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VAAL UNIVERSITY OF TECHNOLOGY
FACULTY OF ENGINEERING
DEPARTMENT OF CHEMICAL ENGINEERING
BACCALAUREUS TECHNOLOGIAE
ENGINEERING: CHEMICAL
Subject
Subject code
Date
Time
ExaminerModerator
MARKS:
Total marks
Full marks
REQUIREMENTS:Calculators
: Heat and Mass Transfer IV
080507503
November 2007
3 Hours
Dr PO OsifoMr D. Gina
145
130
INSTRUCTIONS:1. Answer all the questions2. Start each question on a new page
The question paper consists of cover page, 4 typed pages, and the formulasheet of 8 pages
DO NOT TURN THE PAGE BEFORE PERMISSION IS GRANTED
Heat & Mass Transfer IV - Main Examination - November 2007
QUESTION 1 [30]
1.1. A very long, wide sheet of plastic 4 mm thick and initially at 20 °C is
suddenly exposed on both sides to an atmosphere of steam at 102 °C.
(a) If there is a negligible thermal resistance between the steam and
surface of the plastic, how long will it take for the temperature at the
centerline of the sheet to change significantly (by one 1%)? (b) What
would be the bulk average temperature of the plastic at this time?
For the plastic, k = 0.138 W/m.°C, and a = 0.00035 m2/h' [15]
1.2. Define the meaning of biot number in heat transfer, for a slab the Biot
number is
k
For a slab 2.8 mm thick in size and originally at 78 °C is cooled by using
air whose temperature is at 30 °C. The density of the solid is 1,200
kg/m3, the thermal conductivity is 0.14 W/m-°C, and the specific heat is
1800 J/kg-°C. The external heat transfer coefficient is 50 W/m2.°C. (b)
How long will it take for the average solid temperature to reach 40 °C?
(c) What fraction of the resistance to heat transfer is in external film?
[15]
Heat & Mass Transfer IV - Main Examination - November 2007
Question 2 [20]
Kerosene is heated by hot water in a shell and tube heater. The kerosene is
inside the tube, and the water is outside. The flow is countercurrent. The
average temperature of the kerosene is 43 °C and the average linear velocity
is 2.4 m/s. The properties of the kerosene at 43 °C are: specific gravity, 0.805;
viscosity, 1.5 cP; specific heat, 2.020 J/g-°C; and thermal conductivity, 0.1514
W/m-°C. The tubes are low-carbon steel with 16.7 mm ID and 20 mm OD, and
ks = 45 W/m-°C. The heat transfer coefficient on the shell side is 1702 W/m-°C.
Calculate the overall transfer coefficient based on the outside area of the tube.
Question 3 [25]
A vertical tubular condenser is used to condense 2,100 Kg/h of ethyl alcohol,
which enters at 1 atmosphere. Cooling water is to flow through the tubes at an
average temperature of 30 °C. The tubes are 30 mm OD and 27 mm ID. The
tube water side coefficient is 2,800 W/m2-°C. Fouling factors and the
resistance of the wall may be neglected. If the available tubes are 3 m long,
many tubes will be needed? Data are as follows:
Alcohol
Boiling point of alcohol: T = 78.4 °C
Heat of vaporization: A. = 856 J/g
Density of liquid alcohol: p = 769 kg/m3
/cf = 0.182W/m-°C
uf = 0.85 cP
Cp = 2.64 J/g-°C
Water:
ki= 0.182 W/m-°C
uf = 0.70cP
Heat & Mass Transfer IV - Main Examination — November 2007
Question 4 [40]
Crude oil at the rate of 150, 000 kg/h is to be heated from 20 to 57 °C by heat
exchange with the bottom product from a distillation column unit. The product
at 129,000kg/h is to be cooled from 146 to 107 °C. There is available a tubular
heat exchanger with steel tubes with an inside shell diameter of 590.6 mm
having one pass on the shell side and two passes on the tube side. It has 324
tubes, 19.05 mm OD and 14.83 ID BWG14, 3.7 m long arranged on a 25.4
mm-square pitch and supported by baffles with a 25 percent cut, spaced at
228.6 mm interval. Would the exchanger be suitable; that is, what the
allowable fouling factor? The average properties of the fluid are given in Table
Q4. For metal k = 45 W/m-°C
Table Q4: Fluid properties
Properties
Cp, J/g-°C
M, cP
p, kg/m3
K, W/m-°C
Question 5 [30]
5.1. Show that one-way molecular diffusion for component A is greater than
counter flow diffusion involving component A and B by a factor
Product outside tube
2.20
5.2
867
0.119
Crude, inside tube
1.99
2.9
825
0.137
(\-y)L
when the total molar flux is: NA=(NA+NB) ——D —^- [15]DCT v dx
5.2. The diffusion coefficient for vapors in air can be determined by
measuring the rate of evaporation of a liquid from a vertical glass tube. For
a tube 0.2 cm in diameter filled with n-heptane at 21 °C, calculate the
expected rate of decrease of the liquid level when the meniscus is 1 cm
from the top based on the published diffusivity of 0.071 cm2/s. At 21 °C the
vapor pressure and density of n-heptane are 0.050 atm and 0.66 g/cm3,
respectively. Mw of n-heptane = 100.2 g-mol/g. [15]
Heat & Mass Transfer IV - Main Examination - November 2007
CORRELLATIONS SHEET
Transient ConductionAverage temperature
, 1 O"I c9
i25
Slab Fo atT/s2
-r+ 0.131e -3O.5Fn Cylinder Fo <xtTlr'n
T -T1 s l b
T.-T.+0.13 le~39JSF- Sphere
1 1.00.9
1 0.6n ^
0.4
0.3
1 I 0.1- n no
0.08n r\7
0.06
n C\A
r\ r\n
0.01
f\•\V\\V
t
\
V\\\
\\
\
- \
\
\\\\^
A_\
\
i
\
-\
\\\
\
\\L
V\\\
*
\
\\\\
1
\
i\
\
Slab [Eq: (10.20)]Cylinder [Eq. (10.2111Sphere [Eq. (10.22)
s\
\
\
Figure 1: Average temperature during unsteady state heating or cooling of a largeslab, or an infinitely long cylinder or a sphere
Heat & Mass Transfer IV - Main Examination - November 2007
At low Biot numbers
Tf-Tb = 3U-t{Tf-Ta~ p-Cp-r
Spheres, U~h
InTf-Tb 2U-t
Tf-Ta p-Cp-rLong cylinder, U~h
U-t
Tf-Ta p.Cp-SFlat plate, U~h
1.0
0.8
0.6
0.4
0.2
L 0 1
0.08
0.06
0.04
0.02
0.01
Vs
\
\
\
Vr\\\\\
\
\s
\
A
X
\
- \
\\
k
\\\\
X
N.\
\
k\\\
\ 5
8;
\
\
hr~ L
0.5
N s 1
Sfi
0.2 0.4 0.6 0.8 1.0 1:2 1.4r at
Figure 2: Change with time of the average temperature of a sphere, with externalresistance
Heat & Mass Transfer IV - Main Examination - November 2007
Unsteady state heating or cooling of semi-infinite solid.
1 .\J
i 0.5
/
/
/
/
/
/
/
/
/
— —
.0! 0 1.0
z = -
FIGUREUnsteady-state heating or cooling ofsemi-infinite solid.
2.0
: Z = x/2y/af, dimensionlessra = thermal diffusivityfc~x = distance from surface
• i = time after change in surface temperature, h
Figure 3: Unsteady state heating or cooling of semi-infinite solid.
Heat & Mass Transfer IV - Main Examination - November 2007
Forced Convection — Internal flow
Nu = 4,36Nu = 3,66
/• NO.14
Nu = 0,023 -Re^-Pr^-Pr"
or
> 0 , 1 4
= 0,023 •
Forced Convection - External flow
Laminar, constant q, Gz < 20Laminar, constant Twan, Gz < 20
Laminar, constant Twau, Gz > 20
Turbulent, n = 0,4 for TvaU > Tt
n = 0,3 for Twal!<Tj
Turbulent, L/D> 10
200
**•*••
y
- • ;
< •
%
0.80.6 | ^M-f0.40.3
0.1 1.0 TO 102 103 10" 105
Figure 4: Heat transfer to air flowing normal to a single tube
Nu = Pr0'3 • (o,35 + 0,56i?e0>52) Liquid cross-flow over single cylinder
Nu = 2,0 + 0,60 • ite0-50 • Prm Flow over single sphere
Heat & Mass Transfer IV - Main Examination - November 2007
Natural Convection
Nu = b-{Gr-Pr)n
System
Horizontal cylinder
Vertical plates/walls and cylinders
Horizontal plates/wallsHeated, facing upward orCooled, facing downward
Cooled, facing upward orHeated, facing downward
Range of GrxPr
4-10 1 2
104-109
10 5 -2x l0 7
2xl0 7 - 1010
3xl0 5 -10 1 0
b
0.52
0,59
0,540,14
0,27
n
0,25
0,25
0,250.333
0,25
Where, for cylinders: Gr =
And, for plates/walls: Gr = L 'p 'P'M
For Gases B - —, and for liquids: B = ———^—T p(T2-T2)
Effect of natural convection on laminar flow in tubes:
_ 2,25-(l + 0,010-Grm)
\og(Re)when Gr-Pr—>3000
L
Condensation
Figure 5: Film coefficient for condensation on vertical tubes
Heat & Mass Transfer IV - Main Examination - November 2007
,0,25
h = 0,729 •
Boilin
Horizontal tube
-il/4
,1/4
24 ^ (pL
Film boiling on horizontal tube:
6= 0,59 + 0 , 0 6 9 - - ^ • vPv'
where: A'=A-| 1 +
Shell-and-tube Heat Exchangers
T -T T —T_ _ 1cb 1ca . 7 _1ha l hbIlls — , /-i —
^ Iha~Ica 1cb~1ca
,0,25
0,34-CP-ArV ,1/2
Figure 6: Correction ofLMTDfor 1-2, 1-4, 1-6 and 1-8 heat exchangers
10
Heat & Mass Transfer IV - Main Examination - November 2007
O.T 0.2 0:3 0.4 0.5 0.6 0.7 0.8 0.9
Figure 7: Correction ofLMTDfor 2-4, 2-6 and 2-8 heat exchangers
r \°.14
Nu = 0,2-Re0'6
MwallShell-side heat transfer coefficient
Cross-flow Exchangers
Nu = 0,287 • Re°M • Pr0-33 • Fa
where, values for Fa
Shell-side heat transfer coefficient
P/Dn1,251,52,0
Re = 20000,850,940,95
Plate-type Exchangers
Nu = 0,37- Re0-67 -Pr0-33
Re = 80000,920,900,85
Re = 20 0001,031,061,05
Re = 40 0001,021,041,0
11
Heat & Mass Transfer IV - Main Examination - November 2007
Mass-transfer Correllations
Flow inside pipes\0,14
Sh = 1,62-(Gz'J,\l/3
s. Mwatl
, m K DGz = =—ReSc—
DvLp 4 L
Sh = 0,023-ReOM-ScOM
Sh = 0,0096-Re°-9n-Sc0-346
Laminar
Turbulent, Sc < 430
Turbulent, So 430
0.1
..I
o 0.01
0 001
^ ^ — Mass transfer— — — Heat transfer
•
102 103 104 105
Re = D p G/^
Figure 8: Heat and mass transfer, flow past single cylinders jM =Sh
Re-Sc 1/3
Other:Sh = 1,28 • Re°-S • Sc0-33
Sh = 2,0+ 0,6-Re0-5-Sc0-33
Sh = l,\7-Re°-S*5-Sc0-33
Flow normal to tube bundle
Flow past single sphere
Mass transfer in packed bed
— 12