cpe 5238

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CONFIDENTIAL EH/OCT 2008/CPE523

UNIVERSITI TEKNOLOGI MARAFINAL EXAMINATION

COURSE

COURSE CODE

EXAMINATION

TIME

: TRANSPORT PHENOMENA

: CPE523

: OCTOBER 2008

: 2 HOURS

INSTRUCTIONS TO CANDIDATES

1. This question paper consists of three (3) questions.

Answer ALL questions in the Answer Booklet. Start each answer on a new page.2.

3.

4.

Do not bring any material into the examination room unless permission is given by theinvigilator.

Please check to make sure that this examination pack consists of:

i) the Question Paperii) a two - pages Appendicesiii) an Answer Booklet - provided by the Faculty

DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO

This examination paper consists of 3 printed pages

© Hak Cipta Universiti Teknologi MARA CONFIDENTIAL

8/13/2019 Cpe 5238


CONFIDENTIAL 2 EH/OCT 2008/CPE523

QUESTION 1

a) Using Newton's law of viscosity, define viscosity and give its physical meanings.

(4 marks)

b) Explain the boundary conditions used for fluid-solid and liquid-gas interfaces(6 marks)

c) A viscous liquid overflows from a vertical cylindrical pipe causing a thin liquid film to flowcontinuously on the outside of the pipe. Ignoring end effects, derive the followingvelocity distribution of the film, vz as a function r:

v , = R

where R = outer pipe radius, kR = distance from the center of the pipe to the surface ofthe overflowing liquid film, p = density of the liquid, |j. = viscosity of liquid and g =gravitational constant. Navier-Stokes equations are given in Appendix 1.

(20 marks)

d) List all of the assumptions required for the solution of part (c) above. Give two reasonswhy Bernoulli equation is not satisfactory for solving the problem in part (c) above.

(10 marks)

QUESTION 2

a) The formulae for Biot and Nusselt numbers are similar. Give the physical meanings ofboth Nusselt and Biot numbers and state their differences.

(6 marks)

b) Water at 10 °C enters a smooth heat exchanger tube with inner diameter of 2.5 cm anda length of 3 m. The water flows at 75 L/min and exits at the temperature of 60 °C.

i). Obtain the temperature profile of the water in the tube(10 marks)

ii). Calculate the appropriate (bulk or film) average temperature of the moving water

(4 marks)

iii). For a constant wall temperature of 100°C, calculate the heat transferred to thewater using Colburn analogy.

(10 marks)

Colburn analogy St= — ^ — = - P r2 / 3

pv.Cp 2

0 0791Blasius equation for smooth tube and turbulent flow f =

Re02 5

The properties of water are given in Appendix 2

© Hak Cipta Universiti Teknologi MARA CO NF IDE NT IA L

8/13/2019 Cpe 5238


CONFIDENTIAL 3 EH/OCT 2008/CPE523

QUESTION 3

The general species A diffusion equation in terms of molar fluxes expressed in Cartesiancoordinates is as follows:

A(N )+A(N )+A(N ) + ^ A . _ R = 0

a). Simplify the above equation for steady state, one dimensional diffusion with nohomogeneous reactions.

(4 marks)

b). Derive the molar flux of species A for the case of diffusion through a stagnant gas film.

(10 marks)

c). A pseudo-steady-state Arnold cell is used to determine the diffusivity of methanol in airat 25°C and 1 atm. The cell has a cross sectional area of 0.8 cm2. If the tube was initiallyfilled to within 3 cm of the lip of the tube, calculate the time required for the methanollevel to fall to 4 cm of the lip of the tube. The vapor pressure of methanol is 1.7 x 104 Paand its specific gravity is 0.791 at the system temperature. The molecular mass ofmethanol is 32 and the binary diffusivity of methanol in air is 1.62 x 10"

5 m

2 /s. The

universal gas constant is R = 8.3143 Pam3mor1K"1.(16 marks)

END OF QUESTION PAPER

© Hak Cipta Universiti Teknologi MARA CON FI DE NT IA L

8/13/2019 Cpe 5238


CONFIDENTIAL APPENDIX 1 EH/OCT 2008/CPE523

Navier-Stokes Equation for Cartesian Coordinates

Navier-Stokes Equation for Cylindrical Coordinates

6vr

at

at

5vz

at

5vr

l V r 5r

+ r 5r

5vz

' Vr 5r

r

ve

r

w

r

5vr

56

9Ve

a e

5vz

56

5vr

V z 5z

6vz

V z dz

ve2

r

i i

iJ

lJV |̂

r J

dP

dz^

5F)

5r TH>

15P

r 56

"1 5

r5r

5 |r \ 5

V0

r

+

rv

5r

1

r2

K,

52vz

562

1 52vr 5

2vr 2

CO OZ \

\ . 1 52ve 5

2ve

J r2 562 5z 2

, S 2

v z l

6z2 + pg z

5ve

56

2 i

% 2

1 (

56

P9r

P9e


8/13/2019 Cpe 5238


CONFIDENTIAL APPENDIX 2 EH/OCT 2008/CPE523

Thermo-physical properties of water at atmospheric pressure

T(°C)

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

85

90

95

( k g / m 3)

1 0 0 0

1 0 0 0

999

998

997

996

994

992

990

988

986

983

981

978

975

972

969

965

962

c P(kJ/kg-K)

4.21

4.20

4.19

4.19

4.18

4.18

4.18

4.18

4.18

4.18

4.18

4.18

4.19

4.19

4.19

4.20

4.20

4.21

4.21

H-103

(Pas)

1.518

1.306

1.138

1.002

0.890

0.797

0.719

0.653

0.596

0.547

0.504

0.466

0.433

0.404

0.378

0.354

0.333

0.314

0.297

k(W/m-K)

0.571

0.580

0.589

0.598

0.607

0.615

0.623

0.631

0.637

0.644

0.649

0.654

0.659

0.663

0.667

0.670

0.673

0.675

0.677


cpe 5238

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