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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]


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]


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


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


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.


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


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


,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


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


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

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