8013 [ turn over · b) show that ∇ × v is twice the local angular velocity ( w), where v is the...

8013 [ Turn over

Name : …………………………………………….……………… Roll No. : …………………………………………...…………….. Invigilator’s Signature : ………………………………………..

CS/B.TECH (CHE-NEW) /SEM-8/CHE-801/2011

2011 TRANSPORT PHENOMENA

Time Allotted : 3 Hours Full Marks : 70

The figures in the margin indicate full marks. Candidates are required to give their answers in their own words

as far as practicable.

GROUP – A ( Multiple Choice Type Questions )

1. Choose the correct alternatives for any ten of the following : 10 × 1 = 10

i) The ratio of the thermal boundary layer thickness to the concentration boundary layer thickness is proportional to a) Nu b) Le c) Sh d) Pr.

ii) Normal stress can be related to pressure (P) as a) + P b) nP

c) – P d) P . iii) A steady flow field of an incompressible fluid is given by

,)( jAyiByAxV −+= where ,1,1 11 −− == sBsA and

x, y are in metres. The magnitude of the acceleration )m/sin( 2 of a fluid particle at ( 1, 2 ) is

a) 1 b) 2 c) 5 d) 10 .

CS/B.TECH (CHE-NEW)/SEM-8/CHE-801/2011

8013 2

iv) If ,rwv ×= where w is a constant vector, then w is

a) 1/2 curl v b) 1/2 grad v

c) curl v d) div curl v .

v) For heat transfer in free convection, Nusselt number is

related to

a) Reynolds number, Prandtl number

b) Reynolds number, Grasshoff number

c) Grasshoff number, Prandtl number

d) Reynolds number, Graetz number.

vi) Combined momentum flux tensor is symbolized by

a) Φ b) τ

c) π d) None of these.

vii) Toothpaste is

a) Thixotropic fluid b) Bingham plastic fluid

c) Rheopectic fluid d) Pseudoplastic fluid.

viii) Momentum is a

a) first order tensor b) second order tensor

c) third order tensor d) zero order tensor.

ix) Continuity equation is

a) mass balance equation

b) momentum balance equation

c) both mass and momentum balance equation

d) none of these.


8013 3 [ Turn over

x) The mass diffusivity for a binary system is a function of

a) temperature and pressure

b) temperature and concentration

c) temperature, pressure and concentration

d) temperature only.

xi) Creeping flow around a sphere is defined, when particle

Reynold's number is . a) <2100 b) 10 ⋅<

c) 52 ⋅ d) 500.

xii) For falling film system average velocity is

a) 2/3 of the maximum velocity

b) 3/4 of the maximum velocity

c) 1/2 of the maximum velocity

d) 3/5 of the maximum velocity.

GROUP – B

( Short Answer Type Questions ) Answer any three of the following. 3 × 5 = 15

2. The space between two parallel plates is 0010 ⋅ ft apart, is

filled with oil of viscosity cp.70 ⋅=μ Calculate the steady

state momentum flux yxτ in ,/ftlb 2f when lower plate

velocity is 1 ft/s in the x direction as shown in the figure

below :


8013 4

3. A copper wire has a radius of 2mm and length of 5m. For

what voltage drop would the temperature rise at the wire axis

is ,C10o if surface temperature of wire is ?C20o

4. Carbon monoxide content in off gas from combustion

chamber is 2%. In order to reduce CO content, the gas is

passed through an absorption tower at C20o and

510013251 −×⋅ Pa. If Henry's law constant for CO solvent

system is 91005 ×⋅ Pa (moles of CO per total mole of

solution at saturation). Density of solvent is 1500 3kg/m

and molecular weight 20.

5. The head loss in 70 metre of 14 cm diameter pipe is known

to be 06 ⋅ metre when oil (specific gravity = )80 ⋅ of viscosity

040 ⋅ Newton sec/ 2m flows at .sec/m080 3⋅ Determine the

centreline velocity and the shear stress at the wall of the

pipe.

Data : friction factor ,0340 ⋅=f and fu

u33111

max ⋅+=

6. If ,,,0,0tEH

tHEHE

∂∂

=×∇∂∂

=×∇=⋅∇=⋅∇ then show

that E and H satisfy .2

22

tuu

∂∂

=∇


8013 5 [ Turn over

GROUP – C

( Long Answer Type Questions ) Answer any three of the following. 3 × 15 = 45

7. a) What do you mean by alternating unit tensor ? Explain

why the parameter becomes very important in order to

describe the cross product of two vectors. 5

b) Show that ∇ × v is twice the local angular velocity ( w ),

where v is the velocity vector of the fluid. 5

c) Prove that I : v = ∇⋅ v, where I is a unit tensor. 5

8. In a gas absorption experiment a viscous fluid flows upward

through a small circular tube and then downward in laminar

flow on outside. Derive a relation for flow of a fluid film on

outside of a circular tube.

a) Show that the velocity distribution in falling film

( neglecting end effects ) is

⎥⎥⎦

⎤

⎢⎢⎣

⎡+⎟

⎠⎞

⎜⎝⎛−=

Rra

Rr

μρgRvz ln214

222

8

b) Obtain an expression for mass rate of flow in the film. 4

c) Obtain mass flow rate when film thickness is very

small. 3


8013 6

9. a) A fluid is flowing over a flat horizontal surface under

laminar and straight stream line flow conditions.

Calculate the mass flow rate when kinematic viscosity is

sec,/m10153 24−×⋅ density 33 kg/m10750 −×⋅ , and

film thickness 43 ⋅ mm. Check the Re. No. for the

validity of flow condition. 3

b) Consider the flow of a viscous isothermal liquid film

under the influence of gravity. The falling film is in a

inclined plane. Density is constant but viscosity is

varying as )/(0

δα−= xeμμ where α is constant; μ changes

as x changes and 0μ is viscosity at surface of the film, δ

is film thickness. Deduce an expression for average

velocity. Also deduce the expression when α = 0. 10

c) Write a note on Eyring Model. 2

10. a) Heat is flowing through annular wall of inside radius 0r

and radius 1r . The thermal conductivity varies linearly

with temperature from 0k at 0T to 1k at 1T . Develop an

expression for heat flow through the wall. 8

b) Show that if 001 r/)rr( − is very small then :

⎟⎟⎠

⎞⎜⎜⎝

⎛−−

⎟⎠⎞

⎜⎝⎛ +

=01

10100 2

2rrTTkkLπr Q 7


8013 7 [ Turn over

11. a) Derive an expression for the heat flux distributions in

the fissionable sphere and in the spherical-shell

cladding.

b) How does mass diffusivity depend on temperature and

pressure ?

c) Define the term "momentum diffusivity". How does

momentum diffusivity take part in transport of mass

and heat ? 8 + 3 + 4

8013 [ Turn over

Name : ……………………………………………………………

Roll No. : ……………………………………………..…………..

Invigilator’s Signature : ………………………………………..

CS/B.Tech (CHE)/SEM-8/CHE-801/2012

2012

TRANSPORT PHENOMENA Time Allotted : 3 Hours Full Marks : 70

The figures in the margin indicate full marks.

Candidates are required to give their answers in their own words

as far as practicable.

GROUP – A

( Multiple Choice Type Questions )

1. Choose the correct alternatives for any ten of the

following : 10 × 1 = 10

i) If the Kronecker delta,

!

"qp , is mixed tensor then its rank

is

a) 0 b) 1

c) 2 d) none of these.

ii) If

!

i", j", k" are the unit vectors in x, y and z directions

respectively, then

a)

!

j" # k

" = 1 b)

!

j" # k

" = $ 1

c)

!

j" # k

" = i

" d)

!

j" # k

" = $ i

".


8013 2

iii) An ideal fluid

a) is frictionless and incompressible

b) is one, which obeys Newton’s law of viscosity

c) highly viscous

d) none of these.

iv) The continuity equation

a) is independent of the compressibility

b) is independent upon the viscosity of the fluid

c) represents the conversation of mass

d) none of these.

v) Cross or Vector product of two identical vectors is

a) 1 b) 0

c) infinity d) – 1.

vi) A fluid behaves as a shear thickening fluid when

apparent viscosity

a) increases with increase in stress

b) increases with decrease of stress

c) increases with duration of stress

d) decreases with duration of stress.


8013 3 [ Turn over

vii) Flow behaviour index ( n ) of pseudoplastic plastic is

a) 0 b) < 1

c) > 1 d) infinity.

viii) The non-dimensional group that appears in viscous

heating problem is

a) Brinkman number b) Nusselt number

c) Biot number d) None of these.

ix) In deriving the equation of continuity, the effect of

gravitational force

a) is not required to be taken into account

b) is required to be taken into account for fluids with

very high density

c) is required to be taken into account for fluids

flowing upwards against gravity

d) is required to be taken into account for fluids with

high viscosity.

x) If the Reynolds number in a flow system is very high, it

would mean that

a) the flow is dominated by convection

b) the flow is dominated by diffusion

c) the flow is isothermal

d) none of these.


8013 4

xi) Wilkes equation for estimating mass diffusivity of liquid

may be best used for

a)

!

CCl4

-H2O b)

!

H2SO

4-H

2O

c)

!

KMnO4

-H2O d) none of these.

xii) Newton’s law of cooling is used to define

a) local heat transfer coefficient

b) overall heat transfer coefficient

c) both (a) & (b)

d) none of these.

GROUP – B

( Short Answer Type Questions )

Answer any three of the following. 3 × 5 = 15

2. Compare Fick’s law of diffusion with Newton’s law of visocity

and Fourier’s law of thermal conductivity. To what extent are

these relations analogous ?

3. What is RANS theorem ? Prove that

!

"#

. ( A#

$ r#

) = r#

. curl A#

if

!

"#

$ A#

= O#

.

4. Derive the continuity equation in Cartesian coordinate in

terms of substantial derivative form, considering both of

conductive and convective heat transfers.


8013 5 [ Turn over

5. Show that the following equation describes the pressure field

in an arbitrary fluid under the influence of gravity

– ∇ ρ + ρ g = 0, where the symbols have their usual

meaning.

6. Consider steady state evaporation of chloropicrin

!

CCl3 NO

2( )

liquid into air which may be considered to be a pure

substance. The temperature is 25°C. The liquid chloropicrin

is taken in a tube containing air. Calculate the rate of

evaporation in

!

gm hr"1 of chloropicrin into air.

Data :

Total pressure : 770 mm Hg

Diffusivity [ chloropicrin-air ] :

!

0 "088 cm2 sec

#1

Vapour pressure : 23·81 mm Hg

Distance from liquid level to

top of tube : 11.14 cm

Density of chloropicrin :

!

1·65 g cm"3

Surface area of liquid

exposed for evaporation :

!

2 "29 cm2 .


8013 6

GROUP – C

( Long Answer Type Questions )

Answer any three of the following. 3 × 15 = 45

7. a) Derive the expression for momentum boundary layer

using boundary layer concept and Navier-Stokes

equation.

b) Consider a laminar flow of a Newtonian fluid down an

inclined plate with a free surface as half of the flow

between two fixed parallel plates and obtain the

expression for velocity profile and average velocity. 7 + 8

8. a) Heat is flowing through an annular wall of inside radius

!

r0

and radius

!

r1. The thermal conductivity varies

linearly with temperature from

!

k0

at

!

T0 to

!

k1 at

!

T1.

Develop an expression for heat flow through the wall.

b) Show that if

!

r1 " r

0( ) / r0 is very small then

!

Q = 2"r0

L k

0 + k

1

2

#

$ %

&

' (

T0

) T1

r1

) r0

#

$ % %

&

' ( ( . 8 + 7

9. A liquid of constant density and viscosity is in a cylindrical

container of radius R. The container is caused to rotate

about its own axis at an angular velocity ω. The cylinder axis

is vertical, so that

!

gr = 0, g

" = 0, g

z = # g in which g is the

magnitude of the gravitational acceleration. Stating with

Navier-Stokes equation, find the shape of the free surface of

the liquid when steady state has been established.


8013 7 [ Turn over

10. a) Derive the relevant expression for heat conduction with

a chemical heat source taking into account a chemical

reaction being carried out in a tubular, fixed-bed flow

reactor.

b) A thermocouple, inserted in a cylindrical well, is placed

into a gas stream for measuring the gas temperature of

the flowing gas through the pipe. Estimate the true

temperature of the gas stream from the following

supplied data :

Temperature indicated by thermocouple = 260°C

Pipe wall temperature = 176·6°C

Heat transfer coefficient = 587·546 kcal/hr.m

!

2.°C

Thermal conductivity of well wall = 293·773 kcal/hr.m.°C

10 + 5

11. a) An incompressible Newtonian fluid is flowing between

two co-axial cylinders of which outer cylinder rotates

with constant angular velocity ω. If the surfaces of the

inner and outer cylinders are maintained at

!

T0 and

!

Tb

respectively, develop an expression for the temperature

distribution due to viscous dissipation of heat inside the

cylinders in terms of Brinkman number.

WBUT Chemical Engineering 8thSemester Previous Year Question Paper

Publisher : Faculty Notes Author : Panel Of Experts

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8013 [ turn over · b) show that ∇ × v is twice the local angular velocity ( w), where v is the...

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