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NASA TECH N I CA L. NOTE iS^^ SQ^Jk, NASA TN D-4959

^ ^s^^"T uj^= g

z LOAN COPY: RETURN IUAFWL (WLIL-2)

KIRTLAND AFB, N MEX

HEAT-TRANSFER COEFFICIENTS FORHYDROGEN FLOWING THROUGH PARALLELHEXAGONAL PASSAGES AT SURFACETEMPERATURES TO 2275 K

by Jack G. Slaby and William F. Mattsony ’

Lewis Research Center ’’"Cleveland^ Ohio \

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON, D. C. DECEMBER 1968

JII

NASA TECHNICAL NOTE NASA TN D-4959 (!.. /

LOAN COPY: RETURN IU AFWL (WLlL-2)

KIRTLANO AFB. N MEX

HEAT-TRANSFER COEFFICIENTS FOR

HYDROGEN FLOWING THROUGH PARALLEL

HEXAGONAL PASSAGES AT SURFACE

TEMPERATURES TO 2275 K

by Jack G. Slaby and William F. Mattson

Lewis Research Center

Cleveland, Ohio

.' ~ 'or

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION • WASHINGTON, D. C. • DECEMBER 1968

II

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1 TECH LIBRARY KAFB, NM

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NASA TN D-4959

HEAT-TRANSFER COEFFICIENTS FOR HYDROGEN FLOWING

THROUGH PARALLEL HEXAGONAL PASSAGES

AT SURFACE TEMPERATURES TO 2275 K

By Jack G. Slaby and William F. Mattson

Lewis Research CenterCleveland, Ohio

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

For sole by the Clearinghouse for Federal Scientific and Technical InformationSpringfield, Virginia 22151 CFSTI price $3.00

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TECH LIBRARY KAFB, NM

111111111111111111111111111111111111111111111 0131775

NASA TN D-4959

HEAT-TRANSFER COEFFICIENTS FOR HYDROGEN FLOWING

THROUGH PARALLEL HEXAGONAL PASSAGES

AT SURFACE TEMPERATURES TO 2275 K

By Jack G. Slaby and William F. Mattson

Lewis Research Center Cleveland, Ohio

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

For sale by the Clearinghouse for Federal Scientific and Technical Information Springfield, Virginia 22151 - CFSTI price $3.00

ABSTRACT

Local forced-convection heat-transfer data are presented for hydrogen flowing

through an electrically heated test section composed of 19 hexagonal parallel passages

with length- to equivalent-diameter ratio of 63. 5. The data cover ranges of surface-

to hydrogen-temperature ratios from 1. 43 to 3. 38, bulk Reynolds numbers from 12 950

to 21 960, surface temperatures to 2275 K, and outlet hydrogen temperatures to 747 K.

The results are correlated in terms of Nusselt, Prandtl, and modified Reynolds numbers.

The data fell within about +/-20 percent of the correlating equations. The heat-transfer

sults agreed with those obtained from a parallel flat-plate test section with similar dimen-

sions.

ii

ABSTRACT

Local forced-convection heat-transfer data are presented for hydrogen flowing

through an electrically heated test section composed of 19 hexagonal parallel passages

with a length- to equivalent-diameter ratio of 63. 5. The data cover ranges of surface-

to hydrogen-temperature ratios from 1. 43 to 3.38, bulk Reynolds numbers from 12 950

to 21 960, surface temperatures to 2275 K, and outlet hydrogen temperatures to 747 K. The results are correlated in terms of Nusselt, Prandtl, and modified Reynolds numbers. The data fell within about ±20 percent of the correlating equations. The heat-transfer re­

sults agreed with those obtained from a parallel flat-plate test section with similar dimen­

sions.

ii

HEAT-TRANSFER COEFFICIENTS FOR HYDROGEN FLOWING THROUGH PARALLEL

HEXAGONAL PASSAGES AT SURFACE TEMPERATURES TO 2275 K

by Jack G. Slaby and William F. Mattson

Lewis Research Center

SUMMARY

Local forced-convection heat-transfer data are presented for hydrogen flowing

through a direct-current resistance-heated test section that is composed of 19 hexagonal

parallel passages and has a length- to equivalent-diameter ratio of 63. 5. The experi-

mental data cover ranges of surface- to hydrogen-temperature ratios from 1. 43 to 3. 38,bulk Reynolds numbers from 12 950 to 21 960, surface temperatures to 2275 K, and out-

let hydrogen temperatures to 747 K corresponding to an exit Mach number of 0. 9 at

pressures slightly above 1 atmosphere. The inlet hydrogen temperature was constant at

294 K. The heat-transfer results are presented and correlated by modified Dittus-

Boelter equations with hydrogen gas properties evaluated at the bulk, film, and surface

temperatures. The data fell within about +/-20 percent of the correlating equations.

The heat-transfer results agreed with those obtained from a parallel-flat-plate test

section with a similar equivalent diameter and the identical length and flow rate. This

comparison was made for various power inputs.

INTRODUCTION

Flowing hot gas has been used to evaluate fuel-element designs out-of-pile. The de-

sign and operation of gas heaters capable of heating hydrogen, helium, and nitrogen to

temperatures above 2500 K are reported in references 1 to 3. Gas was heated by flowing

over or through electric, resistance-heated, tungsten heating elements in the form of

either parallel flat plates or interwoven mesh. A tungsten honeycomb structure, consist-

ing of parallel hexagonal passages, was also considered for use as a heater element and

as a fuel element for a gas-cooled nuclear reactor. Evaluating the honeycomb required

special fabrication so that it could be subjected to direct-current resistance heating. One

honeycomb was fabricated so that the flow area, equivalent diameter, length, and electri-

HEAT-TRANSFER COEFFICIENTS FOR HYDROGEN FLOWING THROUGH PARALLEL

HEXAGONAL PASSAGES AT SURFACE TEMPERATURES TO 2275 K

by Jack G. Slaby and William F. Mattson

Lewis Research Center

SUMMARY

Local forced-convection heat-transfer data are presented for hydrogen flowing

through a direct-current resistance-heated test section that is composed of 19 hexagonal

parallel passages and has a length- to equivalent-diameter ratio of 63. 5. The experi­

mental data cover ranges of surface- to hydrogen-temperature ratios from 1. 43 to 3. 38,

bulk Reynolds numbers from 12 950 to 21 960, surface temperatures to 2275 K, and out­

let hydrogen temperatures to 747 K corresponding to an exit Mach number of O. 9 at

pressures slightly above 1 atmosphere. The inlet hydrogen temperature was constant at

294 K. The heat-transfer results are presented and correlated by modified Dittus­

Boelter equations with hydrogen gas properties evaluated at the bulk, film, and surface

temperatures. The data fell within about ±20 percent of the correlating equations.

The heat-transfer results agreed with those obtained from a parallel-flat-plate test

section with a similar equivalent diameter and the identical length and flow rate. This

comparison was made for various power inputs.

INTRODUCTION

Flowing hot gas has been used to evaluate fuel-element designs out-of-pile. The de­

sign and operation of gas heaters capable of heating hydrogen, helium, and nitrogen to

temperatures above 2500 K are reported in references 1 to 3. Gas was heated by flowing

over or through electric, reSistance-heated, tungsten heating elements in the form of

either parallel flat plates or interwoven mesh. A tungsten honeycomb structure, consist­

ing of parallel hexagonal passages, was also considered for use as a heater element and

as a fuel element for a gas-cooled nuclear reactor. Evaluating the honeycomb required

special fabrication so that it could be subjected to direct-current resistance heating. One

honeycomb was fabricated so that the flow area, equivalent diameter, length, and electri-

cal resistance were about the same as one stage of the parallel flat-plate test section de­

scribed in reference 2. The two types of test sections, hexagonal-passage and flat-plate ,

are shown in figures 1 and 2, respectively. Heat-transfer tests with axial temperature

gradients were conducted on the hexagonal-passage honeycomb test section at conditions

similar to those used for the parallel flat-plate test section reported in reference 1.

This report correlates the local hydrogen heat-transfer coefficients, obtained from

the honeycomb test section, in terms of Nusselt number , Prandtl number , and modified

Reynolds number. Hydrogen gas properties are evaluated at bulk, film , and surface tem­

peratures for the different correlations. The same local hydrogen heat-transfer coefficients are also compared with the heat­

transfer coefficients obtained from the parallel flat-plate test section described in r efer­

ence 1. The heat-transfer coefficients are expressed in terms of Nusselt numbers.

2

Outer partia l webs ---<:

I -r Voltage ta ps

,// /

r Molybdenum bus I

C-66-3038

Figure 1. - Hexagonal-passage tungsten tes t section i nst rumented with voltage ta ps .

----,-------- .-- -- - --- -- -

cal resistance were about the same as one stage of the parallel flat-plate test section de­

scribed in reference 2. The two types of test sections, hexagonal-passage and flat-plate ,

are shown in figures 1 and 2, respectively. Heat-transfer tests with axial temperature

gradients were conducted on the hexagonal-passage honeycomb test section at conditions

similar to those used for the parallel flat-plate test section reported in reference 1.

This report correlates the local hydrogen heat-transfer coefficients, obtained from

the honeycomb test section, in terms of Nusselt number , Prandtl number , and modified

Reynolds number. Hydrogen gas properties are evaluated at bulk, film , and surface tem­

peratures for the different correlations. The same local hydrogen heat-transfer coefficients are also compared with the heat­

transfer coefficients obtained from the parallel flat-plate test section described in r efer­

ence 1. The heat-transfer coefficients are expressed in terms of Nusselt numbers.

2

Outer partia l webs ---<:

I -r Voltage ta ps

,// /

r Molybdenum bus I

C-66-3038

Figure 1. - Hexagonal-passage tungsten tes t section i nst rumented with voltage ta ps .

----,-------- .-- -- - --- -- -

Spacer-supported tungsten flat-plate test section of reference 2.

Tungsten plate test section \

,

)

\ \

'-- Voltage tap leads

Figure 2. - Assembled flat-plate test section.

TEST SECTION

Description

C-67-1861

Heat-transfer experiments were performed on the tungsten honeycomb test section shown in figure 1. The honeycomb, fabricated by a powder-metallurgy sintering process,

has a density of about 98 percent of theoretical, as measured by a mercury porosimeter

The overall honeycomb length is 23.5 centimeters, and a 1. 905-centimeter-diameter

circle would encompass the test-section periphery. The circular ends serve as electrical

bus connections and are an integral part of the honeycomb. The test-section length be­

tween buses, the power generation length, was 20. 3 centimeters. The honeycomb test

section consisted of 72 inner webs forming 19 hexagonal passages and 14 outer partial

webs attached to the periphery. These outer webs (the result of the manufacturing proc­

ess) are incomplete hexagonal passages and provided a means for attaching the voltage

taps. The maximum variation between any of the three across-the-flat measurements for

a given passage was not more than 0.254 millimeter. The average flat-to-flat distance

for the 19 passages of the honeycomb heater was 3.20 millimeters. The variation in pas­

sage equivalent diameter was ±O. 051 millimeter from the average equivalent diameter of

3.20 millimeters. The average web thickness was O. 548 millimeter.

These dimensional variations occurred only in the radial direction. In the axial di-

3

Spacer-supported tungsten flat-plate test section of reference 2.

Tungsten plate test section \

,

)

\ \

'-- Voltage tap leads

Figure 2. - Assembled flat-plate test section.

TEST SECTION

Description

C-67-1861

Heat-transfer experiments were performed on the tungsten honeycomb test section shown in figure 1. The honeycomb, fabricated by a powder-metallurgy sintering process,

has a density of about 98 percent of theoretical, as measured by a mercury porosimeter

The overall honeycomb length is 23.5 centimeters, and a 1. 905-centimeter-diameter

circle would encompass the test-section periphery. The circular ends serve as electrical

bus connections and are an integral part of the honeycomb. The test-section length be­

tween buses, the power generation length, was 20. 3 centimeters. The honeycomb test

section consisted of 72 inner webs forming 19 hexagonal passages and 14 outer partial

webs attached to the periphery. These outer webs (the result of the manufacturing proc­

ess) are incomplete hexagonal passages and provided a means for attaching the voltage

taps. The maximum variation between any of the three across-the-flat measurements for

a given passage was not more than 0.254 millimeter. The average flat-to-flat distance

for the 19 passages of the honeycomb heater was 3.20 millimeters. The variation in pas­

sage equivalent diameter was ±O. 051 millimeter from the average equivalent diameter of

3.20 millimeters. The average web thickness was O. 548 millimeter.

These dimensional variations occurred only in the radial direction. In the axial di-

3

rection, the dimensions were uniform, that is, at any position along the test-section

length, a given dimension was corstant. The total tungsten cross section was therefore

constant along the test-section length.

Instrumentation

The test section was instrumented by voltage tap wires that were attached to the

honeycomb through holes disintegrated by electric discharge into the outer partial webs,

as shown in figure 1. Readings from these taps were recorded on a digital voltmeter and

were later used to determine surface temperature profiles. The spacing of the voltage

taps was varied; a closer spacing was used near the hot exit end of the test section to al-

low more accurate determination of the temperature profiles. The voltage taps were

placed along the 20. 3-centimeter test-section length, and these positions were designated

as ratios of the distance from the test-section entrance to the test-section length x/L.The first four voltage taps were spaced at x/L intervals of 0. 125, the next six at 0. 0625,

and the last four at 0. 03125. The voltage profiles are shown in figure 3. The current

flowing through the test section was measured by a calibrated shunt.

The test section was mounted in the test facility described in reference 2. The

heater inlet gas temperature T. was measured by a Chromel-Alumel thermocouple and

was 294 K for each of the four runs. A choked-flow nozzle was used to measure the gas

flow rate, which was set by adjusting the nozzle inlet pressure at room temperature.

Power, P

0 68.3 y />5

A 39.1 / <?D 24.7 V P

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0Ratio of distance from test-section entrance to test-section length, x/L

Figure 3. Comparison of voltage profiles from hexagonal-passage test section for variousamounts of power input. Hydrogen mass flow rate, 10.44 grams per second.

4

rection, the dimensions were uniform, that is, at any position along the test-section

length, a given dimension was cor stant. The total tungsten cross section was therefore constant along the test- section length.

Instrumentation

The test section was instrumented by voltage tap wires that were attached to the honeycomb through holes disintegrated by electric discharge into the outer partial webs,

as shown in figure 1. Readings from these taps were recorded on a digital voltmeter and were later used to determine surface temperature profiles. The spacing of the voltage taps was varied; a closer spacing was used near the hot exit end of the test section to al­low more accurate determination of the temperature profiles. The voltage taps were

placed along the 20. 3-centimeter test-section length, and these pOSitions were designated as ratios of the distance from the test- section entrance to the test- section length x/L.

The first four voltage taps were spaced at x/L intervals of O. 125, the next six at O. 0625, and the last four at 0.03125. The voltage profiles are shown in figure 3. The current

flowing through the test section was measured by a calibrated shunt.

The test section was mounted in the test facility described in reference 2. The heater inlet gas temperature T i was measured by a Chromel-Alumel thermocouple and

was 294 K for each of the four runs. A choked-flow nozzle was used to measure the gas

flow rate, which was set by adjusting the nozzle inlet pressure at room temperature.

6

5

> 4 ",'

0:>

.l9 0 > 3

2

o

4

Power, q,

kW

0 68.3 <> 52.6 6- 39. I 0 24.7

I .1 .2 .3 .4 .5 .6 .7 .8 .9

Ratio of distance from test-section entrance to test-section length, x/L

I 1.0

Figu re 3. - Comparison of voltage profiles from hexagonal-passage test section for various amounts of power input. Hydrogen mass flow rate, 10.44 grams per second.

Constant gas flow could be maintained provided that the exit pressure was not raised suf-

ficiently to unchoke the nozzle. The exit pressure was maintained slightly above 1 atmos-phere. A heat balance on a hydrogen-to-water heat exchanger, located at the test-section

exit, was used as a means of obtaining the outlet gas temperature. The heat-exchangerwater flow rate Wrj was measured with an orifice and the water temperature rise

ATrr o with a differential iron-constantan thermocouple. A detailed description of the2i

flowing gas facility used, including the instrumentation, is given in reference 2.

METHOD OF CALCULATION

Forced-convection heat-transfer coefficients were calculated from the data for hy-

drogen flowing through an electrically heated test section, which was composed of 19 hex-

agonal passages and had a length- to equivalent-diameter ratio of 63. 5, based on the test-section length of 20. 3 centimeters and the average equivalent diameter of 3. 20 millime-

ters. Local coefficients were calculated because the surface temperature, heat flux, and

gas temperature varied significantly along the axial length of the test section. One hydro-

gen mass flow rate was used, and the electrical power to the test section was varied tochange the heat-transfer coefficient.

Wall Temperature Profiles

The wall temperature profiles were obtained in the following manner: Readings from

voltage taps, attached along the honeycomb length, were used to plot the voltage profiles

shown in figure 3. From the profiles, incremental voltages AV corresponding to incre-

mental test-section lengths AL were taken. The AL chosen for these calculations was

2. 03 centimeters, which divided the honeycomb test section into 10 equal parts. The cur-

rent I through the honeycomb cross-sectional area A was measured. The local re-0

sistivity ^ of the tungsten test section can then be calculated by

AV \_I AL

(All symbols are defined in appendix A.) The average incremental test-section surface

temperature was determined from a plot of tungsten resistivity as a function of tempera-ture, as given in reference 4.

The calculated incremental surface temperature T_ is plotted in figure 4 as a func-

tion of test-section length

5

I

Constant gas flow could be maintained provided that the exit pressure was not raised suf­

ficiently to unchoke the nozzle. The exit pressure was maintained slightly above 1 atmos­

phere. A heat balance on a hydrogen-to-water heat exchanger, located at the test-section

exit, was used as a means of obtaining the outlet gas temperature. The heat-exchanger

water flow rate WH 0 was measured with an orifice and the water temperature rise 2

t:. THO with a differential iron-constantan thermocouple. A detailed description of the 2

flowing gas facility used, including the instrumentation, is given in reference 2.

METHOD OF CALCULATION

Forced-convection heat-transfer coefficients were calculated from the data for hy­

drogen flowing through an electrically heated test section, which was composed of 19 hex­

agonal passages and had a length- to equivalent-diameter ratio of 63. 5, based on the test­

section length of 20. 3 centimeters and the average equivalent diameter of 3.20 millime­

ters. Local coefficients were calculated because the surface temperature, heat flux, and

gas temperature varied significantly along the axial length of the test section. One hydro­

gen mass flow rate was used, and the electrical power to the test section was varied to

change the heat-transfer coefficient.

Wall Temperature Profiles

The wall temperature profiles were obtained in the following manner: Readings from

voltage taps, attached along the honeycomb length, were used to plot the voltage profiles

shown in figure 3. From the profiles, incremental voltages t:. V corresponding to incre­

mental test- section lengths t:. L were taken. The t:. L chosen for these calculations was

2.03 centimeters, which divided the honeycomb test section into 10 equal parts. The cur­

rent I through the honeycomb cross-sectional area Ac was measured. The local re­

sistivity ~ of the tungsten test section can then be calculated by

(All symbols are defined in appendix A.) The average incremental test-section surface

temperature was determined from a plot of tungsten resistivity as a function of tempera­

ture, as given in reference 4.

The calculated incremental surface temperature T s is plotted in figure 4 as a func­

tion of test- section length

5

POWER,q,

2500,- kW

68.3 ^^-^2000 ./^

_- ^^ 52^-^^H 150() y^ ^^^

0 .1 ~/i ^3 ^T .5 .6 .7 .8 .9 1.0Ratio of distance from test-section entrance to test-section length, x/L

Figure 4. Comparison of calculated surface temperature profiles from hexagonal-passagetest section for various amounts of power input. Hydrogen mass flow rate, 10.44 gramsper second.

Test-Section Heat Balance

The internal heat generated in a test-section increment AL equals the amount of

heat added to the flowing hydrogen (see assumptions in RESULTS AND DISCUSSION sec-

tion). Thus, for each of the 10 increments from x/L 0 to x/L 1. 0, the following

equation can be written:

Aq AVI W(HQ Hp

where AV can be read directly from the voltage profiles in figure 3 and the current ob-

tained from the tabulation in table I. With the gas flow rate W known, the change in en-

thalpy AH of the gas flowing along an increment can be calculated. After AH is calcu-

lated for the first increment and the heater inlet gas temperature T. is measured, the

outlet gas temperature from the first increment can be determined from the hydrogen

enthalpy-temperature tables of reference 5. The outlet gas temperature from this first

increment becomes the inlet gas temperature for the second or adjacent downstream in-

crement. After the 10 increments are treated in this manner, the test-section outlet gas

temperature T is finally determined. The bulk temperature per increment was calcu-

lated as the arithmetic average of the inlet and exit gas temperatures for each increment.

A plot of the gas temperature as a function of test-section length for various power inputs

is presented in figure 5. The outlet gas temperature for each run is tabulated in table I.

These temperatures were determined by assuming that all the heat generated in the test

section was added to the hydrogen. The validity of this assumption was tested by com-

6

"" V>

l-

E" .a E '" 0-E 2 '" u

~ ::::>

V'l

2500

2000

1500

1000

500

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 Ratio of distance from test-section entrance to test-section length, x/L

Figure 4. - Comparison of calculated surface temperature profiles from hexagonal-passage test section for various amounts of power input. Hydrogen mass flow rate, 10.44 grams per second.

Test-Section Heat Balance

The internal heat generated in a test- section increment b. L equals the amount of

heat added to the flowing hydrogen (see assumptions in RESULTS AND DISCUSSION sec­

tion). Thus, for each of the 10 increments from x/L = 0 to x/L = 1. 0, the following equation can be written:

b.q = b.VI = W(H - H.) o 1

where b. V can be read directly from the voltage profiles in figure 3 and the current ob­

tained from the tabulation in table 1. With the gas flow rate W known, the change in en­

thalpy b.H of the gas flowing along an increment can be calculated. After b.H is calcu­

lated for the first increment and the heater inlet gas temperature T i is measured, the

outlet gas temperature from the first increment can be determined from the hydrogen

enthalpy-temperature tables of reference 5. The outlet gas temperature from this first

increment becomes the inlet gas temperature for the second or adjacent downstream in­

crement. After the 10 increments are treated in this manner, the test-section outlet gas temperature T is finally determined. The bulk temperature per increment was calcu-o lated as the arithmetic average of the inlet and exit gas temperatures for each increment.

A plot of the gas temperature as a function of test-section length for various power inputs

is presented in figure 5. The outlet gas temperature for each run is tabulated in table 1.

These temperatures were determined by assuming that all the heat generated in the test

section was added to the hydrogen. The validity of this assumption was tested by com-

6

TABLE I. TEST-SECTION PARAMETERS AND DATA

(a) Hexagonal-passage test section. Cross-sectional area of current

flow, A 0. 927 square centimeter; free-flow area, A,,1.66 square centimeters; surface area, A 426 square centimeters;sequivalent diameter, D 3. 2 millimeters; test-section length, L,20. 3 centimeters; hydrogen inlet temperature, T_, 294 K; gas flow

rate, W, 10. 44 grams per second

Run Voltage across Current through Outlet gas Power generated

test section, test section, temperature, in test section,

V I, TQ, q,

A K kW

1 2.79 8850 454 24.7

2 4.07 9600 551 39.1

3 5.49 9600 644 52.6

4 6.97 9800 747 68.3

(b) Parallel flat-plate test section. Equivalent diameter, D

0. 285 centimeter; test-section length, L, 20. 3 centimeters

Run Voltage across Current through Outlet gas Power generated

test section, test section, temperature, in test section,

V I, TQ, q,

A K kW

900 3.38 10 800 530 36. 5

901 6.20 11 800 742 73.1

902 8.60 12 000 903 103.1

905 11.70 12 400 1136 145.0

800 pw^’kW

H 400 .---’^300-

--r"--

200 _____________________________I0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

Ratio of distance from test-section entrance to test-section length, x/L

Figure 5. Calculated hydrogen bulk temperature profiles from hexagonal-passage testsection as function of passage length for various amounts of power input. Hydrogenmass flow rate, 10.44 grams per second.

7

""

TABLE I. - TEST-SECTION PARAMETERS AND DATA

(a) Hexagonal-passage test section. Cross-sectional area of current

flow, Ac' 0.927 square centimeter; free-flow area, Af,

1. 66 square centimeters; surface area, As' 426 square centimeters;

equivalent diameter, De' 3.2 millimeters; test-section length, L,

20. 3 centimeters; hydrogen inlet temperature, T i' 294 K; gas flow

rate, W, 10.44 grams per second

Run

1

2

3 4

Run

900

901

902

905

800

700

Voltage across Current through Outlet gas Power generated

test section, test section, temperature, in test section,

V I, To' q,

A K kW

2.79 8850 454 24.7

4.07 9600 551 39.1

5.49 9600 644 52.6

6.97 9800 747 68.3

(b) Parallel flat-plate test section. Equivalent diameter, De'

0.285 centimeter; test-section length, L, 20.3 centimeters

Voltage across Current through

test section, test section,

V I,

A

3.38 10800

6.20 11 800

8.60 12000

11. 70 12400

Outlet gas

temperature,

To' K

530

742

903

1136

Power generated

in test section, q,

kW

36.5

73.1

103.1

145.0

Power, q,

kW 68.3

.i:l I-

~.

.3 E '" 0.. E .e = ::J .c c: '" ~ '0 » :r:

600

SOO

400

300

200 0

1 I .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

Ratio of distance from test-section entrance to test-section length, x/L

Figure 5. - Calculated hydrogen bulk temperature profiles from hexagonal-passage test section as function of passage length for various amounts of power input. Hydrogen mass flow rate, 10.44 grams per second.

7

paring the calculated test-section outlet gas temperature with the gas temperature deter-

mined by a heat balance on the hydrogen-to-water heat exchanger located at the test-

section exit. This calculation was possible because the temperature of the gas leaving the

test section did not drop a significant amount before the gas entered the heat exchanger.

Thus, the heat balance on the hydrogen-to-water heat exchanger could be expressed

WH,(Cp)^o T^W^(C^AT^

^^O^OT + T

V^Specific heat values for hydrogen were taken from reference 6. The balance between the

heat picked up by the heat exchanger and the heat generated in the test section did not dif-

fer by more than +/-10 percent. Thermocouples were not used to measure the exit gas

temperature because prior tests conducted with thermocouples and melting plugs showed

that the heat-balance method of calculating an exit gas temperature was satisfactory.

Heat-Transfer Geometry Factors

The values of the honeycomb test-section parameters, such as the equivalent diam-

eter D the free-flow area Ap, the surface area A and the tungsten cross-sectional

area A were based on average values because the honeycomb transverse dimensionsL/

were not uniform. A shadowgraph of the honeycomb cross section (xlO) was used to

measure the individual dimensions of the passages and webs. These measurements were

used to calculate the geometric parameters.

For each hexagonal passage, the equivalent diameter D which is equal to the dis-

tance across flats for a symmetrical hexagon, was obtained by averaging the three flat-

to-flat dimensions. The maximum flat-to-flat variation for a given passage was not more

than 0. 254 millimeter, and the average equivalent diameter for the 19 passages was

3. 200+/-0. 051 millimeters.

The free-flow area A. on the shadowgraph was measured with a planimeter. As a

check, the free-flow area was calculated on the basis of the average equivalent diameter

of 3. 20 millimeters. Hence,

8

paring the calculated test-section outlet gas temperature with the gas temperature deter­mined by a heat balance on the hYdrogen-to-water heat exchanger located at the test­

section exit. This calculation was possible because the temperature of the gas leaving the test section did not drop a significant amount before the gas entered the heat exchanger.

Thus, the heat balance on the hydrogen-to-water heat exchanger could be expressed

Specific heat values for hydrogen were taken from reference 6. The balance between the

heat picked up by the heat exchanger and the heat generated in the test section did not dif­fer by more than ±10 percent. Thermocouples were not used to measure the exit gas temperature because prior tests conducted with thermocouples and melting plugs showed that the heat-balance method of calculating an exit gas temperature was satisfactory.

Heat-Transfer Geometry Factors

The values of the honeycomb test-section parameters, such as the equivalent diam­

eter De' the free-flow area Af, the surface area As' and the tungsten cross-sectional area Ac' were based on average values because the honeycomb transverse dimensions were not uniform. A shadowgraph of the honeycomb cross section (X10) was used to

measure the individual dimensions of the passages and webs. These measurements were

used to calculate the geometric parameters. For each hexagonal passage, the equivalent diameter De' which is equal to the dis­

tance across flats for a symmetrical hexagon, was obtained by averaging the three flat­

to-flat dimensions. The maximum flat-to-flat variation for a given passage was not more than 0.254 millimeter, and the average equivalent diameter for the 19 passages was

3. 200±0. 051 millimeters. The free-flow area Af on the shadowgraph was measured with a planimeter. As a

check, the free-flow area was calculated on the basis of the average equivalent diameter

of 3.20 millimeters. Hence,

8

/ \ 2

A, IQNf-(R)! tan 30\2 /

where the number of sides per passage N is 6. The planimeter measurement and the

calculated value checked within 2 percent of each other.

The surface area A, of a regular hexagonal passage was calculated bys

A NLD. tan 30s e

In addition, the calculated value of the surface area was checked by using the measured

wetted perimeter of the passages from the shadowgraph in the following expression:

A (Wetted perimeter)x(L)s

The two values checked within 1/2 of 1 percent.

Heat-Transfer Coefficient

The local heat-transfer coefficient per increment of length is then calculated by

h ^^s^s T^

The physical properties of the Nusselt and Prandtl numbers, defined as Nu hD /kand Pr /-iC /k, respectively, were evaluated at the bulk, the film, or the surface tem-

perature. Values for viscosity p. and thermal conductivity k were obtained from ref-

erence 7.The modified Reynolds number (as discussed in ref. 8) was defined as

GD. T.Re --^ J^

^ ^where y was either the surface or the film temperature. The correlating equation used

was of the form

9

II

De 0 ~ )

2

Af = 19N 2 tan 30

where the number of sides per passage N is 6. The planimeter measurement and the

calculated value checked within 2 percent of each other.

The surface area As of a regular hexagonal passage was calculated by

In addition, the calculated value of the surface area was checked by using the measured

wetted perimeter of the passages from the shadowgraph in the following expression:

As = (Wetted perimeter)x(L)

The two values checked within 1/2 of 1 percent.

Heat-Transfer Coefficient

The local heat-transfer coefficient per increment of length is then calculated by

The physical properties of the Nusselt and Prandtl numbers, defined as Nu = hD e /k

and Pr = JlCp/k, respectively, were evaluated at the bulk, the film, or the surface tem­

perature. Values for viscosity Jl and thermal conductivity k were obtained from ref­

erence 7. The modified Reynolds number (as discussed in ref. 8) was defined as

GDe Tb Re =---­

y Jly Ty

where y was either the surface or the film temperature. The correlating equation used

was of the form

9

(^ 0.023(Re)^ 8(Pr)^ 4

Taylor (ref. 9) recommends using a heat-transfer correlation based on bulk proper-

ties and including a surface- to bulk-temperature ratio Tg /T^ raised to a power that is

a function of the length- to equivalent-diameter ratio L/D This correlation, based on

tubes, covers a wide range of conditions, including surface- to fluid-bulk-temperature

ratios to 23. This correlation is represented by

Nu, 0. 023 Re-W- 4 f^exp j- 57 1- 59 ]W \ -x- /Y De ^

RESULTS AND DISCUSSION

The basic heat-transfer results of this investigation were obtained from a

19-parallel-hexagonal-passage tungsten test section with power generation resulting from

direct-current resistance heating. Although this honeycomb was used as a heat-transfer

test section, several features (discussed in appendix B) indicate its potential as a heater

to supply hot gases.

Restrictions and Assumptions

One hydrogen mass flow rate was used, and the electrical power to the test section

was varied to change the heat-transfer coefficient. The correlating parameters were cal-

culated from the experimental data. As is true with most correlations, there were cer-

tain restrictions and assumptions under which the experimental data were used to calcu-

late the heat-transfer parameters. These restrictions and assumptions are

(1) Steady-state conditions are assumed.

(2) The static pressure drop across each of the 19 passages is the same. Because

all the passages are not uniform in flow area, the hydrogen flow will readjust so that the

sum of friction and momentum pressure drop in each passage remains constant for a

given power setting.

(3) Axial conduction is negligible. For the most extreme temperature profile, the

difference between the heat conducted into an increment and the heat conducted out of an

increment is less than 1 percent of the total internal heat generated per increment.

10

(NU)y = O. 023(Re)~· 8(pr)~· 4

Taylor (ref. 9) recommends using a heat-transfer correlation based on bulk proper­

ties and including a surface- to bulk-temperature ratio T s /Tb raised to a power that is

a function of the length- to equivalent-diameter ratio L/D e. This correlation, based on

tubes, covers a wide range of conditions, including surface- to fluid-bulk-temperature

ratios to 23. This correlation is represented by

RESULTS AND DISCUSSION

The basic heat-transfer results of this investigation were obtained from a

19-parallel-hexagonal-passage tungsten test section with power generation resulting from

direct-current resistance heating. Although this honeycomb was used as a heat-transfer

test section, several features (discussed in appendix B) indicate its potential as a heater

to supply hot gases.

Restrictions and Assumptions

One hydrogen mass flow rate was used, and the electrical power to the test section

was varied to change the heat-transfer coefficient. The correlating parameters were cal­

culated from the experimental data. As is true with most correlations, there were cer­tain restrictions and assumptions under which the experimental data were used to calcu­

late the heat-transfer parameters. These restrictions and assumptions are (1) Steady-state conditions are assumed.

(2) The static pressure drop across each of the 19 passages is the same. Because all the passages are not uniform in flow area, the hydrogen flow will readjust so that the

sum of friction and momentum pressure drop in each passage remains constant for a

given power setting. (3) Axial conduction is negligible. For the most extreme temperature profile, the

difference between the heat conducted into an increment and the heat conducted out of an

increment is less than 1 percent of the total internal heat generated per increment.

10

YI (4) Radiation loss is negligible. The outer surface of the honeycomb radiated to the

containment vessel walls. This radiation loss is approximately 1 percent of the total heat

generated. Even for the high-power run (run 4, see table I), a calculated radiation loss

from the highest temperature increment was less than 5 percent of the heat generated in

that increment.

(5) All the heat generated in the 20. 3-centimeter test-section length is transferred

to the gas flowing through the hexagonal passages.(6) At any particular axial position along the hexagonal passage, the transverse sur-

face temperature remains constant. Or stated differently, the wall temperature for a

given power level varies only in the axial direction. The validity of this statement is

based on several self-correcting effects. Radiation heat transfer between hexagonal faces

as well as transverse conduction between webs tends to keep the webs at a uniform tem-perature. In addition, webs that tend to run cooler have lower electrical resistivity, and,consequently, more current can flow in these webs. As a result, the additional currenttends to raise the surface temperature.

(7) The individual passages did not vary along the length of the test section. Post-

test inspection of sectioned portions of the heater showed that variations in equivalent di-

ameter from passage to passage at any given axial position remained constant along the

passage length.

(8) No attempt was made to modify the heat-transfer coefficients for sharp-corner

effects. Reference 10 shows these effects to be secondary in a honeycomb.

(9) The density of the tungsten honeycomb heater was about 98 percent of theoretical.

No correction was applied to the resistivity-temperature relation of tungsten in the calcu-

lation of the wall temperature profiles.

Nonuniform Passage Effect

The significant test-section dimensions are given in table I along with appropriate

test data for both hexagonal-passage and parallel flat-plate test sections. The informa-

tion from table I, when used in conjunction with the voltage profiles of figure 3 and the

tungsten temperature-resistivity relation presented in reference 4, is sufficient to make

the heat-transfer calculations of this investigation.

However, before the heat-transfer data are discussed, it is important to determine

whether or not the variation in equivalent diameter between individual passages

(D 3. 200+/-0. 051 mm) has a significant effect on the heat-transfer results. Conse-

quently, a calculation was made, based on inlet and exit conditions. A severe, but highly

unlikely, condition was considered in which one small passage (D 3. 15 mm) was sur-fci

rounded by six passages with an equivalent diameter equal to the average, D 3. 20 mil-

| n

I

I I I'! I

(4) Radiation loss is negligible. The outer surface of the honeycomb radiated to the

containment vessel walls. This radiation loss is approximately 1 percent of the total heat

generated. Even for the high-power run (run 4, see table I), a calculated radiation loss

from the highest temperature increment was less than 5 percent of the heat generated in

that increment.

(5) All the heat generated in the 20. 3-centimeter test-section length is transferred

to the gas flowing through the hexagonal passages.

(6) At any particular axial position along the hexagonal passage, the transverse sur­

face temperature remains constant. Or stated differently, the wall temperature for a

given power level varies only in the axial direction. The validity of this statement is

based on several self-correcting effects. Radiation heat transfer between hexagonal faces

as well as transverse conduction between webs tends to keep the webs at a uniform tem­

perature. In addition, webs that tend to run cooler have lower electrical reSistivity, and,

consequently, more current can flow in these webs. As a result, the additional current

tends to raise the surface temperature.

(7) The individual passages did not vary along the length of the test section. Post­

test inspection of sectioned portions of the heater showed that variations in equivalent di­

ameter from passage to passage at any given axial position remained constant along the

passage length.

(8) No attempt was made to modify the heat-transfer coefficients for sharp-corner

effects. Reference 10 shows these effects to be secondary in a honeycomb.

(9) The density of the tungsten honeycomb heater was about 98 percent of theoretical.

No correction was applied to the resistivity-temperature relation of tungsten in the calcu­

lation of the wall temperature profiles.

Nonu niform Passage Effect

The significant test-section dimensions are given in table I along with appropriate

test data for both hexagonal-passage and parallel flat-plate test sections. The informa­

tion from table I, when used in conjunction with the voltage profiles of figure 3 and the

tungsten temperature-resistivity relation presented in reference 4, is sufficient to make

the heat-transfer calculations of this investigation.

However, before the heat-transfer data are discussed, it is important to determine

whether or not the variation in equivalent diameter between individual passages

(De = 3. 200±0. 051 mm) has a significant effect on the heat-transfer results. Conse­

quently, a calculation was made, based on inlet and exit conditions. A severe, but highly

unlikely, condition was considered in which one small passage (De = 3. 15 mm) was sur­

rounded by six passages with an equivalent diameter equal to the average, De = 3.20 mil-

11

limeters. The calculation was subject to the same assumptions discussed earlier in this

section; that is, constant static pressure drop across all the passages and constant wall

surface temperature at a particular axial position. The heat-transfer surface area perpassage is proportional to the passage equivalent diameter, and the passage free-flowarea is proportional to the square of the equivalent diameter.

Under these conditions, the calculated difference in the average heat flux (heat trans-ferred per unit surface area) between the small and average size passages for run 4 (thehigh-power run) is less than 1 percent. The heat transferred between passages is not the

same: the variation is about 2 percent. Under the conditions of this investigation, the

heat-transfer coefficient is approximately proportional to the heat flux. Therefore, the

conclusion was that the variation in equivalent diameter was not a significant factor in the

heat-transfer results of this investigation. However, as described in reference 11,cases exist where the heat generated per passage remains constant (nuclear rocket appli-

cation) and variations in equivalent diameter can cause significant surface temperaturevariations.

Heat-Transfer Correlations

The local heat-transfer coefficients of the honeycomb were calculated from the wall

surface temperature profiles shown in figure 4. For the hexagonal-passage test section,the value of L/D was 63. 5. Ten equally spaced increments were chosen along the

t/

length of the test section to calculate the local heat-transfer coefficients. The values of

the ratio x/D ranged from 3. 17 (at the center of the first increment) to 60. 3 (at the

center of the last increment). Ten local heat-transfer coefficients were calculated for

each of the four different power inputs to the test section. The test runs are character-

ized by the power input to the heater. The maximum exit Mach number was 0. 9.

Hexagonal and flat-plate test data. The first heat-transfer equation correlating the

data consists of a modified Dittus-Boelter equation of the form

Nu^ 0. 023(Re^)- s(Pr^o 4

where the hydrogen physical properties are evaluated at the film temperature. This

method of correlation was used to compare the heat-transfer results of the hexagonal-passage data with those obtained from the parallel flat-plate data of reference 1. The

parallel flat-plate data correlated best with the Dittus-Boelter equation when the massvelocity was based on the minimum cross-sectional flow area (at a position where the

plate supporting spacers were located). In addition, the surface area of the 10 sets of

spacers exposed to the hydrogen was used as part of the heat-transfer surface area.

12

limeters. The calculation was subject to the same assumptions discussed earlier in this section; that is, constant static pressure drop across all the passages and constant wall

surface temperature at a particular axial position. The heat-transfer surface area per passage is proportional to the passage equivalent diameter, and the passage free-flow area is proportional to the square of the equivalent diameter.

Under these conditions, the calculated difference in the average heat flux (heat trans­ferred per unit surface area) between the small and average size passages for run 4 (the high-power run) is less than 1 percent. The heat transferred between passages is not the same: the variation is about 2 percent. Under the conditions of this investigation, the heat-transfer coefficient is approximately proportional to the heat flux. Therefore, the conclusion was that the variation in equivalent diameter was not a Significant factor in the heat-transfer results of this investigation. However, as described in reference 11, cases exist where the heat generated per passage remains constant (nuclear rocket appli­cation) and variations in equivalent diameter can cause significant surface temperature variations.

Heat-Tra nsfer Correlations

The local heat-transfer coefficients of the honeycomb were calculated from the wall surface temperature profiles shown in figure 4. For the hexagonal-passage test section,

the value of L/De was 63.5. Ten equally spaced increments were chosen along the length of the test section to calculate the local heat-transfer coefficients. The values of

the ratio X/De ranged from 3.17 (at the center of the first increment) to 60.3 (at the center of the last increment). Ten local heat-transfer coefficients were calculated for each of the four different power inputs to the test section. The test runs are character­ized by the power input to the heater. The maximum exit Mach number was 0.9.

Hexagonal and flat-plate test data. - The first heat-transfer equation correlating the data consists of a modified Dittus-Boelter equation of the form

where the hydrogen physical properties are evaluated at the film temperature. This

method of correlation was used to compare the heat-transfer results of the hexagonal­passage data with those obtained from the parallel flat-plate data of reference 1. The parallel flat-plate data correlated best with the Dittus-Boelter equation when the mass velocity was based on the minimum cross-sectional flow area (at a pOSition where the plate supporting spacers were located). In addition, the surface area of the 10 sets of spacers exposed to the hydrogen was used as part of the heat-transfer surface area.

12

,

I

fThus, the modified film Reynolds number (given in ref. 8) was calculated as

^naA ^^ T;

and the correlating equation was

Nu^ 0. 023(Re^)- 8(Pr^o 4

All the honeycomb data fell within a band of +17 and -22 percent of this film correlation.

The hydrogen mass flow rate through both test sections was identical, and the L/Dgand equivalent diameter of both test sections were similar (see table I). However, a com-

parison of the local turbulent heat-transfer coefficients in figures 6 (a) and (b) shows that

the honeycomb data fell below the flat-plate spacer-supported data. Possibly the hydro-

gen flow around the 10 sets of spacers increased the turbulence sufficiently to cause the

flat-plate data to fall higher than that of the honeycomb. In figure 7, the honeycomb data

were plotted by using a modified Reynolds number based on the honeycomb surface tem-

perature; and the hydrogen physical properties were evaluated at the surface temperature.

The data fall in a more orderly trend around the correlating line, which is represented by

1001 i^.

8o! ^--

-^60

V // VrtS^

60 /^/ 40 svy^a i^^^gtffr A’y-

^ ^1 ^i ? / t-^y 20 ^^I" ^& Power, ^ Run power.

^’i i20 A" ^ /

^e ^^ 0 6810

/ = A 9()5 145-0 =^1 / a ^S 8 / G 902 103.1

\. .2: a / o / 0 TO1 73.1

S / -= ^24;7 ^== ^^ 900 36!58 / ---I---I 4’ J---I4 8 10 20 40xl03 4 8 10 20 40x103

I Modified film Reynolds number, Re(, (GDefufllT^T;) Modified film Reynolds number, fGmax^WV^1(a) Test section consisting of 19 parallel hexagonal passages. Corre- (b) Test section consisting of five flat plates separated by spacerslating line, NU( 0.023 Re^Pr0-4. (ref. 1). Correlating line, NU(0.023[(G^^axDe/uf)(TbfTf)]o’8pr?’4

Figure 6. Correlation of local turbulent heat-transfer coefficients. Hydrogen mass flow rate, 10.44 grams per second.

?

I| 13

I !

I i i.1

", J"

(,'

,

Thus, the modified film Reynolds number (given in ref. 8) was calculated as

and the correlating equation was

All the honeycomb data fell within a band of +17 and -22 percent of this film correlation.

The hydrogen mass flow rate through both test sections was identical, and the LID e and equivalent diameter of both test sections were similar (see table I). However, a com­parison of the local turbulent heat-transfer coefficients in figures 6(a) and (b) shows that

the honeycomb data fell below the flat-plate spacer-supported data. Possibly the hydro­gen flow around the 10 sets of spacers increased the turbulence sufficiently to cause the flat-plate data to fall higher than that of the honeycomb. In figure 7, the honeycomb data

were plotted by using a modified Reynolds number based on the honeycomb surface tem­

perature; and the hydrogen physical properties were evaluated at the surface temperature. The data fall in a more orderly trend around the correlating line, which is represented by

'ri Power, q,

kW

068.3 052.6 I:::. 39.1 024.7

I 2 4 6 8 10 20

Modified film Reynolds number. Ref, (GDel~f)(TilTf)

la) Test section consisting of 19 parallel hexagonal passages. Corre­lating line, NUf = 0.023 ReV· 8Prp· 4.

20 Run Power,

q, kW

I:::. 905 o 902 o 901 o 900

I 46810 20

Modified film Reynolds number, (GmaxDel~f)(TblTf)

145.0 103.1 73.1 36.5

40x103

(b) Test section conSisting of five flat plates separated by spacers (ref. 1). Correlating line, NUf = 0.023[(GmaxDd~f)lTilTf)]0.8PrV.4.

Figure 6. - Correlation of local turbulent heat-transfer coefficients. Hydrogen mass flow rate, 10.44 grams per second.

13

801---------

I "E^ <^/& 40 ..IP"-s^ a^I =3" .<p&

^ ^r Power,S | 20 f^ q,

^ 1 .^ kw

S 4’ 0 68.31 S 00 52-6

^ 10 -----7’^^----- A 39.1^6____________ a 24.7 I

-S /.___

^0

2 4 6 8 10 20 40xl03Modified surface Reynolds number, Re, (GDg/pgXTiyT^)

Figure 7. Correlation of local turbulent heat-transfer coefficients.Hydrogen mass flow rate, 10.44 grains per second; test section con-sisted of 19 parallel hexagonal passages. Correlating line,

NUs’O^RefpPrI?^.

the following equation given in reference 8:

1^ \0. 8Ap \0. 8

Nu^ O. ,.3 ^ g" (P^V^-s / Vs/

Eighty-five percent of the data fall within a band of +20 and -10 percent of this cor-

relating line. Of even more significance is the fact that the points which deviate the most

from the correlating line are either test-section entrance points, where the amount of

heat transferred is low, or test-section exit points, where the surface temperature is

high. Points away from both the entrance and exit regions correlate well with the modi-

fied surface Reynolds number equation. Apparently, the heat-transfer results from par-

allel flow in 19 hexagonal passages, as well as results from flow between five parallel

flat plates supported by spacers, correlate well when the smooth-tube correlations of ref-

erence 8 are used.

Figures 8 and 9 are based on the data of run 4, the high-power run, and illustrate the

typical axial variation of the significant heat-transfer parameters for a given gas flow

rate. The similarity between the shapes of the incremental heat-transfer rate (incre-mental heat generation rate) and the curves of the honeycomb surface temperature occurs

because the electrical resistivity of tungsten varies almost linearly with temperature.

For a given run, the current is constant, and the incremental heat generation varies as

the tungsten resistivity.

The decrease in the modified surface Reynolds number from inlet to exit is a

14

~ :::===---,-------1 I I II~ ~/ ~ I II .jffi/ II

E"". 40 I----+_ ~ ~ n I o>~~~p ,1 '" '" ~ ~~ 20 ~ q, -t--

i~ I p~ 0 6:~3 ~ E l20 0 52.6 '0 a.. 10 / I T b. 39. I --._!:! 8 f----/~ i I I I I 0 24 7 --'" / I i --cr: 6'---_v-'----- I I I I I I

I 2 4 6 8 10 20 Modified surface Reynolds number, Ref, (GDellls)(Ti/Tsl

Figure 7. - Correlation of local turbulent heat-transfer coefficients. Hydrogen mass flow rate, 10.44 grams per second; test section con­sisted of 19 parallel hexagonal passages. Correlating line, Nus = 0.023 Re2·8Pr2·4.

the following equation given in reference 8:

(GD )0. 8(T )0.8 Nus = 0. 023\Y'se T: (Pr s)o. 4

Eighty-five percent of the data fall within a band of +20 and -10 percent of this cor­

relating line. Of even more significance is the fact that the points which deviate the most

from the correlating line are either test-section entrance points, where the amount of

heat transferred is low, or test-section exit points, where the surface temperature is

high. Points away from both the entrance and exit regions correlate well with the modi­

fied surface Reynolds number equation. Apparently, the heat-transfer results from par­

allel flow in 19 hexagonal passages, as well as results from flow between five parallel

flat plates supported by spacers, correlate well when the smooth-tube correlations of ref­

erence 8 are used. Figures 8 and 9 are based on the data of run 4, the high-power run, and illustrate the

typical axial variation of the significant heat-transfer parameters for a given gas flow

rate. The similarity between the shapes of the incremental heat-transfer rate (incre­

mental heat generation rate) and the curves of the honeycomb surface temperature occurs

because the electrical resistivity of tungsten varies almost linearly with temperature.

For a given run, the current is constant, and the incremental heat generation varies as

the tungsten resistivity.

The decrease in the modified surface Reynolds number from inlet to exit is a

14

\

"I

I 4.0[- 4000i- 16,-

3 5 3500 14 ./^’^S ^---7^--^

"^ Temperature ratio~-^^/~^^^3.0-^3000- <1. 12- /" / \

/ /- ^ E / /|- 2.5-l 2500-| io- / /Su E -S / /

\\ I 2.0-t 2000-| 8- ^^ / ^^" ^ -s ^----^^^’^ / -/^E ^," 5 / /\^ 1.5-| 1500- | 6- y /

^^ ^’ ’^ Average surface1.0- 1000- 4- Incremental heat- ^^^ ^^ temperature

transfer rate-^^^___^^^^^^ ^^^^5 500 2 ----^----I-~~^~~~~^ _10 -1 -2 .3 .4 .5 .6 .7 .8 .9 1.0

Ratio of distance from test-section entrance to test-section length, x;L

Figure 8. Typical variation of temperatures and heat-transfer rate with test-sectionlength. Hydrogen mass flow rate, 10.44 grams per second, power input, 68.3 kilowatts;test section consisted of 19 parallel hexagonal passages.

14000,- 35i- 3400 ------I~~^

-^^^

{ 12000 30 -JR3200 ^---^ surface NLSsel: nunber"-01 E ^^-

^^^10 000 sf 25 i 3000 \a" =. Modified surface \

& s --Reynolds number ’<8000 H 20 --’2800 ^ ~---^^ \

^ a^ ^^ ’^^^ \

I a0. | l5 -|2600 s^ ^ \s ^ ---transfer ^^ \

^ S coefficient \. ^^^ 4000 10-^2400 ^^ \ ^\5 . \

^^^^,

I 2000 5- 2200 ^^ ~~~------^^:--^^^^0 n- 2000

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0Ratio of distance from test-section entrance to test-section length, x/L

’!’’’

Figure 9. Typical variation of Reynolds number, Nusselt number, and heat-transfer co-efficient with test-section length. Hydrogen mass flow rate, 10.44 grams per second;power input, 68.3 kilowatts; test section consisted of 19 parallel hexagonal passages.

15

(

!

i ~ Ii I' f I, I ,

.c

S I-

~~

E E .3 E a.> Cl.

E a.> I-

4.0

3.5

3.0

2.5

2.0

1.5

1.0

.5

4000

3500

"" 1-'" 3000 E' .3 E 2500 a.> Cl.

E .!!l a.>

~ 2000 :::J Vl

a.>

'" E 1500 a.> >

...;

1000

500

16

14 s: """ a <J

12 <u'

E L.

~ 10 C

E 1: ro a.> 8 .<=

ro C a.> E E 6 u E

Incremental heat-'- Average surface

4 temperature transfer rate...,

2 ~ 0 .1 .2 .3 .4 .5 .6 .7 .8 .9

Ratio of distance from test-section entrance to test-section length, x/L 1.0

Figure 8. - Typical variation of temperatures and heat-transfer rate with test-section length. Hydrogen mass flow rate, 10.44 grams per second, power input, 68.3 kilowatts; test section consisted of 19 parallel hexagonal passages.

34001

Q32001 c.J"

E u ~3000

c'2800 a.>

;g Q;

82600

~ c

~ 2400 ro a.>

.<=

g 2200 -'

r--r--r-- I I I I I I I---~,Urface Nusselt number

""I' ... Modified su rface ""

·r:-:N~'~1:~ "'", J h,t;;:-t'--- ~t'---t'--- 1"'-1"'-

-r---- transfer '" ~ ' ........ coefficient "'- 1'-........" '"

I "'-r--,I'-- "''--.. "i ........ -..t---i---i

I-I--

t-I--

2000 o

1llllh~c-C- ,~~ .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

Ratio of distance from test-section entrance to test-section length, x/L

Figure 9. - Typical variation of Reynolds number, Nusselt number, and heat-transfer co­efficient with test-section length. Hydrogen mass flow rate, 10.44 grams per second; power input, 68.3 kilowatts; test section consisted of 19 parallel hexagonal passages.

15

hydrogen-property effect influenced by the increase in hydrogen viscosity with tempera-

ture. Concurrent with this behavior is the inverse effect of the ratio T /T, This ratio

begins to increase rapidly at an x/D of about 0. 45 and then levels off before decreasing

near the test-section exit. The Nusselt number curve, with a slight variation due to a

Prandtl number effect, varies in a manner similar to the shape of the modified surface

Reynolds number curve.

Consider the heat-transfer coefficient along the test section. For a given equivalent

diameter and constant hydrogen thermal conductivity, the heat-transfer coefficient would

vary directly with the Nusselt number curve. This variation is shown over about half the

test-section length. However, as the hydrogen thermal conductivity increases with tern-

perature along the length of the test section (particularly along the latter half), the heat-

transfer coefficient then varies directly with both the Nusselt number and the hydrogen

thermal conductivity. The thermal conductivity of hydrogen, at about atmospheric pres-

sure, increases rapidly with temperature, particularly at high temperatures. As a con-

sequence, the heat-transfer coefficient levels off at x/L of about 0. 8 and begins to in-

crease in the region near the test-section exit.

Heat-transfer coefficient modified for effect of length- to equivalent-diameter

ratio. For symmetrically heated straight tubes, Taylor (ref. 9) recommends a correla-

tion line that will predict local single-phase forced-convection heat-transfer coefficients

for turbulent flow over a much greater range of conditions than was previously possible.

The correlation line that Taylor used for surface- to fluid-bulk-temperature ratios up to

23 is represented by

Nu^ O. O^ Re^Pr^ ^exp jo. ST l^j\ V

where the Nusselt, Reynolds, and Prandtl numbers are all evaluated at the fluid bulk tem-

perature but are modified by a ratio of surface to bulk temperature raised to a power that

is a function of x/D the distance along the test section.t?

The data of the present investigation, correlated with this equation, are shown in fig-

ure 10. Eighty-five percent of the data fall within +/-15 percent of the correlating line.

The points that deviate the most from the correlating line are the entrance points from

the three higher power runs and some of the intermediate points from the low-power run.

Nevertheless, all the data points fall within +/-20 percent of the correlating line used by

Taylor.

16

hydrogen-property effect influenced by the increase in hydrogen viscosity with tempera­

ture. Concurrent with this behavior is the inverse effect of the ratio T s /T b. This ratio begins to increase rapidly at an x/De of about 0.45 and then levels off before decreasing

near the test-section exito The Nusselt number curve, with a slight variation due to a

Prandtl number effect, varies in a manner similar to the shape of the modified surface

Reynolds number curve.

Consider the heat-transfer coefficient along the test section. For a given equivalent

diameter and constant hydrogen thermal conductivity, the heat-transfer coefficient would

vary directly with the Nusselt number curve. This variation is shown over about half the

test-section length. However, as the hydrogen thermal conductivity increases with tem­

perature along the length of the test section (particularly along the latter half), the heat­

transfer coefficient then varies directly with both the Nusselt number and the hydrogen thermal conductivity. The thermal conductivity of hydrogen, at about atmospheric pres­

sure, increases rapidly with temperature, particularly at high temperatures. As a con­

sequence, the heat-transfer coefficient levels off at x/L of about 0.8 and begins to in­crease in the region near the test-section exit.

Heat-transfer coefficient modified for ~ffect of len~h- to equivalent-dia~eter

ratio. - For symmetrically heated straight tubes, Taylor (ref. 9) recommends a correla­tion line that will predict local single-phase forced-convection heat-transfer coefficients

for turbulent flow over a much greater range of conditions than was previously possible.

The correlation line that Taylor used for surface- to fluid-bulk-temperature ratios up to

23 is represented by

NUb" O. 023 Re~· 8Pr~· 4 (::}xp - 0.57

where the Nusselt, Reynolds, and Prandtl numbers are all evaluated at the fluid bulk tem­

perature but are modified by a ratio of surface to bulk temperature raised to a power that

is a function of x/De' the distance along the test section. The data of the present investigation, correlated with this equation, are shown in fig­

ure 10. Eighty-five percent of the data fall within ±15 percent of the correlating line. The points that deviate the most from the correlating line are the entrance points from

the three higher power runs and some of the intermediate points from the low-power run.

Nevertheless, all the data points fall within ±20 percent of the correlating line used by

Taylor.

16

---_._-". __ ._- ,,- --_ ...... __ .. " . _ ... _-_._ ... III •• _. I I 11 ••• , ••• __ ,., •••••••• ,1, •••••

k

:{’ 100 ~~^-90 ^---\ ’^ 80 ^ //

^ 70 ^^60 ^. T^K 5lc3^?1 power’

: 50 0^^ w<? / 0 68.3

T / 0 52-6~o A 39.1

??’ i D 24.7

^lO 20 30 40x103Bulk Reynolds number, Re^, GDgfp^

Figure 10. Correlation of local heat-transfer coefficients

by method of reference 9. Hydrogen mass flow rate,10.44 grams per second. Test section consisted of 19

parallel hexagonal passages. Correlating line,

Nun- 0.023 Re^Prg-^nb)-^’’7-1-59’0^’]-

SUMMARY OF RESULTS

An investigation of heat transfer from parallel hexagonal passages to flowing hydro-

gen was conducted on a test section with a length- to equivalent-diameter ratio of 63. 5.The data cover ranges of surface- to hydrogen-temperature ratios from 1. 43 to 3. 38,bulk Reynolds numbers from 12 950 to 21 960, surface temperatures to 2275 K, and outlet

hydrogen temperatures to 747 K. The inlet hydrogen temperature was constant at 294 K,and the maximum exit Mach number was 0. 9.

Local turbulent heat-transfer coefficients obtained experimentally from a 19-parallel-

hexagonal-passage test section correlated when a modified Dittus-Boelter equation was

used with hydrogen properties evaluated at the film, surface, and bulk temperatures.The film and surface correlating equations were of the form

(^ ^^(Re)0- ^)^- 4

where y was either the film or surface temperature. All the data based on the film

equation fell within +17 and -22 percent of the film correlating equation. Eighty-five per-

cent of the data based on the surface equation fell within a band of +20 and -10 percent of

the surface correlating equation.

’! The correlating equation based on bulk properties is represented by

17

i,

I

i 'I]

i :~

I _

= OJ o :3 ~

, r­

'" o -:c t-

'" t--iT 9=> c.. -:0 :::J Z

100[ 90

so, 70,

60

1 50[

40

30 10

Power, q,

kW

o 6S.3 o 52.6 l:; 39.1 o 24.7

I 20 30 40xl03

Bulk Reynolds number, Reb' GDe/J.lb

Figure 10. - Correlation of local heat-transfer coefficients by method of reference 9. Hydrogen mass flow rate, 10.44 grams per second. Test section consisted of 19 parallel hexagonal passages. Correlating line, NUb = 0.023 Reg· sprg· 4(T sIT bdo. 57-1. 59f(xlDe)]·

SUMMARY OF RESULTS

An investigation of heat transfer from parallel hexagonal passages to flowing hydro­

gen was conducted on a test section with a length- to equivalent-diameter ratio of 63. 5.

The data cover ranges of surface- to hydrogen-temperature ratios from 1. 43 to 3. 38,

bulk Reynolds numbers from 12 950 to 21 960, surface temperatures to 2275 K, and outlet

hydrogen temperatures to 747 K. The inlet hydrogen temperature was constant at 294 K,

and the maximum exit Mach number was 0.9.

Local turbulent heat-transfer coefficients obtained experimentally from a 19-parallel­

hexagonal-passage test section correlated when a modified Dittus-Boelter equation was

used with hydrogen properties evaluated at the film, surface, and bulk temperatures.

The film and surface correlating equations were of the form

(Nu)y = O. 023(Re)~· 8(pr)~· 4

where y was either the film or surface temperature. All the data based on the film

equation fell within +17 and -22 percent of the film correlating equation. Eighty-five per­

cent of the data based on the surface equation fell within a band of +20 and -10 percent of

the surface correlating equation.

The correlating equation based on bulk properties is represented by

17

Nu^ 0. 023 Re;;-^ 4 f^exp (o. 57 L-59]W \ -x- j\ V

This correlation is based on bulk properties and includes a surface- to fluid-bulk-

temperature ratio T /T^ raised to a power that is a function of the length- to equivalent-S D

diameter ratio x/D Eighty-five percent of the data fell within +/-15 percent of this cor-^t/

relating line, and all the data fell within +/-20 percent of it.

In this investigation, local heat-transfer coefficients, expressed in terms of the di-

mensionless parameters Nusselt number, Prandtl number, and Reynolds number

showed good agreement when they were compared with the results obtained from a test

section consisting of five parallel spacer-supported flat plates. The comparison was

made for various power inputs. The hydrogen flow rate was identical in both tests, and

the lengths of the test sections as well as the equivalent diameters were also approxi-

mately equal.

Lewis Research Center,National Aeronautics and Space Administration,

Cleveland, Ohio, October 7, 1968,120-27-04-54-22.

\

18

J

This correlation is based on bulk properties and includes a surface- to fluid-bulk­

temperature ratio T s /Tb raised to a power that is a function of the length- to equivalent­

diameter ratio x/De' Eighty-five percent of the data fell within ±15 percent of this cor­relating line, and all the data fell within ±20 percent of it.

In this investigation, local heat-transfer coefficients, expressed in terms of the di­mensionless parameters - Nusselt number, Prandtl number, and Reynolds number -

showed good agreement when they were compared with the results obtained from a test

section consisting of five parallel spacer-supported flat plates. The comparison was

made for various power inputs. The hydrogen flow rate was identical in both tests, and

the lengths of the test sections as well as the equivalent diameters were also approxi­

mately equal.

Lewis Research Center,

18

National Aeronautics and Space Administration,

Cleveland, Ohio, October 7, 1968,

120-27 -04- 54-22.

I

II

V

APPENDIX A

SYMBOLS

IA cross-sectional area of current Aq incremental rate of heat transfer

j flow, cm2 to gas, kW

I A. free-flow area, cm2 Re^ Reynolds number, GDg/^i’1 9t A surface area, cm Re- modified film Reynolds number,’i’ 2 (GD /u. (T /T )j’ AA incremental surface area, cm e’ ^i" b’ f

s

,!’ C specific heat of hydrogen at con- ^s modified surface Reynolds num-p

stant pressure, J/(g)(K) ber, (GD^)(T^/T,)

D equivalent diameter, cm T temperature, K

// 2\ AT change in temperature, KG mass velocity, g/(sec)(cm

AV incremental voltage drop, VG mass velocity at spacer cross ’’max "9

section, g/(sec)(cm W gas flow rate, g/sec

H enthalpy, (kW)(sec)/g x distance from entrance of test

AH change in enthalpy, (kW)(sec)/g section, cm

h local heat-transfer coefficient, ^ absolute viscosity of hydrogen,

JAsecXcm2)^) g/(sec)(cm)

I current A c resistivity of tungsten, ohm-cm

k thermal conductivity of hydrogen, Subscripts:

J/(cm)(sec)(K) b bulk (when applied to properties,

indicates evaluation at averageL test-section length, cm

bulk temperature T,

AL incremental test-section length,f film (when applied to properties,

/ indicates evaluation at averageN number of sides per passage

^ temperature T^)Nu Nusselt number, hD^/k g heat-exchanger exit gaspr Prandtl number, Cp^/k hydrogen

q rate of heat transfer to gas, kW

19

I.iiIsJ

~ "

I

! .j

1 I l ,I

i I I

,J

I '1 •

I I I

A c

H

~H

h

I

k

L

~L

N

Nu

Pr

q

APPENDIX A

SYMBOLS

cross-sectional area of current ~q

flow, cm2

free-flow area, cm2 Reb

surface area, cm2 Ref

incremental surface area, cm2

specific heat of hydrogen at con- Res

stant pressure, J/(g)(K)

equivalent diameter, cm

mass velocity, g/(sec)(cm2)

mass velocity at spacer cross

section, g/(sec)(cm2)

enthalpy, (kW)(sec)/g

change in enthalpy, (kW)(sec)/g

local heat-transfer coefficient, 2

J/(sec)(cm )(K)

current, A

T

~T

~V

W

x

incremental rate of heat transfer

to gas, kW

Reynolds number, GD e / flb

modified film Reynolds number,

(GDe /flf) (Tb /T f)

modified surface Reynolds num-

ber, (GDe/fls)(Tb/Ts)

temperature, K

change in temperature, K

incremental voltage drop, V

gas flow rate, g/sec

distance from entrance of test

section, cm

absolute viscosity of hydrogen,

g/(sec)(cm)

resistivity of tungsten, ohm-cm

thermal conductivity of hydrogen,

J/(cm)(sec)(K)

Subscripts:

test-section length, cm

incremental test-section length,

cm

number of sides per passage

Nusselt number, hD e /k

Prandtl number, Cpfl/k

rate of heat transfer to gas, kW

b bulk (when applied to properties,

f

indicates evaluation at average

bulk temperature T b)

film (when applied to properties,

indicates evaluation at average

film temperature T f)

heat- exchanger exit gas

hydrogen

19

Subscripts: s surface (when applied to properties,

indicates evaluation at averageHnO water

+ rr.^ surface temperature Ti hydrogen inlet to test section

y indicates either film or surface

o hydrogen outlet from test section temperature evaluation of prop-

erties

,

v

20

Subscripts:

H 20 water

i

o

20

hydrogen inlet to test section

hydrogen outlet from test section

s

y

surface (when applied to properties, indicates evaluation at average surface temperature T s)

indicates either film or surface temperature evaluation of prop­

erties

Ill

APPENDIX B

ADVANTAGES OF HONEYCOMB AS HOT-GAS HEATER OVER PARALLEL

FLAT-PLATE AND MESH-TYPE HEATERS’^

The honeycomb test section was far easier to instrument with voltage taps along its

length than were the parallel flat-plate heater (ref. 1) and the mesh heating elements

(ref. 3). This ease of instrumentation made it possible to obtain more measurements in

,̂f regions of steep temperature gradients and thus to determine better the wall temperature

profile.

At present, the main disadvantage in using a tungsten honeycomb heater, rather than

a parallel flat-plate or a mesh-type heater, is the high initial cost. However, as the

tungsten fabrication technology advances, the tungsten honeycomb heaters will probably

become more economical. When it is used with nonoxidizing gases, a honeycomb heating

element has many advantages over both the parallel flat-plate and mesh-type heaters.

Some of these advantages are listed as follows:

(1) A strong structure for a given surface- to-volume ratio.

No spacers are required as supports; thus, less pressure drop occurs for a given mass

J velocity and L/D(2) Continuous flow passages along the length of the test section, which prevents

cross flow between passages.

No outside insulating housing is needed to surround the test section; consequently, a

higher outlet gas temperature can be obtained for a given maximum surface temperature.

(3) Relative thermal expansion between insulating housing and heater element is not

I,’ a concern.

No insulating housing is required.

21

t

APPENDIX B

ADVANTAGES OF HONEYCOMB AS HOT-GAS HEATER OVER PARALLEL

FLAT-PLATE AND MESH-TYPE HEATERS

The honeycomb test section was far easier to instrument with voltage taps along its

length than were the parallel flat-plate heater (ref. 1) and the mesh heating elements

(ref. 3). This ease of instrumentation made it possible to obtain more measurements in

regions of steep temperature gradients and thus to determine better the wall temperature

profile.

At present, the main disadvantage in using a tungsten honeycomb heater, rather than

a parallel flat-plate or a mesh-type heater, is the high initial cost. However, as the

tungsten fabrication technology advances, the tungsten honeycomb heaters will probably

become more economical. When it is used with nonoxidizing gases, a honeycomb heating

element has many advantages over both the parallel flat-plate and mesh-type heaters.

Some of these advantages are listed as follows:

(1) A strong structure for a given surface- to-volume ratio. No spacers are required as supports; thus, less pressure drop occurs for a given mass

velocity and LID . e (2) Continuous flow passages along the length of the test section, which prevents

cross flow between passages. , "! No outside insulating housing is needed to surround the test section; consequently, a ,

i ! , , i! , I

I" I',

i I

higher outlet gas temperature can be obtained for a given maximum surface temperature.

(3) Relative thermal expansion between insulating housing and heater element is not

a concern. No insulating housing is required.

21

REFERENCES

1. Slaby, Jack G. Maag, William L. ; and Siegel, Byron L. Laminar and Turbulent

Hydrogen Heat Transfer and Friction Coefficients Over Parallel Plates at 5000 R.

NASA TN D-2435, 1964.

^- 2. Slaby, Jack G. Siegel, Byron L. Mattson, William F. and Maag, William L. A

4500 R (2500 K) Flowing-Gas Facility. NASA TM X-1506, 1968.

3. Siegel, Byron L. Design and Operation of a High-Temperature Tungsten-Mesh Gas

Heater. NASA TM X-1466, 1967. ’^4. Weast, Robert C. ed. Handbook of Chemistry and Physics. 37th ed. Chemical

Rubber Publ. Co. 1955, p. 2360.

5. Keenan, Joseph H. Kaye, Joseph: Gas Tables Thermodynamic Properties of Air,Productions of Combustion and Component Gases and Compressible Flow Functions.

John Wiley & Sons, Inc. 1948.

6. Svehia, Roger A. Estimated Viscosities and Thermal Conductivities of Gases at

High Temperatures. NASA TR R-132, 1962.

7. Grier, Norman T. Calculation of Transport Properties and Heat-Transfer Param-

eters of Dissociating Hydrogen. NASA TN D-1406, 1962.

8. Humble, Leroy V. Lowdermilk, Warren H. and Desmon, Leiand G. Measure-

ments of Average Heat-Transfer and Friction Coefficients for Subsonic Flow of Air

in Smooth Tubes at High Surface and Fluid Temperatures. NACA Rep. 1020, 1951.

9. Taylor, Maynard F. Correlation of Local Heat Transfer Coefficients for Single

Phase Turbulent Flow of Hydrogen in Tubes with Temperature Ratios to 23. NASA

TN D-4332, 1968.

10. Deissler, Robert G. and Taylor, Maynard F. Analysis of Turbulent Flow and Heat

Transfer in Noncircular Passages. NASA TR R-31, 1959.

11. Reshotko, Meyer: Flow and Wall-Temperature Sensitivity in Parallel Passages for

Large Inlet to Exit Density Ratios in Subsonic Flow. NASA TN D-4649, 1968.

22 NASA-Langley, 1968 33 E-4640

REFERENCES

1. Slaby, Jack G.; Maag, William L.; and Siegel, Byron L.: Laminar and Turbulent

Hydrogen Heat Transfer and Friction Coefficients Over Parallel Plates at 50000 R.

NASA TN D-2435, 1964.

~' 2. Slaby, Jack G.; Siegel, Byron L.; Mattson, William F.; and Maag, William L.: A

45000 R (25000 K) Flowing-Gas Facility. NASA TM X-1506, 1968.

,/ 3. Siegel, Byron L.: Design and Operation of a High-Temperature Tungsten-Mesh Gas

Heater. NASA TM X-1466, 1967. \~

4. Weast, Robert C., ed.: Handbook of Chemistry and PhYSics. 37th ed., Chemical

Rubber Publ. Co., 1955, p. 2360 0

5. Keenan, Joseph H.; Kaye, Joseph: Gas Tables - Thermodynamic Properties of Air,

Productions of Combustion and Component Gases and Compressible Flow Functions.

John Wiley & Sons, Inc., 1948.

'" 6. Svehla, Roger A.: Estimated Viscosities and Thermal Conductivities of Gases at

High Temperatures. NASA TR R-132, 1962.

7. Grier, Norman T.: Calculation of Transport Properties and Heat-Transfer Param­

eters of Dissociating Hydrogen. NASA TN D-1406, 1962.

8. Humble, Leroy V.; Lowdermilk, Warren H.; and Desmon, Leland G.: Measure­

ments of Average Heat-Transfer and Friction Coefficients for Subsonic Flow of Air

in Smooth Tubes at High Surface and Fluid Temperatures. NACA Rep. 1020, 1951.

9. Taylor, Maynard F.: Correlation of Local Heat Transfer Coefficients for Single

Phase Turbulent Flow of Hydrogen in Tubes with Temperature Ratios to 23. NASA

TN D-4332, 1968.

10. Deissler, Robert G.; and Taylor, Maynard F.: Analysis of Turbulent Flow and Heat

Transfer in Noncircular Passages. NASA TR R-31, 1959.

11. Reshotko, Meyer: Flow and Wall-Temperature Sensitivity in Parallel Passages for

Large Inlet to Exit Density Ratios in Subsonic Flow. NASA TN D-4649, 1968.

22 NASA-LangleY,1968 - 33 E-4640

i(E

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OFFICIAL BUSINESS FIRST CLASS MAIL

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-NATIONAL AERONAUTICS AND SPACE ACT OF 1958

NASA SCIENTIFIC AND TECHNICAL PUBLICATIONS

TECHNICAL REPORTS: Scientific and technical information considered important, complete, and a lasting contribution to existing knowledge.

TECHNICAL NOTES: Information less broad in scope but nevertheless of importance as a contribution to existing knowledge.

TECHNICAL MEMORANDUMS: Information receiving limited distribution because of preliminary data, security classifica­tion, or other reasons.

CONTRACTOR REPORTS: Scientific and technical information generated under a NASA contract or grant and considered an important contribution to existing knowledge.

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SPECIAL PUBLICATIONS: Information derived from or of value to NASA activities. Publications include conference proceedings, monographs, data compilations, handbooks, source books, and special bibliographies.

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r I I

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