS OF ;;

K1 K 4

K 3 :c6

OEG C U N I T S OF

D Z o K

1 8 0 3 . 0 0 2 2 59 3 T U / C H H - F T - F )

. 7 0 3 . 2 4 6 3 3 '. :

3 . 2 4 3 7 3 . 2 3 3 3 . " • . 2 3 3 2

9 8 2 . 2 3 1 2 5 5 . UATT/CNETER-:O

3 9 0 . 4 2 7 2 .41

'J . 41 c 6 ~ . 1 5 rj

3 . 3 9 3 5 0 . 4 1 2 3

13 5 3 . ' 3 0 2 3 3 9 3 T U / C H R - F T - F )

. 7 3 C . 2 5 C 6 0 . 2 4 4 2

0.2442 3.2431

0 . 2 3 3 2 3 . 2 4 1 5

1 0 1 0 . 0 1 1 2 0 3 VATT/CMETE^-IO

. I 7 0 . 4 3 3 3 "3 . 4 2 2 6

J . 4 2 2 6 • '< . 4 2 6 3

0 . 4 3 3 5 0.413v:

1 9 0 3 . 3 0 2 3 5 9 , B T U / C H R - F T - F )

7 3 £ . 2 5 4 4 3 . 2 4 7 6

3 . 2 4 7 7 3 . 2 4 6 4

0 . 2 3 6 3 •3 . 2 4 4 7

1 0 3 7 . 7 8 1 3 1 3 UATT/CMETSR-IO

. 9 4 0 . 4 4 3 4 0 . 4 2 8 6

3 . 4 2 3 6 0 . 4 ^ 6 5

3 . 4 3 3 4 0 . 4 2 3 6

1 9 5 0 . 0 0 2 4 3 9 , B T U / C H R - F T - F )

7 0 0 . 2 5 8 2 0 . 2 5 1 1

3 . 2 5 1 1 3 . 2 4 9 7

0 . 2 3 3 7 0 . 2 4 79

1 3 6 5 . 5 6 1 3 3 8 ' • ' A T T / C M E T E R - i O

. 7 2 0 . 4 4 6 9 3 . 4 J 4 o

3 . 4 3 4 6 3 . 4 3 2 2

3 . 4 1 3 2 ' 3 . 4 2 9 1

2 0 0 0 . 0 0 2 4 5 9 B T U / C H P - F T - F )

• 7W £ . 2 6 1 9 J . 2 5 4 3

3 . 2 5 4 3 . 2 5 3 C

li: . 2 4 1 4 3 . 2 5 1 1

1 0 9 3 . 3 4 1 3 6 6 , •.'ATT/CMETER-IO

5 0 C . 4 5 3 3 3 . 4 4 3 4

3 . 4 4k? 5 3 . 4 3 7 9

3 . 4 1 7 9 0 . 4 3 4 6

69

Table A.5 THER'IAL CONDUCTIVITY OF HELIUM AT 1500 PSIA

THERMAL CO-A/JCTI V1TY OF HELI JM COMPUT '.-J ••IITH DIFFERENT EO.JATI0W3

REFERENCE LIST:

XI; RL SO R£PT 224. X2; OA CO. X3J J.P. SANDERS* ORNL. X4JD.L. MC ELROY* 3RNL :C5; JUL I CH* REPT XFA-IRE- 1 7/72 . KO; ASHRAE* THERMOPHYS. PROP.*1973.

PRESSURE = 1530 PSIA = 102.069 ATM = 133.423 3AR



XI X 4 X 5

X 3 X 6

DEG C DEG X UNITS OF X

50.00 509.70 BTU/CHR-FT-F)

10.01 283.17 UATT/CMETER-X)

100.00 559.70 BTU/CHR-FT-F)


150.00 609.70 BTU/CHR-FT-F)


200.00 659.70 BTU/CHR-FT-F)


250.00 709.70 BTU/CHR-FT-F)

121.12 394.28 UATT/CMETER-X)

0.0377

0.1517

0 .0936

0.1619

0.0993

0.1719

0.1049

0 . 1 8 1 6

0.1104

0.1913

0.0925 0.0846

0 . 1 6 0 0 0.1464

0.0981 0.0905

0.169 7 3. 1-567

0.1035 0 .3964

0.1792 0 . 1 6 6 3

0 .1083 3. IE20

3.1383 0.1766

3 . 1 1 43 0 .1076

3. 19 73 3.1362

3.0917 0.0343

0.1583 3.1459

0.0968 0.0901

0.1675 0.1559

0.1017 0.0957

3.1760 0. 1657

0 . 1 0 6 6 0.1013

0.1345 0.1754

0.1115 3.1069

0.1929 0.1350

70


THERMAL CONDUCTIVITY OF HELIUM COMPUTED VITH DIFFERENT EQUATIONS

PRESSURE = 1500 PSIA = 102.069 ATM = 103.423 IIAR

TEMPERATURE

DE3 F DEG UNITS OF K

DEG C DEG UNITS OF X

;u K4

THERMAL CONDUCTIVITY

K 2 ;<5

K 3 iv6

300.00 759.70 BTU/CHR-FT-F)

148.90 422.06 UATT/CMETER-K)

350.00 309.70 BTU/CHR-FT-F)

176.67 449.83 WATT/(METER-K)

400.00 359.70 BTU/CHR-FT-F)

204.45 477.51 WATT/CMETER-K)

450.00 909.70 BTU/CHR-FT-F)

232.23 505.39 VATT/C METER-JO

500.00 959.70 BTU/CHR-FT-F)

260.01 533-17 UATT/CMETER-K)

553.30 1339.73 BTU/CHR-FT-F)

237.73 560.94 UATT/C METE T-K)

0. 1 157

3.2003

0 . 1 2 1 0

0.2094

0.1261

3.2183

0.1312 0.1323

3.2270 0.2290

0.1361 0.1368

3.2356 0.2367

0.1410 3.1412

3.2441 0.2444

0.1191 0 . 1 1 3 1

0 . 2 0 6 1 0. 19 57

0.1240 0.1134

0.2146 0.2049

0.1289 0.1236

0.2230 0 . 2 1 40

0. 1336 0.1238

3-2313 0.2229

3.133 3 0 . 1 3 3 9

0.2393 0.2317

0.1429 3.1339

0.2473 0.2404

O . 1 1 6 2 0.1123

0.2012 0.1944

0. 1209 0.I 177

0.2093 0.2037

0.1256 0.1230

0.2174 0.2129

0.1332 0.1232

0.2253 0.2219

0.1347 0.1334

Q.2 332 0.2308

0.1392 0.1334

3.2409 0.2396

71


T H E R M A L COtJD'JOTI VIT t OF HZLl'J.I JOMP'JTZJ '..'ITH IJI r'F £ i-.1T VJJATIO.'J

PRESSURE = 1513(5 P S I A = 1 3 2 . 0 6 9 AT:: = 1 3 3 . 4 2 3 3A' :

T E M P E R A T U R E THERMAL CO.MD'JCTI V I TV

DEG F DEG R U N I T S OF K X4

:I 3 K 6

DE'3 C DEG K U N I T S OF K

630.00 10 59.70 3TU/C H R - F T - F )

0 .1456 0 . 1456

3 .1474 •3. 1433

0.1436 0. 1433

3 1 5 . 5 6 588.72 W A T T / ( M E T E R - K )

0.2524 0 .2520

0.2551 0.2489

3.2485 0.2481

650.00 1109.70 B T U / C H R - F T - F )

0.150 6 0.1500

0.1519 3.148 6

0.1479 0. 1482

3 4 3 . 3 4 616.50 '/ATT/C M E T E R - K )

0 . 2 6 3 7 0 . 2 5 9 6

3.2628 0.2573

0.2560 0 . 2 5 6 4

700.00 1159.70 B T U / C H R - F T - F )

0.1553 0.1543

0.1563 0 . 1 5 3 4

0. 1522 0.1529

371.12 644.28 U A T T / C M E T E R - K )

0.2 688 0.2671

0 . 2 7 0 4 0.2655

0 . 2 6 3 4 0.2646

750.00 1209.70 B T U / C H R - F T - F )

0.1599 0.1586

0.1606 0 . 1 58 1

0. 1564 0.1575

398.90 672.06 U A T T / C M E T E R - K )

0.2768 0.2745

0.2779 0.2737

0 . 2 7 0 7 0.2726

8 0 0 . 0 0 1259.70 B T U / C H R - F T - F )

0.1645 0.1629

0.1649 0.1623

0.1606 0.1620

426.67 699.83 T/ATT/C M E T E R - K )

0.2847 0.2819

0.2853 0.281 7

0.2779 0.2804

8 5 0 - 0 0 1309.70 3 T H / C H R - F T - F )

3.1690 0.1671

0.1691 3. 1673

0 . 1 64 7 0.1665

4 5 4 . 4 5 727.61 W A T T / C M E T E R - K )

0.2925 0.289 3

3.2926 0.2396

0 .2350 0.2881

72


T H E R M A L c o n d u c t i v i t y OF H E L I ' T M COMP'"""-:^ W I T H D I F F E R E N T E 1 UAT I O N S

P R E S S U R E = 1 5 3 0 P S I A = 1 0 2 . 0 6 9 AT M = l f 0 3 . 4 2 3 3i\~l

T E M P E R A T U R E THER1AL C O N D U C T I V I T Y

DEG F DEG U N I T S OF I ;

R iCl K 4

X3 Kr>

DEG c DEG :: U N I T S OF :c

9 0 0 . 0 0 1 3 5 9 . 7 0 3TU/C H R - F T - F )

4 3 2 . 2 3 7 5 5 . 3 9 U A T T / C M E T E R - K )

9 5 0 . 0 0 1 4 0 9 . 7 0 3 T U / C H R - F T - F )

5 1 0 . 0 1 7 3 3 . 1 7 U A T T / C M E T E R - K )

1 0 0 0 . 0 0 1 4 5 9 . 7 0 3 T U / C H R - F T - F )

5 3 7 . 7 3 S I P . 9 4 U A T T / C M E T E R - X )

1 0 5 0 . 0 0 1 5 0 9 . 7 0 3 T U / C H R - F T - F )

5 6 5 . 5 6 8 3 6 . 7 2 "ATT/C M E T E R - K )

1 1 0 0 . 0 0 1 5 5 9 . 7 0 B T U / C H R - F T - F )

5 9 3 . 3 4 3 6 6 . 5 0 V A T T / C M E T E P - X )

1 1 5 0 . 3 ? 1 6 0 9 . 7 0 3 T U / C H R - F T - F )

6 2 1 . 1 2 3 9 4 . 2 3 * TATT/CMETEP-X)

0 . 1 7 3 5 0 . 1 7 1 3

0 . 3 0 0 2 O . 2 9 6 5

0 . 1 7 7 9 O . 1 7 5 5

O . 3 0 7 S 0 . 3 3 3 7

0. 1822 0 . 1 7 9 6

3 . 3 1 5 4 3 . 3 1 0 9

3 . 1 fa 3 . 1 6 3 7

3 . 3 2 2 9 3 . 3 1 3 3

3 . 1 9 0 8 3 . 1 3 7 8

3 . 3 3 3 3 3 . 3 2 5 3

3.1951 3.1913

3 . 3 3 7 b 3 . 33c ! t J

0 . 1 7 3 2 3 . 1 7 1 3

3 . 2 9 9 8 0 . 2 9 7 3

CI. 1 7 7 3 3 . 1 7 6 2

0 . 3 3 6 9 3 . 3 0 5 3

.1314 3.1335

? . 3 1 VJ

M . 1 3 5 4 3 . 1 3 4 3

3 . 3 2 3 9 0.3196

3 . 1 3 9 4 3 . 1 3 3 9

.3273

. 3 2 7 3

. 1 9 3 3 0 . 1 9 3 0

3 . 3 3 4 6 ' 3 . 3 3 4 1

0.I 6b7 2 . 1 7 0 3

3 . 2 9 2 0 3 . 2 9 5 6

3 . 1 7 2 7 0.1751

0 . 2 9 8 9 0 . 3 0 3 0

0 . 1 7 6 6 0 . 1 7 9 3

0 . 3 3 5 6 0 . 3 1 0 3

y . 1 3 3 4 3 . 1 3 3 4

0 . 3 1 2 3 2 . 3 1 7 4

0 . 1 3 4 2 0 . I c i 7 5

0 . 3 1 3 3 C . 3 2 4 4

0 . 1 3 7 9 3 . 1 9 1 4

3 . 3 2 5 3 . 3 3 1 3

73


~ A S I u i A L C O N D U C T I V I T Y J ; - i Z L I U . l CJ.l.' ''it V I TH D I r T - ' . Z N T 1AT I U i u

P i K S ^ r . Z = 1 5 0 0 P S I A = 1 . i T ; = 1 H 3 . 4 2 3 3 A . .

T E M P E R A T U R E r i Z R M a L C 3 J . ' S ' C T I V I "

D E u F DEG R U N I T S OF I t

XI X4 X 3

.C3

DEG C DEG U N I T S OF it

1 2 0 3 . 0 0 1 6 5 9 . 7 0 B T U / C H P . - F T - F )

U . 1 9 9 2 0 . 1 9 5 8

3.1972 3.1973

3 . 1 9 1 6 3 . 1 9 5 4

6 4 8 . 9 0 9 2 2 . 3 6 V A T T / C M E T E R - K )

3 . 3 4 4 8 0 . 3 3 8 9

3 . 3 4 1 4 G . 3 4 1 3

0 . 3 3 1 6 3 . 3 3 8 1

1 2 5 0 . 0 0 1 7 0 9 . 7 0 B T U / C H R - F T - F )

0 . 2 3 3 4 0 . 1 9 9 8

G . 2 0 1 1 0 . 2 3 0 9

3 . 1 9 5 2 0 . 1 9 9 2

6 7 6 . 6 7 9 4 9 . 8 3 U A T T / C I 1 E T E R - K )

0 . 3 5 2 0 0 . 3 4 5 8

0 . 3 4 8 3 0 . 3 4 7 7

0 . 3 3 7 8 0 . 3 4 4 3

1 3 0 0 . 0 0 1 7 5 9 . 7 0 B T U / C H R - F T - F )

3 . 2 0 7 5 0 . 2 3 3 7

G . 2 0 4 9 0 . 2 0 4 7

0 . 1 9 8 7 0 . 2 0 3 0

7 0 4 . 4 5 9 7 7 . 6 1 U A T T / C M E T E R - K )

0 . 3 5 9 2 0 . 3 5 2 5

0 . 3 5 4 7 0 . 3 5 4 4

0 . 3 4 3 9 0 . 3 5 1 4

1 3 5 0 . 0 0 1 8 0 9 . 7 3 B T U / C H R - F T - F )

3 . 2 1 1 6 0 . 2 0 7 6

3 . 2 3 3 7 3 . 2 - 3 3 5

0.2022 0 . 2 3 6 8

7 3 2 . 2 3 1 0 0 5 . 3 9 V A T T / C M E T E R - K )

3 . 3 6 6 2 0 . 3 5 9 3

0 . 3 6 1 2 3 . 3 6 0 8

3 . 3 5 3 0 0 . 3 5 7 8

1 4 0 0 . 0 0 1 3 5 9 . 7 0 B T U / C H R - F T - F )

0 . 2 1 5 6 W . 2 1 1 4

0 . 2 1 2 5 3 . 2 1 2 2

0 . 2 0 5 6 0 . 2 1 0 4

7 6 0 . 0 1 1 0 3 3 . 1 7 V A T T / C M E T E R - X )

0 . 3 7 3 2 3 . 3 6 5 9

0 . 3 6 7 7 0 . 3 6 7 Z

0 . 3 5 5 9 0 . 3 6 4 2

1 4 5 0 . 0 0 1 9 0 9 . 7 0 B T U / C H R - F T - F )

3 . 2 1 9 7 0 . 2 1 5 2

0.2162 0.2158

0 . 2 0 9 0 0 . 2 1 4 1

7 3 7 . 7 8 1 0 6 0 . 9 4 V A T T / C M E T S R - K )

0 . 3 8 0 2 0 . 3 7 2 5

3 . 3 7 4 1 3 . 3 7 3 4

3 . 3 6 1 7 0 . 3 7 0 5

7h

Table t\.6 (Continued)

THERMAL CONDUCTIVITY OF HELIUM CO/IP'JTED VJITH DIFFERENT EQUATIONS



DEG F DEG R UNITS OF IC

K1 K4

X 2 K5

X 3 K 6

DEG C DEG X UNITS OF K

1500.00 1959.70 BTU/CHR-FT-F)

0 .2236 0.2190

0.2199 3.2193

0.2122 0.2177

815.56 1088.72 UATT/CI1ETER-K)

0.3871 0 .3793

0.380 5 0.3796

0.3673 Q.3767

1550.00 2009.70 BTU/CHR-FT-F)

0.2276 0 .2227

0 .2235 0.2228

0.2155 0.2212

843.34 1116.53 UATT/CMETER-K)

0.3939 0 .3355

0.38 69 0.33 56

0.3729 0.3828

1600.00 2059.70 BTU/CHR-FT-F)

0.2315 0.22 64

3.2271 0.2263

0 . 2 1 8 6 0.224 7

871 .12. 1 144.23 UATT/CMETER-K)

0.4007 3 . 3 9 1 9

3.3931 0.3916

0.3784 0.3339

1650.00 2 109.72 BTU/CHR-FT-F)

0 .2354 0.2301

0.23 3 7 0.2297

0.2217 0.2281

898.90 1172.06 • FATT/C METER-K 5

O.4374 S .3932

0.3994 0.3975

0.3333 0.3949

1700.00 2159.70 BTU/CHR-FT-F)

3.2393 0.2343 3.2331

3.2248 0.2315

926.67 1199.33 '•TATT/C METER-K)

0.4141 0.4345

0C40 55 0.4034

0.3890 0.4307

1750.00 2209.73 BTU/CHR-FT-F)

0.2431 0.2373

0.2379 3.236 5

0.2277 0.2349

954.45 1227.61 '/ATT/C METER-K)

0.42O3 0.4107

3.4117 0.4092

0.3942 £.4065

75

Table -\.6 (Continued)

T H E R M A L CONDUCTIVITY OF HELIUM C O M M U T E 0 VI TH DIFFERENT E J U A T I O N :

P R E S S U R E = 1530 POIA = LU2.E)JW ATM = 133.423 JAR

T EM :J E RA T! .-T E

DEG R DEG F U N I T S o r

T.IE ;M; :JUJTIV1TY

K1 (4 i t s

;c3

DSG C DEG ;•: UNITS OF X

1800.03 2 2 5 9 . 7 0 B T U / C H R - F T - F )

0.24 69 IL .2403

0.2414 0.2393

0.2307 0.2382

9 8 2 . 2 3 1255.39 U A T T / C M E T E R - K )

3.42 74 3 . 4 1 6 a

3.4173 3.41 5«J

3.3992 0.4123

1850.30 2309.73 BT'J/CHR-FT-F)

3.2507 0 .2444

0.2449 Z.2431

3.2335 3 . 2 4 1 5

1010.01 1233.17 U A T T / ( M E T E R - K )

3.4339 0 .4229

3.4233 0.4208

3.4U42 0.4133

1903.00 2359.70 3 T U / C H R - F T - F )

3.2545 3.2476

3.2483 3.2464

0.2363 0.2447

1037.73 1310.94 U A T T / ( M E T E R - K )

3 . 4 4 0 4 0 .4239

3.4293 3.4265

0.4090 0.4236

1950.00 2409.73 3 T U / C U R - F T - F )

0.2532 0.2513

3.2518 3.2497

3.2390 0.2479

1065.56 133S.72 U A T T / C M E T E R - K )

3.44 69 0.4349

3.4353 3.4322

0 . 4 1 3 7 0.4291

2003.00 2459.7 0 B T U / C H R - F T - F )

0.2619 3 .254 7

0.2552 0.2530

3.2417 0 . 2 5 1 1

1093.34 1366.50 U A T T / C M E T E R - K )

3.4533 0.4407

0 . 4 4 1 7 0.4379

3 . 4 1 8 3 0.434 6

76

Table A.7

THERMAL CONDUCTIVITY OF .P.MI! AT 2000 PSIA

THERMAL C O N D U C T I V I T Y OP . i E L l U M COMPUTED ' T I T H D IFFERENT EQUATIONS

REFERENCE L I S T :

.'Ci; R I S C RE?T 2 2 4 . X2J 3A CO. : ; 3 ; J . P . SANDERS* 0RN_ • X4J D . L . MC ELH3Y* ORNL K5J J ' J L I C H * REPT X F A - I U E - 1 7 / 7 2 . X 6 ; ASHRAE* THEHMOPUYS• P R O P - * 1 9 7 3 .

PRESSURE = 2030 P3I« = 136-091 ATM = 137.393 i iAR

T E M P E R A T U R E THERMAL C O N D U C T I V I T Y

DEI F DEG P. UNITS OF X

DEG c DEG x UNITS OF x

50.00 509.70 3 T U / C H R - F T - F )

10.01 283.17 V A T T / C M E T E R -X )

100.00 559.70 B T U / f H R - F T - F )

37.78 310.94 UATT/C METER-.'C)

150.00 609.70 3 T U / C H R - F T - F )

65.56 333.72 ' ! A T T / ( M E T E R - K >

200.00 659.70 3TU/C H R - F T - F )

93.34 366.50 *'ATT/(METER-X )

250.00 709.70 3TU/C H R - F T - F )

121.12 394.23 U A T T/CMETER-K)

XI X4

0.0382

0. 1527

0.3941

0.1629

0.0999

0.1728

3 .1354

0. 1 325

'3 . 1 109

3.1919

X 5

0.0933 0.0346

3.1609 0 . 1 4 6 4

0 . 0 9 8 6 0.0905

0.1707 3 . 1 56 7

0.1041 0 .0964

3.1301 0.1663

0 . I 09 4 0.1£520

3.139 3 3.1766

3 . 1 1 4 5 3 . 1376

3. 1932 3 . 1 3 6 2

K3 K6

0.0920 3.3843

0. 1 59 3 0.1459

3.0971 0.0901

0. 1633 0.1559

0.132 1 3.0957

3 . 1 7 6 7 0.1657

3.1070 3.1013

3.1852 0.1754

3.1119 3.1369

3.1936 3.1353

77


T.TZRMAL C J.-'DUCT I TY OF HELIUM COMPUTED '.'I TH DIFFERENT EAUATIO.03

P R E S S U R E = 2033 PSIA = 136.39 1 iiT '. = 137.193 3mR


DEG F DEG R •INITS OF

Al :C4

2 5

C3 M6

DEI C DEG K UNITS OF K

300.00 759.70 3TU/C H R - F T - F )

0.1162 0.1196 0.1131

0.1167 0. 1 123

145.90 422.06 'JATT/C MSTER-X )

0 .2012 J.2073 3.1957

0.2019 3.1944

350.00 339.70 BTU/C HR-FT-F)

0.1215 3.1245 . 1 1 3 4

3.1214 3.1177

176.67 449.83 ''ATT/C M E T E R - K )

0.2102 3.2155 . 2 349 3.2337

400.00 359.70 3TTJ/C HR-FT-F)

3. 12 66 3. 1294 3. 1236

0 , 2 2 6 1 0. 1230

204.45 477.61 '7ATT/< M E T E R - K )

0.2191 3.22 39 3.2140

0 . 2 1 8 2 3.2129

450.03 909.70 3T'J/C HR- FT-F)

3.1316 0.1329

0. 1341 3.1238

3. 133 7 C .1232

232.23 505.39 VATT/C METER-X )

0 .2273 3.2330

3.2322 3.2229

3.2262 3.2219

530.00 9 5 9 . 7 0 B T U / C H R - F T - F )

3.13 66 J. 1373

3 . 1333 3.1339

1353 3.1334

260.01 533.17 "T AT T/C M ETZR-K)

3.23 64 A .2377

3.240 3 -1.231 7

3.234 1

550C03 1339.70 BT'J/CHP-FT-F)

3.1415 3.1417

3. 1434 3. 1 33 9

.1397

. 1 3 3 '1

287.78 563.94 ;7ATT/CMETER-;C>

3.2443 3 .2453

4.2432 3.2 <' i 'i

3.2419 3.239 6

78


THERMAL C O N D U C T I V I T Y Of" H E L I U M COMPUTED V I TH D I F F E R E N T E Q U A T I O N S

PRESSURE = 2 0 3 0 P S I A = 1 3 6 . 0 9 1 ATM = 1 3 7 . 3 9 4 dAR

TEMPERATURE THERMAL C O N D U C T I V I T Y

DEG F DEG R U N I T S OF it

i t l K'J K 5

IC3 K 6

DEG C DEG K U N I T S OF i<

6 0 0 . 0 0 1 0 5 9 . 7 3 B T U / C H R - F T - F )

3 . 1 4 6 3 3.1461

3 . 1 4 7 9 3 . 1 4 3 8

0 . 1 4 4 2 0 . 1 4 3 3

3 1 5 . 5 6 5 S 8 . 7 2 V A T T / C M E T E R - i t )

3 . 2 5 3 2 0 . 2 5 2 9

3 • 2 5 6 1 0 . 2 4 3 9

0 . 2 4 9 5 0 . 2 4 8 1

6 5 0 . 0 0 1 1 0 9 . 7 0 BTU/CHR-FT-F)

0 . 1 5 1 0 3 . I 5 3 5

0 . 1 5 2 4 ' 3 . 1 4 8 6

3 . 148 5 0 . 1 4 8 2

3 4 3 . 3 4 6 1 6 . 5 0 V A T T / C M 2 T E R - K )

3 . 2 6 1 3 0 . 2 6 0 4

0 . 2 6 3 8 3 . 2 5 7 3

3 . 2 5 7 0 0 . 2 5 6 4

7 0 3 . 0 0 1 1 5 9 . 7 0 BTU/CHR-FT-F)

0 . 1 5 5 7 3 . 1 5 4 8

0 . 1 5 6 3 0 . i 5 3 4

0 . 1 5 2 8 0 . 1 5 2 9

3 7 1 . 1 2 6 4 4 . 2 3 V A T T / C M E T E R - K )

0 . 2 6 9 4 0 . 2 6 7 9

0 . 2 7 1 4 3 . 2 6 5 5

0 . 2 6 4 5 0 . 2 6 4 6

7 5 0 . 0 0 1 2 0 9 . 7 0 3 T U / C H R - F T - D

3 . 1 6 0 3 0 . 1 5 9 1

3.1611 0 . I 53 1

0 . 1 5 7 0 3 . 1 5 7 5

3 9 3 . 9 3 6 7 2 . 0 6 V A T T / C M E T E R - K )

0 . 2 7 7 4 •3 . 2 7 5 3

3 . 2 7 3 8 3 . 2 7 3 7

0 . 2 7 1 8 & . 2 72 6

3 0 0 . 0 0 1 2 5 9 . 7 0 S T U / C H R - F T - F )

0 . 1 6 4 3 0 . 1 6 3 3

3 . 1 6 5 4 0 . 1 6 2 8

3 . 1 6 1 2 3 . 1 6 2 0

4 2 6 . 6 7 6 9 9 , 8 3 U A T T / C M E T E R - K )

3 . 2 3 5 2 3 . 2 3 2 6

0.2862 3 *2317

0 . 2 7 9 0 0 . 2 8 0 4

3 5 0 . 3 0 1 3 0 9 . 7 0 B T ' T / C H R - F T - F )

3 . 1 6 9 3 3 . 1 6 7 5

3 . 1 6 9 6 3 . 1 6 7 3

0 . 1 6 5 3 3 . 1 6 6 5

4 5 4 . 4 5 7 2 7 . 6 1 V A T T / C M E T E R - * )

v) . 2 9 3 ^ Z . 2 3 3 9

3 . 2 9 3 5 0 . 2 3 9 6

0 . 2 3 6 1 0 . 2 3 3 1


THERMAL CONDUCTIVITY 0r HZLlUu COMPUTED WITH DIFFERENT EQUATIONS

P R E S S U R E = 2 0 0 0 P S I A = 1 3 6 . 0 9 1 ATM = 1 3 7 . 3 9 5 DAR



KI K 4

;c2 ICS

K 3 :C6

DEG C DEG K U N I T S OF i t

9 0 0 . 0 0 1 3 5 9 . 7 0 B T U / C H R - F T - F )

0 . 1 7 3 7 0 . 1 7 1 7

O . l 7 3 3 0 . 1 7 1 8

0 . 1 6 9 3 0 . 1 7 0 3

4 8 2 . 2 3 7 5 5 . 3 9 W A T T / C M E T E R - K )

0 . 3 0 0 7 R . 2 9 72

0 . 3 3 0 7 0 . 2 9 7 3

0 . 2 9 3 1 0 . 2 9 5 6

9 5 0 . 0 0 1 4 0 9 . 7 0 8 T U / C H P . - F T - F )

0 . 1 7 3 1 0 . 1 7 5 9

0 . 1 7 7 9 0 . 1 7 6 2

0 . 1 7 3 3 J . 1 7 5 1

5 1 0 . 0 1 7 3 3 . 1 7 V A T T / C M E T E R - K )

0 . 3 0 8 3 0 . 3 0 4 4

O . 3 0 7 9 0 . 3 0 53

0 . 3 3 3 3 0 . 3 0 3 3

1 0 0 0 . 0 0 1 4 5 9 . 7 0 B T U / C H R - F T - F )

0 . 1 3 2 5 0 . 1 3 0 3

0 . 1 3 1 9 3 . 1 u O 5

0 . 1 7 7 2 0 . 1 7 9 3

5 3 7 . 7 3 3 1 0 . 9 4 V A T T / C M E T E R - K )

0 . 3 1 5 8 0 . 3 1 1 5

0 . 3 1 4 9 0 . 3 i 2 5

0 . 3 0 6 7 0 . 3 1 0 3

1 0 5 0 . 0 0 1 5 0 9 . 7 ' ? 3 T ' J / C H R - F T - F )

O . 1 8 6 8 3 .18 '41

3 . 1 8 6 0 0 . 1 3 4 3

0 . 1 8 1 1 0 . 1 8 3 4

5 6 5 . 5 6 3 3 3 . 7 2 U A T T / C M E T C R - K )

3 . 3 2 3 2 0 . 3 1 3 6

O . 3 2 i 3 3 . 3 1 9 3

0 . 3 1 3 4 0 . 3 1 7 4

5 1 0 3 .2(3 1 5 5 9 . 7 0 B T U / C H R - F T - F )

3 . 1 9 1 0 3 . 1 3 3 1

3 . 1 3 9 9 •J . 1 3 3 9

0 . 1 3 4 8 3 . 1 3 7 5

5 9 3 . 3 4 8 6 6 . 5 0 V A T T / C M Z T E R - K )

0 . 3 3 3 6 3 . 3 2 5 6

3 • 3 2 o 7 3 . 3 2 7 0

0 . 3 1 9 9 0 . 3 2 4 4

1 1 5 0 . 3 3 1 6 0 9 . 7 3 3 T U / C H R - F T - F )

3 . 1 9 5 2 •3 . 1 9 2 1

H . 1 9 3 9 0 . 1 9 3 3

0 . 1 3 3 6 0 . 1 9 1 4

6 2 1 . 1 2 3 9 4 . 2 3 U A T T / C M E T E R - K )

3 . 3 3 7 9 112 b

0 . 3 3 5 5 3 . 3 3 4 1

3 . 3 2 6 3 0 . 3 3 1 3

80


T H E R M A L C O N D U C T I V I T Y O F H E L I U M C O M P U T E D U I T H D I F F E R E N T E Q U A T I O N S

P R E S S U R E = 2C33 PSIA = 133.391 ATM = 137.393 UAR

T E M P E R A T U R E THERMAL CONDUCT! VI TY

DEO F DEG R U N I T S OF X

XI X 4

K3 X6

DEG C DEG K U N I T S OF X

1200.30 1659.70 B T U / C H R - F T - F )

0.1994 0.1961

3.1973 O.19 70

0. 1922 0. 1954

648.90 922.06 W A T T / C M E T E R - X )

0 .3451 0 . 3 3 9 4

0.3423 O.3410

0.3327 3.3381

1250.00 1709.70 B T U / C H R - F T - F )

3.2035 0.2001

0.2016 3 .2009

0.1958 0. 1992

676.67 949.83 *?ATT/C M E T E R - K )

0.3522 0.3463

0.3490 0.3477

0.3389 0 . 3 4 4 8

1300.00 1759.70 B T U / C H R - F T - F )

0.2076 0.2040

0.2054 0 . 2 0 4 7

0. 1993 0.2030

704.45 977.61 U A T T / C M E T S R - K )

0 .3593 0.3530

0 . 3 5 5 6 0 .3544

0.3450 3.3514

1350.00 1309.70 3 T U / C H R - F T - F )

0.2117 0.2073

0 .209 2 3.2035

0 . 2 0 2 3 0.2068

732.23 1005-39 U A T T / C M E T E R - K )

0.3663 0 .3597

0.3621 3.3608

0.3510 0.3578

1400.00 1859.70 BTU/C H R - F T - F )

0.2157 0.2117

0.2130 0.2122

0.2062 0.2104

760.01 1033.17 U A T T / C M E T E R - K )

0.3733 0.3664

0.3686 3.3672

0.3563 0.3642

1450.00 1909.70 B T U / C H R - F T - F )

0.2197 0.2155

0.2167 0 . 2 1 5 B

0.2095 3.2141

787.7S 106P.94 •'ATT/CMETER-X)

3.3302 0.3 729

3.3751 0 . 3 7 3 4

3.3626 0. 3 70 5

81


T H E R M A L C O N D U C T I V I T Y OF H E L I U M C O M P U T E D UL TH DIFFERENT E Q U A T I O N S

P R E S S U R E = 2000 PSIA = 136.091 ATM = 137.393 BAR

T E M P E R A T U R E T H E R M A L CONDUCTIVITY


XI X4

X 2 X 5

K 3 X6


1500.00 1959.70 B T U / C H R - F T - F )

0 . 2 2 3 6 0.2192

0 . 2 2 0 4 0.2193

0 . 2 128 0 . 2 1 7 7

8 1 5 . 5 6 1088.72 U A T T / C M E T E R - K )

0.3870 0.3795

0 . 3 3 1 4 0 .3795

0 . 3 6 8 3 0 . 3 7 6 7

1550.00 2009.70 B T U / C H R - F T - F )

0.2275 0.2230

• 3.2241 0.2228

0.2160 0.2212

843.34 1116.50 WATT/CN ! ;i X)

0.3938 0.3859

0.3373 0.3856

0.3738 0 . 3 8 2 8

1600.00 2059.70 B T U / C H R - F T - F )

0 . 2 3 1 4 0 . 2 2 6 7

0 . 2 2 7 7 0.2263

0.2191 0 . 2 2 4 7

371.12 1144.28 UATT /CM ETER- K

0 .4005 0 .3923

0.3941 0.3916

0.3793 0.3889

1650.00 2 1 B T U / C H R - F T - F )

!'i3 •"I

2 . 2 3 1 3 « . 2 2 9 I

0.2222 0.2281

398.91! 117^ VJATT/ CM' I I , ; ,1 I

• I 7 2 U .-I : i,

! :|003 IL . 3 9 7 5

0 . 3 8 4 6 0.3949

1700.00 2159.70 nTU/Clllv K T - M

il - ~< )D 1 H. ',23 39

0 . 2 3 4 9

n, n;i3l 0 , n'V32 0 . ^ 3 1 5

926.67 1199.33 UATT/C ML I : ' )

0 . 4 1 3 9

0 . 4 0 4 9 0 . 4 0 6 5 0 . 4 0 3 4

0.3893 0.400 7

1 750 .05" ;H?09.70 3 T U / C H R - F T - F )

0 .2429 0.2375

0 . 2 3 8 4 3 . 2 3 6 5

0.2282 0.2349

9 5 4 . 4 5 1227.61 U A T T / C M E T E R - X )

0.4205 0.4111

0 . 4 1 2 6 0 . 4 0 9 2

3.3949 0 . 4 0 6 5

82


T H E R M A L C O N D U C T I V I T Y Or H E L I U M C3.:PUTZG VITH D I F F E R E N T R u U A T I 0i« j

P R E S S U R E = 2 3 3 3 P S I A = 1 3 6 . . 0 9 1 A T . L = 1 3 7 . A A R

T E M P E R A T U R E THER M AL CONJUCTIVITY


XI X 4 X 5

X3 X 6

DEG C DEG K UNITS OF X

1303.30 2259-70 3 T U / C H R - F T - F )

0.24 67 0.2411

3 .2419 •3 .2393

0.2311 0.2362

982.23 2255.39 U A T T / C M S T E R - X )

0 .4273 0.4172

0 .41 3 7 0.4150

0.3999 0.4123

1850.00 2309.70 3 T U / C H R - F T - F )

3.2505 0.244 6

6 . 2 4 5 4 3 .2431

0.2339 0.2415

1010.01 1233.17 VATT/C ME'TER-K)

0.4335 0.4233

3.4247 II.4233

3.4048 0.4180

1900.00 2359.70 B T U / C H R - F T - F )

0.2542 3.2433

3.2439 0 . 2 4 6 4

0 . 2 3 6 6 0 . 2 4 4 7

1037.73 1310.94 V A T T / C M E T E R - K )

0.4400 0.4293

0 . 4 30 7 3.4265

3.4096 0 . 4 2 3 6

1950.00 2409.70 3 T U / C H R - F T - F )

3.2579 0.2515

0.2523 3.249 7

0.2393 0 . 24 79

1065.56 1338.72 7ATT/C M E T E R - X )

0 .4464 0.4352

3.4367 3.4322

0.4142 0 .4291

2000.00 2459.70 B T U / C H R - F T - F )

3.261 6 0.2543

3.2 557 3 . 2 53'3

0.2423 3.2511

1093.34 1366.50 " A T T / C M E T E R - X )

3 .4528 3.4411

3.4426 0.4379

0.4133 3 . 4 3 4 6

83

( 2 ) E q u a t i o n A . p u b l i s h e d b y t h e G e n e r a l A t o m i c C o . , ( R e f . 2 0 ) a l s o

p r o d u c e s h i g h e r v a l u e s o f c o n d u c t i v i t y t h a t a r e e q u a l o r v e r y n e a r l y

e q u a l t o t h o s e c a l c u l a t e d w i t h E q . A.3B.

( 3 ) T h e c o n d u c t i v i t i e s c o m p u t e d w i t h E q . A . 5 a t p r e s s u r e s ( p s i a ) o f

5 0 0 , 7 5 0 * a n d 1 5 0 0 -were o b t a i n e d b y l i n e a - r i n t e r p o l a t i o n b e t w e e n c o n -

d u c t i v i t i e s c a l c u l a t e d a t 1 0 0 , 1 0 0 0 , a n d 2 0 0 0 p s i a .

( k ) I n u s i n g E q . A . 7 t h e p r e s s u r e ( d e n s i t y ) c o r r e c t i o n w a s c o m p u t e d

w i t h t h e a s s u m p t i o n t h a t h e l i u m i s a p e r f e c t g a s . T h i s i s a c o m p r o m i s e ;

t h e e x p r e s s i o n f o r d e n s i t y i n R e f . 8 i s a n i m p l i c i t f u n c t i o n o f d e n s i t y

a n d , c o m p u t a t i o n a l l y , v e r y a w k w a r d . B e c a u s e p r e s s u r e e f f e c t s o n c o n -

d u c t i v i t y a r e s m a l l , t h i s a l t e r a t i o n i s c o n s i d e r e d i n s i g n i f i c a n t .

( 5 ) T h e ASHRAE e x p r e s s i o n f o r c o n d u c t i v i t y , E q . A . 8 i s a p p a r e n t l y

b a s e d o n t h e r e c e n t w o r k o f H o , P o w e l l a n d L i l e y ( R e f . 2 2 ) .

SUMMARY OF EQUATIONS DEVELOPED FOR EVALUATING THE THERMAL CONDUCTIV ITY OF H E L I U M

A . F r o m R e f . 1 .

K 1 = ( 2 . 6 8 2 x l O - 3 ) ( 1 . 0 + 1 . 1 2 3 * 1 0 ~ 3 P ) T - 7 1 ( 1 - . 0 0 0 2 P ) ( A . 3 A )

K l = w / O n 3 K / m )

T = t e m p e r a t u r e , K

2 7 3 K £ T < 1 8 0 0 K

P = b a r ; 1 b a r = 105 N / n P = 0 . 9 8 6 9 a tm

i n B r i t i s h u n i t s

K1 = (1.5U9* LO-^KL.O + 7.7U3 I 0 - 5 P ) [ ^ Q ] . 71 ( 1 .0-1. 379x1 O~5P) (A. 3B)

K 1 = ( B t u / h r ) / ( f t s - F / f t )

T = t e m p e r a t u r e , ° R

^ 6 0 ° R £ T < 3 2 U 0 ° R

0 ° F 5 T < 2 7 8 0 ° F

P = a b s o l u t e p r e s s u r e , p s i a

T h e p r e s s u r e e f f e c t i s v e r y s m a l l a n d c a n b e n e g l e c t e d i n m o s t e n g i n e e r i n g

c o m p u t a t i o n s .

8U

B . F r o m R e f . 2 0 :

A n e q u a t i o n f o r h e l i u m c o n d u c t i v i t y i n r e c e n t u s e ( 1 9 7 * 0 J "by t h e

G e n e r a l A t o m i c Company i s :

K 2 = 1 . 2 9 x 1 0 - 3 T 0 - 6 7 4 + ( 8 . 1 5 * 1 0 ~ J t ) ( P - l U . T ) 0 ' 2 8 ( A . U )

K 2 = t h e r m a l c o n d u c t i v i t y , ( B t u / h r ) / ( f t a - ° F / f t )

T = t e m p e r a t u r e , ° R a n k i n e

P = p r e s s u r e , p s i a .

C . F r o m R e f . 2 :

E q u a t i o n s h a v e b e e n d e v e l o p e d b y S a n d e r s 2 u s i n g d a t a p r e p a r e d b y

W i l s o n a n d p u b l i s h e d b y t h e G e n e r a l D y n a m i c s C o r p o r a t i o n . S a n d e r s d e -

v e l o p e d p o l y n o m i a l f i t t i n g e q u a t i o n s f o r c o m p u t i n g t h e t h e r m a l c o n d u c -

t i v i t y o f h e l i u m a s a f u n c t i o n o f t e m p e r a t u r e a t d i f f e r e n t p r e s s u r e s .

T h e s e e q u a t i o n s h a v e t h e g e n e r a l f o r m

K 3 = A + B T + C T * ( A . 5 )

K 3 = ( B t u / h r ) / ( f t 3 - ° F / f t )

T = t e m p e r a t u r e , ° F

T h e c o n s t a n t s , A , B , a n d C a r e s l i g h t l y p r e s s u r e d e p e n d e n t a s shown i n

t h e f o l l o w i n g t a b l e .

P r e s s u r e A B C ( p s i a )

1U.7 0.0809175 9 . 9 9 3 6 x 1 0 - 5 - 1 . 1 0 0 2 5 X 1 0 - 8

100.0 0.085^957 10.08U2 x 1 0 - 1 . 1 3 5 9 8 X 10 - 8

1 0 0 0 . 0 0.0863791 10.1611 X 1 0 - 5 -1.20^05 x 1 0 - 6

2000.0 0.0869068 10.3098 X 10'-5 -1.2782k X l O - 8

D . F r o m R e f . 2 1 :

M c E l r o y , w i t h d a t a f r o m R e f . 2 2 , d e v e l o p e d a s e c o n d d e g r e e e q u a t i o n

t o d e s c r i b e t h e t h e r m a l c o n d u c t i v i t y o f h e l i u m a t 1 . 0 a t m p r e s s u r e . A n

a d d i t i v e d e n s i t y c o r r e c t i o n f o r o t h e r p r e s s u r e s f r o m t h e e x p e r i m e n t a l

w o r k o f T s e d e r b e r g 2 3 i s i n c l u d e d . T h e s e e q u a t i o n s , i n m e t r i c u n i t s , a r e :

85

(KU) = 0.714046 X 1CT3 + 0.328159 X 10-5 T - 0.1+2803 X 10"9 T3 o

(A.6A)

KI( = (KU) + (1.73 x icr4) (P/T)1*17

(k4)q = thermal conductivity of helium. at 1.0 atn pressure, W/(CEP K/cm)

KU = thermal conductivity, of helium, w/(cm2 K/cm) T = temperature, K

500K < T < 1500K P = pressure, atm

In British units: (KU) = 0.01+226 + (1.0534 X lCT* )T - (7.6331 X lCr^)!2 (A.6B)

KU = (KU) + (8.568 X 1CT^) (P/T)1-17 o

KU = thermal conductivity of helium, (Btu/hr)/(ft2-°F/ft) (KM = thermal conductivity of helium at 1 atm (= IU-.696 psia)

0 pressure T = temperature, 0Rankine

900°R (=44O*F) < T < 2700°R (=22U0°F) P = pressure, psia

E. From Ref. 8: IKS) -(2 97 x 10-3) T'69 + (9-23 X 1(f ) (T - 273.16) . . (K5)q x 10 ) t + (T - 273.16)5 - 4.29 x 1014 (A.7A)

K5 = (K5) + 2.33 X 1CH+ p + 2.39 X lor® ps o

(K5) = thermal conductivity, w/m-K at P £ 1 bar

(Btu/hr)/(fts-°F/ft) = 0.5779 X (w/m K) • 1 bar = 106 N/BP = O.9869 atm

K5 = thermal conductivity, w/m k P > 1 bar

p = density, kg/m3

lb/ft3 = 0.062428 x kg/m3

T = temperature, °K .

86

In British units:

( K 5 ) = ( L . H A X 1 0 - ) T . A S + ( 2 - 9 6 X ^ P ) ( T - ^ 9 1 . 7 ) O (5.292X10 2)(T-U91.7)5 + (U.29X1014)

K5 = (K5) + (5.536 x 10"6)(P/T) + (2.378 x IXf9 (P/T)s r • A A\J J\JT{±J T A J.W \Cf a"*2 'o

K5 = thermal conductivity, (Btu/hr)/ (ft2 -°F/ ft")

(A.7B)

P £ 1 bar = 1 atm (K5)Q = thermal conductivity, (Btu/hr)/(ft2-°F/ft)

T = temperature, °R P = pressure, psia

F. From Ref. 24:

K6 = ,b/(A + B/T + C/Of3 + D/T3) (A.8A) K6 = sm/(CE? K/cm) T = K

The constant terms and applicable temperature ranger, are shown on the following table.

5K to 45K 9°R ia> 8l°R -451°f to -379°P

50K to 200K 90°R to 360°R -370°F to -100°F

200K to 500K 360°R to 900°R -100°F to 440°F

50CK to 1000K 900°R to l800°R 440°F to 1340°F

A 1^.7978 B 48.29403 c -30.03851 D 0.0

Avg. 0.5 Deviation, # Max. 1.9 at 45K Deviation,$

9.97104 590.260 -26632.5 522649 0.2 0.3 at 130K

6.61227 2429.73

-376539 23473100 0.0

0.1 at 240K

7.48415 1429-50

-45815.2 0.0 0.1 0.2 at 900K

87

For the temperature range 0°F to 131+0°F the above formula in British units is:

K 6 = 0 . 0 I + 3 0 7 T ° * E / ( 7 . W 1 H 5 + 2 5 7 3 . 1 / T - lMQhKi/y?) ( A . 8 B )

KO = (Btu/hr )/ ( ft2 -°F/F t) T = "Rankine

88

Appendix B

Thermal Conductivity of Helium-Nitrogen Mixtures This appendix describes, in detail, the procedure and the supporting

data used to develop Eq. IV.A3 used in the CACHE program to evaluate the thermal conductivity of mixtures of helium with air and air-like gases having molecular weights in the region 28 to 32.

Thermophysical data on the transport properties of these mixtures is scarce and does not cover the complete range of compositions and temperatures required for HTGR applications. The tabulations and curves of conductivity in Ref. 10 are the bases for Eq. IV.A3 in Section IV of this report. The data, Fig. 10, Section IV. of nitrogen-helium con-ductivity at 601°F versus the mole fraction of nitrogen was used to produce a fitting equation representing the variation of conductivity •with composition. The effect of gas temperature was obtained from the data at 601°F and 219°F. In the unlikely event that a Design Basis De-pressurization Accident (BBDA.) occurs, followed by the ingress of air into the Prestressed Concrete Reactor Vessel (PCRV), it is expected that a portion of the core graphite will be partially oxidized producing carbon monoxide. The core coolant gas will consist principally of helium diluted with nitrogen and carbon monoxide. The composition will change with elapsed time after the B3UA. Because no data on the characteristics of such three component mixtures was located, and because the molecular weights, conductivities, and viscosities of air, carbon monoxide and nitrogen are similar (Fig. 7 in Section IV and Table C2 in Appendix C), it has been assumed that the helium-nitrogen data is applicable to the post-DBDA atmosphere in the PCRV.

Equation IV.A3 was developed in two parts. The first describes the variation of mixture conductivity with composition at 601°FJ the second is a term supplying the temperature variation. The step-by-step pro-cedure follows:

(l) It may be observed, Fig. 8 and Fig. 9> that the general shape of the curves of conductivity, k, versus F, the mole fraction of Ns or Qs, for mixtures of helium with nitrogen or oxygen resembles a hyperbola. Therefore, an equation of the form

89

k l = BTF was used to obtain an approximate fit to the data. In this equation

k = thermal conductivity, (Btu/hr)/fts-°F/ft) F = mole fraction of the diluent gas, 1J2 or CO.

A,B = constants

The constants, A and B, were determined so that the "correct" value at 6oi°F for pure helium (F = 0) from Eq. I.A3 and the experimental value at F = 0.6 in Table 85b, Ref. 10, were satisfied. The resulting equation is

It was not anticipated that this simple equation would be adequate. Additional terms were added to reduce the errors, defined thus:

E(F) = k e x p " ^ (B.2A)

E(F) = error, the difference between the experimental values cf k for F > 0 and ki defined by Eq. B.1B.

kexp = k l a t f r o m Tatlle Ref. 10, except at F = 0 as noted above.

The error, E(F), -was approximated by a least squares fitting pcly-a in F £

6oi°F became nomial in F and the final equation for mixture conductivity, kQ, at

ko = kexp = k l + E ( F )> (EWhr)/(ft2-0F/ft) (B.2B)

E(F) = - 0.003196 + 0.0701^F - 0.157671s + 0.086321® (B.2C) and

k 0 = o°2°7i6+p ~ -003196 + 0.07011+F - 0.157671® - 0.08622F3

(B.3A)

This equation, B.3A, fits the data at 6oi°F within 3% over the entire range of nitrogen-helium composition. In the range of interest, when the mixture molecular weights are from 6.0 to seldom or ever more than 20 corresponding to mole fractions, F, of air (nitrogen) from 0.08

90

to 0.66, the maximum error is the order of 1.5$. Tahle B.l lists the experimental and calculated values at 601°F, their differences, and their ratios.

The dependence of thermal conductivity with temperature was assumed to be of the form:

k(T) = k Q (T/Tq)X (3.4A)

k Q = k at 601°F (=106l°R), (from Eq. B.3A) T = 106l°R o T = absolute temperature of mixture, °R

The exponent, x, is based on the data in Table 85b , Ref. 10, which shows values of k versus F at temperatures of 32°F, 86^, 113°F, 219°F, and 601°F. Using the tabulated values of k at 219°F and 601°F, x was evaluated -with the relation

x = log (k/ko)/log (T/Tq) (B.5A)

k, k Q - thermal conductivities, Table 85b, of a helium-nitrogen mixture both with the same mole fraction, F, of nitrogen at temperature T = 6T9°R and Tq = 106l°R.

after inserting temperatures x = -2.2k log (k/kQ) (B.5B)

Figure B.l shows the exponent, x, plotted as a function of F. The vari-ation of x is, unfortunately, larger than desirable; from a minimum of 0.53 to a maximum of 0.82. Because this variation did not have a regular pattern, it was arbitrarily decided to establish x as a constant by using the aritlimetic average, 0.66, of the values of x shown in Fig. B.l. The final equation for the thermal conductivity of these helium-nitrogen mixtures is

k = .2771E+F " • 0 0 3 1 9 6 + 'c701^F - .15767F2 + .08612F3 66

(B.6A) (Also IV.A3)

Figure 10 in Section IV displays curves of k from Eq. B.6A as a function of temperature and composition. The data for pure helium and pure nitro-gen are also shown for comparison. The agreement, when F = 0, with the

91

ORNL-DI/VG 76-2172

Mole fraction of He 1.00 0.80 0.60 D-Uo Q.20 o

0 . 8 0

+-> c

o.?o

o rg 0 . 60

0.50

© ®

<

•

• •

• • i Av g.=0.66

• • •

0 0.2 0.U 0.6 0.8 1.0 Mole fraction of

Fig. B.l. Variation of the exponent of temperature in an equation for thermal conductivity of helium-nitrogen mixtures assumed to have the form,

k = k T*; T = absolute temperature At F = 0; x i 0.71 for pure helium, Ref. 1 or Eq. I.A3 At F > 0; x has been calculated from experimental values of thermal

conductivity at temperatures of 377.2K and 589.2K, Table 85b, Ref. 10.

92

pure helium' data is excellent. The agreement, when F = 1.0, with the nitrogen data is not as close, but no situations have been postulated in which F, the mole fraction of nitrogen in the mixture, is above 0.6. Furthermore, the exact composition of PCRV atmospheres after DBDAs can-not be forecast with extreme accuracy. The uncertainties in forecasting the post-D3DA gas compositions and their variation with elapsed time after reactor shutdown will, in all likelihood, be greater than errors in evaluating gas mixture thermal transport properties.

Table B.l. Comparison of experimental* and calculated** thermal conductivities of helium-nitrogen

gas mixtures at 601°F

F, Mole

fraction nitrogen,

Thermal conductivity, (Btu/hrV(fts-°F/ft)

Experimental, Calculated k k exp. calc

Ratio, k n /k calc' exp

0 0.1434 0.140764 0.981618 0.05 0.1184 0.121886 1.02944 0.1 O.IO69 0.108118 1.0114 0.15 0.0976 9.74761E-2 0.998731 0.2 0.0896 8.88345E-2 0.991457 0.25 0.0826 8.15197E-2 0.986922 0.3 0.0763 7.51137E-2 0.984452 0.35 6.99000E-2 6.93524E-2 O.992166 0.4 0.0641 6.406882-2 0.999513 0.45 0.0589 5.91596E-2 1.00441 0.5 0.054 5.45646E-2 1.01046 0.55 0.0495 5.02541E-2 1.01523 0.6 0.0455 4.62194E-2 I.01581 0.65 0.0419 4.2468XE-2 1.01356 0.7 3.88000E-2 3.90191E-2 1.00565 0.75 0.0362 3.59005E-2 0.991725 0.8 0.0337 3.31468E-2 0.983585 0.85 0.0315 3.07982E-2 0.977721 0.9 0.0295 2.88989E-2 0.979622 0.95 2.76000E-2 2.74963E-2 0.996243 1 2.58000E-2 2.66407E-2 1.03259

•"•Experimental data from Table 85b, Ref. 10.

**kcsac = "O?2T7I6+F " 0 , 0 0 3 1 9 6 + O.070I4F - 0.15767F3 + 0.08622F3

N

93

Appendix C

The Viscosity of Helium

The Viscosity of Pure Helium

The information in this appendix was developed in the procets of obtaining the equations in Sections I and IV describing the viscosity of pure helium and helium-air mixtures.

Before finally selecting Eq. I.B2 (Section I), several sources of viscosity data on pure helium -were located and reviewed. In a sub-sequent paragraph six equations and their sources are listed. All give similar numerical results at 650°F. This is a representative value for the mean helium film temperature in the central region of an HTGR Core Auxiliary Heat Exchanger. The similarity is illustrated by Table C.l.

Table C.l. The viscosity of pure helium at 650°F evaluated with Equations C.1B through C.6B, inclusive.

Equation Reference Viscosity, lbm/(ft-hr) C .IB Riso Report 22U, Ref. 1 0.0798 C. 2 GA Co., Ref. 20 0.0779 C. 3 J. P. Sanders, Ref. 2 O . O 7 8 9 c.Hc Bonka and Vogt, Ref. 8 0.0777 C.5B J. M. Wright, Ref. 6 O .O778 C.6B ASHRAE, Ref. 2h 0.0738

Equation A.2B in Appendix A is a method of estimating the effect of small variations or differences in viscosity on the film coefficient of heat transfer. The film coefficient is less sensitive than for similar changes in conductivity and therefore no detailed comparative tabulations of viscosities based on these equations are provided. For example, in Table C.l the maximum and minimum values, 0.0798 and 0.0777, ditfer by 0.0021. The effect of this incremental difference in a typical CAHE per-formance computation will be less than 1.0$.

94

It has been stated elsewhere in this report that the viscosities of air, nitrogen, carbon monoxide, and oxygen are generally similar and follow similar trends with temperature. Figure C.l shows these viscosi-ties based on equations in Ref. 24 and Ref. 25. Table C.2 provides calculated viscosity data in British and metric units.

Equations for Calculating the Viscosity of Helium:

A. From Ref. 1.;

H = (3.674 X 10"?)T°*70 (C.1A)

ji - viscosity, kg/(m-sec) T = temperature, K

273 K £ T < 1800 K in British units

H = (5.890 x 10~4 )T0'70 (C.1B) (identical to

|i = viscosity, lb /(ft-hr) Eq. I.B2) T = temperature, °R

460°R £ T z 324O°R 0°F s T s 2780°F

Petersen1 states: "The standard deviation, a, is about 0.4$ at 273 K and 2.7$ at 1800 K, i.e., a = 0.0015 T9&."

B. From Ref. 20 ; V. = 6.9 X 10"4 T 0 , 6 7 4 Ib^/ft-hr (C.2)

I = °Rankine

C. From Ref. 2.:

Sanders, using Ref. 3 for source material, presents this empirical equation for helium viscosity:

\i = ( 6 . 7 X 10"4)To,ee l\/(ft-hr) (C.3)

T = temperature, °R

Helium viscosity is stated to be independent of pressure from atmos-pheric to 2000 psia.

95

O R N L DWG 75 9 9 5 ?

Toopcracurc, *F

F i g . C . l . T h e v i s c o s i t y o f common g a s e s w i t h m o l e c u l a r w e i g h t s f r o m 2 8 t o 3 2 , c o m p u t e d w i t h e q u a t i o n s i n R e f . 2k a n d 2 5 •

96

VISC0SITIES 0F NITROGEN, OXYGEN* AND AIR

COMPUTED FROM EQUATIONS IN THERMOPHVSICAL PROPERTIES OF REFPIGERANTS. ASHRAE 1973.

TEMPERATURE V»NP V'02 V* AIR

OFG P DEG C

DEG R DEG K

LB/FT-HR KG/M-S

LE/FT-HP KG/M-S

IB/FT-HR KG/M-S

SO 10

509.7 283.I6T

4.J2544F-2 1.70537E-5

4.77162E-2 1 .9724SE-5

4.28033E-2 I .76940E-5

100 37.7778

559.7 310.944

4.43696E-2 1.83414E-5

5.14883E-2 2. 12842E-5

4.S9921E-2 1.90121E-5

150 FI5.5556

609.7 338.722

4.73615E-2 1.95782E-S

5.51149E-2 2.27833E-5

4.90520E-2 2.02770E-5

200 93.3333

659.7 366.5

5.02412E-2 2.07686E-5

5.86075E-2 2.42271E-5

5.19954E-2 2.14938E-5

250 121.111

709.7 394.278

5.30184E-2 2.19167E-S

6.19770E-2 2.56200E-5

5.4833IE-2 2.2A668E-5

300 I£8.889 *

759.7 422.056

5.57015E-2 2.30258E-5

6.52331E-2 2.69660E-5

5.75743E-2 2.38000E-5

350 176.667

809.7 449.833

5.829B3F-2 2.40993E-5

6.83847E-2 2.82688E-5

6.02270E-2 2.48966E-5

400 204.444

859.7 477.611

6.08154E-2 2.51398E-5

7.14395E-2 2.95356E-5

6.27983E-2 2.59595E-5

450 232.222

9 0 9 . 7 505.389

6.31159E-2 2K 60908E-5

7.44626E-2 3.07812E-5

6.S2945E-2 2.69913E-5

500 260

959.7 533.167

6.54510E-2 2.70560E-S

7.73523E-2 3. 19758E-5

6.77210E-2 2.79944E-5

550 287.778

1009.7 560.944

6.77213E-2 2.79946E-S

8.01643E-2 3.31384E-5

7.00828E-2 2.89707E-5

600 315.556

1059.7 588.722

6.99317E-2 2.89083E-5

8.29052E-2 3.42712E-5

7.23843E-2 2.99221E-5

650 343.333

1109.7 616.5

7.20862E-2 2.97989E-5

8.55781E-2 3.53762E-5

7.46294E-2 3.08502E-5

VISCOSITIES 0F NITROGEN. 0XYGEN» AMD AIR

C O M P U T E D FROM F O H A T I 0 N S !N TMERM0PHY!»I CAL P R O P E R T I E S OF R F F P I G F R A N T S . A S H R A E 1973.

T E M P E R A T U R E V » 0 2 Vi-AIR

>FG F >EG C

O E G R D E G K

L B / F T - H R K G / M - S

L B / F T - H R K G / M - S

L B / F T - H R K G / M - S

7 0 0 371.111

1 1 5 9 . 7 6 4 4 . 2 7 8

7 . 4 1 8 8 7 E - 2 3 . 0 6 6 8 0 F - 5

8 . 8 1 R 7 8 E - 2 3 . 6 4 5 5 0 E - 5

7. 6 8 2 1 7 E - 2 3 » 1 7 5 6 5 E - 5

750 3 9 E.BB9

1209.7 6 1 2 . 0 5 6

7 . 6 2 4 2 5 E - 2 3. i s n o E - s

9 . 0 7 3 8 1 E - 2 3 . 7 5 0 9 2 E - 5

7 . 8 9 6 4 5 E - 2 3 . 2 6 4 2 2 E - 5

1300 4 2 6 . 6 6 7

1259.7 6 9 9 . 8 3 3

7 . 8 2 5 0 7 E - 2 3 . 2 3 4 7 2 E - S

9 . 3 2 3 2 5 E - 2 3 . 8 3 4 0 3 E - 5

8 . 1 0 6 0 6 E - 2 3 . 3 5 0 8 7 E - 5

8 5 0 4 5 4 . 4 4 4

1309.7 727.611

B . 0 2 1 5 9 E - 2 3 . 3 1 5 9 5 E - 5

9 . 5 6 7 4 1 E - 2 3 . 9 5 4 9 6 E - 5

8 . 3 1 1 2 8 E - 2 3 . 4 3 5 7 0 E - 5

9 0 0 4 8 2 . 2 2 2

1 3 5 9 . 7 7 5 5 . 3 8 9

8 . 2 1 4 0 7 E - 2 3 . 3 9 5 5 2 E - 5

9 . 8 0 6 5 9 E - 2 4 . 0 S 3 8 4 E - 5

8 • 5 1 2 3 4 E - 2 3 . 5 1 8 8 2 t > 5

9 5 0 5 1 0

1 4 0 9 . 7 7 8 3 . 1 6 7

8 . 4 0 2 7 3 E - 2 3 . 4 7 3 5 1 E - 5

0.100411 4 . 1 5 0 7 6 E - S

8.709 4 7 E - 2 3 . 6 0 0 3 1 E - 5

1000 5 3 7 . 7 7 8

1 4 5 9 . 7 8 1 0 . 9 4 4

8 . 5 8 7 7 8 E - 2 3 . 5 5 0 0 1 E - S

0.10271 4 . 2 4 5 8 3 E - 5

8 . 9 0 2 8 7 E - 2 3 . 6 8 0 2 6 E - 5

1050 5 6 5 . 5 5 6

1 5 0 9 , 7 8 3 8 . 7 2 2

8 . 7 6 9 4 0 E - 2 3 . 6 2 5 0 S E - S

0 . 1 0 4 9 6 8 4 . 3 3 9 1 5 E - 5

9 . 0 9 2 7 3 E - 2 3 . 7 5 8 7 4 E - 5

1 100 5 9 3 . 3 3 3

1559.7 8 6 6 . 5

8 . 9 4 7 7 7 E - 2 3 . 6 9 8 8 2 E - 5

0 . 1 0 7 1 8 5 4 . 4 3 0 7 9 E - S

9 . 2 7 9 2 3 E - 2 3 . 8 3 5 8 4 E - 5

1150 621.111

1 6 0 9 . 7 8 9 4 . 2 7 8

9 . 1 2 3 0 5 E - 2 o . 7 7 l 2 7 E - 5

0 . 1 0 9 3 6 3 4 . 5 2 0 3 5 E - 5

9 . 4 6 2 5 3 E - 2 3 . 9 1 1 6 1 E - 5

1200 6 4 8*889

1 6 5 9 . 7 9 2 2 . 0 5 6

9.29 5 3 8 E - 2 3 . 8 4 2 5 1 E - 5

0 . 1 1 1 5 0 5 4 . 6 0 9 3 9 E - 5

9 . 6 4 2 7 7 E - 2 3 . 9 8 6 1 1 E - S

1250. 6 7 6 . 6 6 7

1 7 0 9 . 7 9 4 9 . 8 3 3

9 . 4 6 4 9 0 E - 2 3 . 9 1 2 5 9 E - 5

0 . 1 1 3 6 1 2 4 . 6 9 6 4 8 E - 5

9 . 8 2 0 0 9 E - 2 4 . 0 5 9 4 2 E - 5

1300 7 0 4 * 4 4 4

1 7 5 9 . 7 9 7 7 . 6 1 1

9 . 6 3 1 7 3 E - 2 3 . 9 8 1 5 5 E - 5

0 . 1 1 5 6 8 5 4« 7 8 2 1 9 E - 5

9 . 9 9 4 6 2 E - 2 4 . 1 3 1 5 6 E - 5

1350 7 3 2 . 2 2 2

1 8 0 9 . 7 1005.39

9 . 7 9 6 0 0 E - 2 4 . 0 4 9 4 6 E - 5

0 . 1 1 7 7 2 7 4 . 8 6 6 5 7 E - 5

0 . 1 0 1 6 6 5 4 . 2 0 2 6 1 E - 5

98

D. From Ref. 8.:

Bonka and Vogt give these equations for helium viscosity:

= (3.78 X 1Q"7)T + (5 * 1 0 ~ 7 ) / ( 0 . 5 2 + T / 5 6 9 . 6 )

H = + ( 2 . 6 7 X 1 0 " l o ) p 2

M . Q = v i s c o s i + . v , N s/sP

(C.UA)

(C.fcB)

P s i bar p. = viscosity, N s/n?

P > 1 bar T = temperature, K p = density, kg/m3

The density correction is negligible, 1 part in 109, and can be ignored in HTGR computations.

In British units the equation for viscosity is:

H c = (6.095 X 10~4) T 0' 6 9 + 1.2095 X 10~3/(.52 + 9.7534 X 10-4T) (C.UC)

H o = viscosity lt>m/ft-hr T = temperature, °R

E. From Ref. 6.:

J. M. Wright proposes this equation for helium viscosity:

M, = viscosity, poises = g/(cm-sec) T = temperature, K

15K s T £ 1090K

After re/irranging and converting to British units, the equation is written:

H = (3.75 X 10-4) T (0.l8._ To-7s + i / o . ^ T 0 ' 7 5 ) - 0 - 4 7 (C.5B)

p. = viscosity, lbm/(ft-hr) T = temperature, °R

27°R s T s 1960°R -433°F s T S 1500°F

Wright states that the average error in this equation is 0.8$.

H = (2.79 X 10~6) T [(T/5.3)0'75 + (T/5.3) ] (C.5A)

99

F. From Ref. 2h. :

This ASHRAE publication contains an equation having the general form:

H = T°'5/(A - B/T - C/T2 + D/T3) (C.6A)

H = viscosity, (H s/m2) x 10~6

1J s/n? = kg/m-sec T = temperature, K

The constants and the accuracy of the fit are tabulated for three tempera-ture ranges.

Temperature range 1.25 K to 20.0 K 20 K to 300 K 300 K to 1000 K 2.25°R to 36.0°R 36.0oR to 5Uo*F 5^0°R to l800°R

- U57.U°f to -k23.1°T -U2U°F to S0°F 80°F to 13U0°F

A 1.11871 0.83^77 0.55797 B 3.307^1 2.U2&! 180.017 C -0.18070 -592.753 -!i0566.2 D -1.13103 5650.18 1.131360

Avg. uev. 0.2$ 1.1$ 0.0$ Max. dev. 0.7$ at 20 K l.jfc at 300 K 0.5$ at 950 K

In British units th Ls equation becomes

H = ( 1 . 8 0 3 1 X 10"3) T0,5/Z

Z = 0 . 5 5 7 9 7 + 3 2 U . 0 3 1 / T - 131U3VT3 25,8U3,700/T3 (C.6B) u = lbjn/ft-hr T = temperature, °R

5^0° R s t s l800°R 80°F <; T * 13^0°F

100

Appendix D

The Specific Heat of Heliun-Air Mixtures

When the composition of a gas mixture is known or established, and the specific heats of the individual gases in the mixture are known, the specific heat of the mixture is easily determined. In strict terms a mixture of air and helium consists of three components) however, since the thermal transport properties of air are well established, it will be considered as a single component gas. Gas composition is usu-ally expressed in terms of mole fractions of the components or the molec-ular weight of the mixture. Mixture specific heat, is dependent on the weight fractions of the constituent gases. The equations that inter-relate these modes of stating composition are simple and well known; they are included as a matter of convenience. For a two component gas, air and helium, the composition equations are outlined below.

1. Symbols:

Subscripts a, h, and m refer to air, helium and mix-tures of air with helium respectively.

A = molecular weight A A = 2 8 . 9 7

AJJ = 4 . 0 0

F = mole fraction, moles/mole of mixture W = weight/mole, lbs/mole of mixture Y = "weight fraction, lbs/lb of mixture C = specific heat, Btu/lb-°F

101

2. 'Weight fractions when the molecular weight of the gas mixture is given:

V. A (A - A. ) A - 4.00 - r - ctMT - (~ 2 ~a )

ni nr a n' m

W. A. (A - A. ) .A - 28.97 ^ ' r r A ( : = -0.160. ( - a - t m mv n a7 m

3- Mole fractions when the weight fraction is given:

Ya k' 0 0 Y a Fq = v~fl—x fi _ v Aa = I m v u. OH Q-7 M _ v ^ (D--4.)

Yh Aa 2 8 , 9 7 Yh Fh - Y h Aa + (1 - Yh)Ah - 28.97 Y h * 4.0C (l - ( D*' A )

4. Mole fractions when the molecular weight is given:

A - A, A - 4.00 F- V 9 7 JD-5A)

A -m Ah A - A, a h A - A n a A h " A a - * V 9 T ( D ' 6 A )

5. Specific Heat:

( CP} m = W a + V V h = W a + ( l " Ya>

The specific heat at constant pressure, (C )a °f air was obtained from a tabulation* of enthalpy versus temperature in Ref. 26, thus:

A least squares fit (Ref. 11) with a second degree polynomial was used to approximate the tabulated values of (c ) so obtained. The resulting p a equation is:

*This tabulation has been abstracted from Ref. 27.

102

(c L = 0,230^ t (3.7672 x 10-e)T - (U.80O X io" 9 )T 2 (D.8A) p " " T = °F (Also Eq. IV.C3)

Table D.I., the printout of the fitting program, contains the tabulated values of Ah/AT and (C_)_ computed with Eq. D.SA. A graphic p a * comparison of (C ) a from Eq. D.8A with the tabulated values in Ref. 27

in Fig. D.l. Figure in Section IV shows curves of the specific heat of air-helium mixtures at 500°F and 900°F, computed by substituting Eq. D.8A into Eq. D.7A.

^ 0 • Table D. 1. The specific heat of air at constant pressure; a comparison of tabula tec; va.l u't *' with a '.;econ<i decree polynomial fit 0

Temperature Specific heat fBtu/(lb-0F)"l Difference Pem-nt (°F) (Ref. P.d) (Eq. D.8A) Difference

300 .21(3 .2'; 121-5 3.75505 X io"a 'V'(>• 95 390 .21*5 .2U 33J- 6.66'- 77 X JO-4 .272732 )(50 .21)6 .2'»63')9 -3.1.8996 X 10"4 -.11'1667 »+90 .2l'7 .21*7673 -6.73137 X JO"4 -.271785 590 .25 .250915 -9.151-53 X 10"4 -.361)81.5 690 .253 ,25'J06l -1.06057 X 10_a 17'. '.6 790 .256 .257108 -1.1081.8 X 10"" -J-31.133 890 .26 .260059 -5 • 93 9'-"! X lb"1' .-7605 X .10 990 .263 .262913 8.72973 X 10"s 3.32038 y .10 1050 .265 .2 6') 578 'i .2i8'-6 >: JO"4 . 159it,il 1090 .265 .265669 -6.690.15 X 10"4 -.?5J8r3 1150 .267 .267276 -2.761^.6 y JO"4 -.1033.18 1190 .269 .268328 6.7187'' X 10~4 .250393 1290 .271 .27099 .1.0996 X ]u"4 J* .09533 > 30 1390 .27!) .273355 6.1*525 2 X 10"4 .23601.9 1^90 .276 .275722 2. r/7J>2 X JO"4 ..100733 1550 .278 .277096 9.03803 X 10~4 . 32660? 1590 .279 .277993 3.007'- 3 X 30":' . 362 396 1650 .28 .279308 6.91903 X J0~4 .?,iY'/2 1690 .28 .280366 -I.656Y6 X 10"4 -5.9J 35.1 X 10' 1720 .281 .280799 2.03 J,'.5 X io"4 7.3 7 O1' 6 y 10 r,5o .281 .28jli23 -1..22886 X 3 0_4 -.j 5 Of-167 1790 .282 .28221)2 -2.1)1585 X JO"4 -8.55953 10' 1850 .283 .283't'i -1) .1)0') f't X 10"4 -. 355!|03 1900 .281) .P8'M)3 3 -i). J28JB X JO"4 1950 .285 .285361 - 3•60862 X JO"4 -. J26't58 2000 .286 .286285 -2.81.606 X 10"4 -9-9^137 y JO'

0.2301' t (3.7672 X 10_C)T - (>1.86 X TO"9)?2, Eq. D.8A

104

ORNL—DVVG 76-2173

Temper,'it,, ••(;, °F

a b Fig. D.l. Calculated and tabulated values for the specific heat

of air at constant pressure. continuous curve represents the equation: C = 0.2304 + (3.7672 x 10 - 5) T r (4.86 x 1Q"9) T2; T = °F

b O , From Keenan and Kaye, "Gas Tables," Ref. 27.

105

ORNL—DWG 75 -9956

Temperature, °F

Fig. D.2. The specific heats at constant pressure of the gases that dilute the helium in the FCRV after a DBDA-LOMLC.

106

References

1. Helge Petersen, The Properties of Helium: Density, Specific Heats, Viscosity, and Thermal Conductivity at Pressures from 1 to 100 Bar and From Room Temperature to About l800 K, Ris8 Report No. 22k, (September 1970).

2. J. P. Sanders, Oak Ridge National Laboratory, private communication (Nov. 20, 1970).

3. M. P. Wilson, Jr., Thermodynamic and Transport Properties of Helium, GA-1355 (January 1960).

1+. Jesse T. Simmons, The Physical and Thermodynamic Properties of Helium, Tech. Report D-9027, Wm. R. Whittaker Co., Ltd., Los Angeles, Calif. (July 1, 1957).

5. Roger A. Svehla, Estimated Viscosities and Thermal Conductivities of Gases at High Temperatures, NASA Technical Report R-132 (I962).

6. J. M. Wright, Calculated Thermal Conductivities of Pure Gases and Gaseous Mixtures at Elevated Temperatures, AECD-U197, General Electric Corp., Hanford Works (1951).

7. J. Phys. Chem. Ref. Data, 1, 279-^21 (1972).

8. H. Bonka and G. Vogt, H-S-Diagranun fur Helium Nach den Paten von Cederburg, U. A., Internal Report KFA-IRE-17/72, Kern forschungsan-lage .Tulich, Geselleschaft mit Beschrankter Hattung; Instiiut fur Reactorent wicklung.

9. J. P. Moore and D. L. McElroy, private communication.

10. Y. S. Touloukian, P. E. Liley and S. C. Saxena, Thermophysical Properties of Matter, vol 3, Thermal Conductivity of Nonmetallic Liquids and Gases, IFI/PLENUM, New York-Washington (1970).

11. "P0LFIT, A Program to Fit Least Square Polynomials to Bivariate Data Using an Orthogonal Polynomial Method," Call-A-Computer Co.

12. C. A. Meyer, et al., ASME Steam Tables, The American Society of Mechanical Engineers, 1967•

13- Steels for Nuclear Applications — Mechanical and Physical Properties of Steels for Nuclear Applications, vol 3, United States Steel Corp. Pittsburgh, Pa., (1967).

ll+. Pipe and Tubes for Elevated Temperature Service, National Tube Division, United States Steel Corporation, Bulletin No. 26.

15. R. C. Reid and T. K. Sherwood, The Properties of Gases and Liquids, Their Estimation and Correlation, McGraw-Hill, New York, 1958.

107

1 6 . R. S. 3rokaw, "Estimating Thermal Conductivities for Nonpolar Gas MixturesInd. Eng. Chem., 47, (ll), 2398-2400 (November 1955).

17. C. A. Johnson, Viscosity of Gas Mixtures, Report Ch. E. 273~566F3, Syracuse University Research Institute (July 1, 1956).

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19. J- P. Sanders, HTGR Safety Studies Progress Report for the Period Ending June 30, 1974, GCR-DL: 74-2 (Aug. 22, 1974).

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21. D. L. McElroy, Oak Ridge National Laboratory, private communication (1972).

22. C. Y. Ko, R. W. Powell and P. E. Liley, Thermal Conductivity of the Elements, NSRDS-NBS, Category 5, U. S. Government Printing Office, Washington, D. C.

23. N. V. Tsederberg, Thermal Conductivity of Gases and Liquids, The MIT Press, Cambridge, Mass., 1965.

24. Thermophysical Properties of Refrigerants, American Society of Heating, Refrigerating, and Air-Conditioning Engineers, 1973.

25. Joseph Hilsenrath and Y. S. Touloukian, "The Viscosity, Thermal Conductivity, and Prandtl Number for Air, 0 ?, N , NO, H , CO, CO , He, and A," ASME Trans, vol 7 6 , 967~85 (August 1954).

26. W. C. Reynolds, Thermodynamics, McGraw-Hill, New York, 1965*

27- J- H. Keenan and J. Kaye. Gas Tables, Wiley, New York, 1948.

Documents

The Thermal Transport Properties of Helium, Helium-Air