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CON FIDENTIAL EH/JAN 2013/CPE523

UNIVERSITI TEKNOLOGI MARA

FINAL EXAMINATION

COURSE

COURSE CODE

EXAMINATION

TIME

TRANSPORT PHENOMENA

CPE523

JANUARY 2013

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..

3. Do not bring any material into the exam ination room unless permission is given by the

invigilator.

4. Please check to make sure that this examination pack consists of

i) the Question Paperii) a one - page Append ixHi) an Answ er Booklet - provided by the Faculty

DO NOT TURN T IS P GE UNTIL YOU RE TOLD TO O SO

This examination paper consists o 4 printed pages© Hak Cipta Universiti Teknologi MARA C O N F ID E N T IA L

8/13/2019 Cpe 5231


CONFIDENTIAL 2 EH/JAN 2013/CPE523

QUESTION 1

P 01 ,C 02 , C 2 .C 3 )

a) Figure 1 illustrate the buildup to the steady-state and laminar velocity profile for afluid contained between two plates. Explain briefly the conce pt of N ewton s Law ofviscosity by showing the related equation which contributes to transmit themomentum.

Figure 1 Laminar velocity profile

(3 marks)

b) Figure 2 shows a coating experime nt involving a flat pho tographic film that is beingpulled up from a processing bath by rollers with a steady velocity U at an angle to

the horizontal. As the film leaves the bath, it entrains some liquid, and in thisparticular experiment it has reached the stage where: (a) the velocity of the liquid incontact with the film is v x = U a t y = 0, (b) the thickness of the liquid is constant at avalue ± 5 , and (c) there is no net flow of liquid (as much is being pulled up by the filmas is falling back by gravity). Clearly, if the film w ere to retain a perm anent coating, anet upwards flow of liquid would be needed.

Moving photo

graphic film

Figure 2 Liquid coating on a photographic film

© Hak Cipta Universiti Teknologi M ARA CONFIDENTIAL

8/13/2019 Cpe 5231



i) Derive the liquid velocity distribution of the fluid, v x as a function of y using equationof motion. Equa tions of motions are given in Append ix 1 . State your assumptions.

(15 m arks)ii) Ske tch the veloc ity profile v x by labeling all important features.

(2 marks)

QUESTION 2( P01 . C03 , C3 . C5 , C5 )

a) A very long rod (circular cross section) initially at 1 50°C is sudde nly imm ersed in afluid at temperature 30°C. The radius of the rod is R.

i) Derive the radial temperatu re profile in the rod as a function r.(10 marks)

ii) Justify your assump tions.(6 marks)

b) The S chmidt num ber for a gas at constant pressure usually remains fairly constantover a large temperature range, while the Lewis and Prandtl number changesmarkedly. Discuss your justification.

(4 marks)

QUESTION 3

( P 0 1 , C 0 4 , C 2 , C 3 )

a) The general species A diffusion equation in terms of molar fluxes expressed inCartesian coordinates is as follows:

A N )+A N )+A N + ^ _ R A .odx

K ** Sy

v A y / Sz

v NL ) St

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

(4 marks)

© Hak Clpta Universlti Teknolog i MARA CONFIDENTIAL

8/13/2019 Cpe 5231



b) An air supply is transported through a porous iron pipe subm erged in water as shownin Figure 3. Th e air, specifically the oxyge n in the air, diffuses throu gh the pipe wall to

the o uter surface of the pipe with diffusivity 2>. Deve lop a following mod el for thesteady-state diffusion of the oxygen through the pipe wall, providing an expressionfor the oxygen concentration as a function of radial position with oxygen

concentration in the pipe wall is C f| at r = n and C h at r = r 2.

Cr2

I n ry

C -CW l W 2

Water

Air Water

Figure 3 Porous iron pipe

(16 marks)

END OF QUESTION PAPER

© Hak Cipta Universal Teknologi MARA CONFIDENTIAL

8/13/2019 Cpe 5231


CONFIDENTIAL APPENDIX 1 EH/JAN 2013/CPE523

The E quat ion o f Mot ion for a Newtonian F lu id wi th Constant p and u

[pDv/Dt = -{V-p +V2\/ + pg]

C a r te si a n c o o r d i n a t e s {x,y,z):

dv r dv , dvr dv.

dt• + v .

' + v '+ v .

dy dz

dp— - ju

dx

d2v, d

2vx d

2vr

+ r -dx

2 dy

2 dz

2 + Pg

dv

dt

y fay dV

x dx

y

dv ^y yy + v

ydy dz

dp= — - ju

dy

d2v., d

2v„ d

2v,

• + •

dx 1 dy

1 dz

1 + Pg

dv, dv, dv , dv.

dt+ v „ — - + v .

dx dy+ v.

dz

dp

dz+ M

d2v, d

2v, d

2v,

• +

dx2 dy

2 dz

1 + Pg;

Cyl indr ica l coord inates r,0,z):

dt• + v .

dv. va dv. dv r v2\

dr r dO- v.

dz

dp

dr+

»

dfld, A 1 d2vr d

2vF

- — ( r v r ) + — — f + dr

2 dv.

r dr r2 dO

2 dz

2 r2 dO

dVff dv„ va dv,

dt dr r 86

v.v,oe , * r*e

dz r

\ 1 dp= — +

rdO dr\rdr

1 d2ve d

2ve 2 dv r

+ r

T~d B

r+ dz

2 r

2 dO

(d v2 dv z

— - + V r — - +{8 t dr r dO

v„ dv, dv,9 i- + v.

2

dp

dz ) dz+ H LJL

r dr

dv A 1 8-

dr,+ •

•2 80

2

v . 82v,

+ dz

2 + Pg:

© Hak Cipta Universiti Teknologi MARA CONFIDENTIAL

cpe 5231

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