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.
CS/B.TECH (CHE-NEW)/SEM-8/CHE-801/2011
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 :
CS/B.TECH (CHE-NEW)/SEM-8/CHE-801/2011
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
∂∂
=∇
CS/B.TECH (CHE-NEW)/SEM-8/CHE-801/2011
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
CS/B.TECH (CHE-NEW)/SEM-8/CHE-801/2011
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
CS/B.TECH (CHE-NEW)/SEM-8/CHE-801/2011
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
".
CS/B.Tech (CHE)/SEM-8/CHE-801/2012
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.
CS/B.Tech (CHE)/SEM-8/CHE-801/2012
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.
CS/B.Tech (CHE)/SEM-8/CHE-801/2012
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.
CS/B.Tech (CHE)/SEM-8/CHE-801/2012
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 .
CS/B.Tech (CHE)/SEM-8/CHE-801/2012
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.
CS/B.Tech (CHE)/SEM-8/CHE-801/2012
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
Type the URL : http://www.kopykitab.com/product/10218
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