UNIT I
TRANSPORT
PHENOMENA BY MOLECULAR MOTION
PART
A (2 MARK)
1.
What
is the importance of Transport Phenomena?
2.
Explain
the analogous nature of the different divisions of Transport Phenomena.
3.
What
is substantial time derivative?
4.
What
do you mean by reference frames?
5.
Compare
Newton’s law of Viscosity with Hook’s law of elasticity
6.
What
is the science of Rheology?
7.
What
are the units of dynamic viscosity and kinematic viscosity?
8.
Define
Newtonian Fluids.
9.
What
is a pseudo plastic?
10.
What
is Bingham plastics?
11.
Define
Viscosity.
12.
What
is meant by Thixotrophic fluid?
13.
What
is the difference between dilatant and pseudoplastic fluids?
14.
Define
nonNewtonian fluids.
15.
Explain
Newton’s law of viscosity.
16.
What
is slip velocity?
17.
State
and explain power law of viscosity.
18.
List
some models to characterize nonNewtonian fluids.
19.
What
are boundary conditions?
20.
What
is the velocity of fluid at the wall of a pipe?
21.
What
is Oswaldde Waele model?
22.
Explain
the Eyring model.
23.
What
is Ellis model?
24.
How
does the viscosity vary with temperature for liquids?
PART
B
1. Write short notes on (a) Conservation
Laws, (b) Continuous concept, (c) Field and reference frames, (d) Substantial
Derivative, (e) Total derivative and (f) Boundary conditions.
2. What are the different methods of analysis adopted for experimental
data? Differentiate between Differential and Integral analysis.
3. Develop
the concept of Viscosity for the Newtonian Fluids and the corresponding
rheological property terms for the Newtonian fluids.
4. Write
Short Notes on: a) Newtonian Fluids, b) Bingham plastics, c) Oswald Dewaele
Model, d) The Ellis model, e) The ReinerPhilippof model.
5. Discuss the theories
of of viscosity of gases and
liquids in respect of effect of temperature and pressure.
6. Discuss the theories
of of thermal conductivity of gases
and liquids in respect of effect of temperature and pressure.
7. Discuss
the theories of of diffusion of gases
and liquids in respect of effect of temperature and pressure.
8.
Compute the viscosity of CO_{2} at 300 K and 1 atm pressure
Given: e / R= 190 K; s = 3.996 A^{o} and W_{m}
= 1.286
9. Discuss
in detail the various models explaining the nonnewtonian behavior of fluids.
10. Discuss
in detail about the laws of conservation of momentum, energy and mass for
engineering flow systems.
11.
Write briefly on the theory of viscosity of liquids
12.
Describe the phenomenological equations for momentum, heat and mass transfer.
UNIT II
ONE DIMENSIONAL
TRANSPORT IN LAMINAR FLOW (SHELL BALANCE)
PART
A (2 MARK)
(1) Define
Lorenz number. What are its units?




(2) What is
the coefficient b
for an ideal gas?




(3) Write the
units of Viscosity and Thermal conductivity.




(4) What is
the effect of temperature on thermal conductivity?




(5)What is
meant by slip flow regime and Knudsen flow regime?




(6)Write
down shell momentum balance equation.




(7) What is
HagenPoisceulle Equation and when is it used?




(8)Define compressible
and incompressible fluids?




(9) State the
Newton’s second law of motion.




(10) Write the
HagenPoiseuille equation.




(11) What is
the proportion of Average velocity with the maximum velocity for flow of
Newtonian fluids through circular ducts under laminar flow conditions?




(12) Define
Reynolds number. What are its dimensions?




(13) What are
the implied assumptions in the derivation of the HagenPoiseuille equation?




(14) What is
hydraulic radius?




(15) Compare
Fourier’s law with Newton’s law of viscosity.




(16)
What is free convection?




(17) What is
Forced convection?




(18) Define
Nusselts number.




(19) State
DittusBoeltier equation.




(20)
A vessel at a higher temperature is insulated with two
different insulating materials. The first layer has a higher thermal
conductivity than the second. In which layer the temperature drop will be
more?




(21) Define
Prandtl number.




(22) What is
Brinkman number?




(23) Write down Grashof number and
indicate it as the ratio of forces.




(24) Define
effectiveness of a fin.




(25) Differentiate
between natural convection and forced convection.


(26) What are
the dimensionless numbers that characterize free convection?




(27) Compare thermal resistances in
series and the electrical resistances in series.




(28) What is
the significance of N_{pr} and N_{sc} ?




(29) Explain
equimolar counter diffusion with an example




(30) Define mass average velocity.




(31) Give a comparative account of diffusion and heat
transfer.
(32) Define
mass transfer coefficient.


(33) State
Fick’s law of diffusion.




(34) Define
molar average velocity.




(35) What is
the effect of pressure on diffusivity?




(36) Define
mass flux.




(37) What is
diffusion?




(38) Define
molar flux.




(39) What is
the effect of temperature on diffusivity ?




(40) Define
Sherwood number.




(41) What are
the units of diffusivity?




(42) What are
the units of mass transfer coefficient.




(43) Write the
dimensionless numbers significant for fluid flow processes.




(44) What
purpose does wetted wall column serve?




(45) Write
down the shell mass balance equation




(46) State the
criteria for Boundary conditions in diffusion problems






(47) Compare
and contrast homogenous and heterogeneous reactions.


(48) What is
the relationship between friction factor and J_{H} factor.




(49) Compare and contrast conduction
and convection.

PART
B
1.
A fluid with constant viscosity and density flows along an inclined flat
surface under the influence of gravity with no ripples. Derive the equations
for momentum flux and velocity distribution.
Mention all your assumptions.
2.
Two immiscible incompressible fluids are flowing in the zdirection in a
horizontal thin slit of length ‘L’ and
width W under the influence of a pressure gradient. The fluid rates are so
adjusted that the slit is half filled with Fluid I (the more dense phase) and
half filled with Fluid II (the less dense phase). Analyze the system in terms of the distribution of
velocity and momentum flux.
Show how if the viscosities of both the
liquids are same the results simplify to the parabolic velocity for laminar
flow of pure fluid in a slit.
3.
For flow of a viscous liquid in laminar flow in a slit formed by two parallel
plates with a distance 2b apart. The wall length is ‘L’ and width “W” Make
differential momentum balance and obtain the expression for the volumetric flow
for the slit.
4.
Derive the momentum flux and velocity distribution equations for a fluid
flowing through an annulus of inner radius ‘KR’, outer radius ‘R’ and Length ‘L’. The density of the fluid is
constant and the flow is steady and laminar.
5. A
nonNewtonian Fluid, described by Bingham Model.
t
=t _{0 }  m_{0} [dv_{z} / dr] if r > r_{0} and
t = 0 if t
£ t _{0}
is
flowing through a vertical tube as a result of a pressure gradient. The radius
and length of the tube are ‘R’ & ‘L’ respecttively. Obtain a relationship
between the volumetric flow rate ‘Q’ and the pressure gradient by shell balance
technique. Also show that for t _{0 }= 0, the relationship
reduces to HaeganPoiseulle Eqn.
6.
Derive the equation for the temperature distribution for heat conduction with a
viscous heat source.
7.
Derive an equation for heat transfer in a cooling rectangular fin.
8.
An electric current passes through a wire of circular cross section with radius
R and electrical conductivity K_{e}.
The current density is I. Rate of heat production per unit volume is S = [I^{2} / K_{e }] . Surface of the wire ia at
a temperature T_{0}.
Derive an equation to determine the radial temperature distribution.
9.
Derive the equation for the rate of mass transfer in respect of ‘diffusion
through a stagnant film’.
10.
Derive the concentration profile in the gas film for diffusion with
heterogeneous chemical reaction.
11. Glycerine
is flowing through a horizontal tube of 0.5 m long and 3 mm inside diameter.
For a pressure drop of 3 atm., the flow rate is 0.0002 m^{3} / min. The
density of glycerine is 1.26 g / cc. From the flow data find the viscosity of
glycerine.
12. Determine the heat transfer per
square meter of wall area for a furnace wall with inside gas at 1500 K. The
furnace wall is composed of 0.108 m layer of fire clay brick and 0.7 cm
thickness of mild steel at the outer surface. Heat transfer coefficient h_{i} = 5,110 W/m^{2}K and h_{o} = 25 W/m^{2}K
respectively. Calculate the temperature at each surface and at the bricksteel
interface.
13. An oil is acting as lubricant for
a pair of cylindrical surfaces. The angular velocity of the outer cylinder is
7,900 rpm. Outer cylinder has a radius of 6 cm and the clearance between the
cylinders is 0.02. What is the maximum temperature of the oil if both wall
temperatures are at 160^{0}C.
The physical properties of the oil are m = 92.3 x 10^{3} N.s/m^{2}; r = 1200 Kg/m^{3} and k = 2.5 W/m^{0}C
14.
A fluid is flowing through a circular tube of length ‘L’ and radius ‘R’.
Viscosity and density are constant. The flow is laminar. Derive an equation for
HagenPoiseuille. Indicate all the assumptions you have made.
15. Derivation of Flow through a circular tube under
laminar conditions will lead to the Hagen Poiseuille equation. Page No. 4246.
Figure is to be drawn and the final expression for the volumetric flow
rate Q as:
Q = p [(P_{o}
 P_{L} ) R^{4}/8 m L]
16. Develop an equation for heat
conduction through composite cylindrical walls.
17. Derive the concentration
distribution and molar flux distribution for diffusion with homogeneous
chemical reaction.
18. Derive the differential equation
for the absorption of a gas in a falling liquid film.
UNIT III
EQUATIONS OF CHANGE
AND THEIR APPLICATION
PART
A (2 MARK)
(1) Explain
partial time derivative. Enunciate with example




(2) Explain
Total time derivative. Give example




(3) What
is NavierStokes equation?




(4) Explain
Stokes’ Law.




(5) Explain
Euler’s Equation.




(6) Write the dimensionless numbers significant for fluid
flow processes.




(7) Define
friction factor.




(8) Define
the terms isothermal and nonisothermal systems.




(9) What
is drag coefficient?




(10) What
purpose does wetted wall column serve?




(11) Write
down the Equation of Continuity for binary mixture.




(12) Write
Blake Kozney equation.




(13) What is the Laplacian operator?


(14) Write
down the qcomponent of the Equation of
motion in Cylindrical coordinates




(15) Write
down the Equation of Continuity in rectangular and cylindrical coordinates.




(16) Write
down the time smoothed equation of motion




(17) Write
down the rcomponent of the Equation of motion in Cylindrical coordinates




(18) Write Blake Kozney
equation.



PART
B
(1)

Derive
the equations of continuity for a binary mixture.



(2)

Derive the Navier – Stoke’s
equation through shell momentum balances.


(3)

Derive
the equation of Continuity from shell mass balances in three dimensional
Cartesian coordinates



(4)

Determine
the velocity distribution for the laminar flow of an incompressible fluid
flowing through a cylindrical tube. The following equation is given for the
zcomponent of the equation of motion:
0 =  (dP / dz) + m _{r} d/d r [r (dV_{z} / dr)]



(5)

Derive
the Hagen–Poisueille equation by the application of NavierStoke’s equation.



(6)

Write
Continuity equation, NavierStoke’s equation, Euler equation and explain
their field of application.



(7)

A
hollow steel sphere, 5 mm diameter with a mass of 0.05 g, is released in a
column of liquid and attains a terminal velocity of 0.5 cm/sec. The liquid
density is 0.9 g/cc. The local acceleration due to gravity is 981 cm/s^{2}. The sphere is far enough
from the container walls so that their effect may be neglected.
(a)
Compute the drag force; (b) Compute the drag coefficient
(c)
Determine the viscosity of the liquid.



(8)

A
fluid 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, W. The cylinder axis is vertical. Find
the shape of the free surface when steady state is established.
Given: r
[v_{q}^{2}/
r] = (dP
/ dr)
; m(d / dr)[(1/r)
(d / d
r)(r v_{q})] = 0
& [dP/dZ] =  r. g



(9)

Write
Continuity equation, NavierStoke’s equation, Euler equation and explain
their field of application.

UNIT IV
TRANSPORT IN
TURBULENT AND BOUNDARY LAYER FLOW
PART
A (2 MARK)
(1)Write
Blassius formula




(2) State
Deissler’s empirical formula for the region near the wall.




(3) Define
Prandtl mixing length.




(4) What is
Von Karman’s Similarity hypothesis?




(5) What is
a Boundary layer?




(6) State
if the momentum boundary layer thickness is lower than the thermal boun dary
layer thickness.




(7) What is
eddy viscosity?




(8) Define
porosity.




(9) Define
“Instantaneous Pressure” and “Time smoothed Pressure”.




(10) Write
down the BurkePlummer equation.




(11) Write
down the Ergun’s equation.




(12) Define
mass average velocity.




(13) What
is Turbulence?




(14) What
are the ranges of Reynolds number for flow over a flat plate.


(15) Write
down the 1/7^{th} power law.




(16) Write
down the time smoothed equation of motion




(17) Write
the expression for hydrodynamic boundary layer thickness for flow past a flat
plate.




(18) Write
down the expression for D=d_{T}/d for the situation when D< 1




(19) Write down the expression
for D=dC/d for the situation when D< 1



(20) Write the relationship
between friction factor ‘ f ’ and
Reynolds number.
PART
B
1. Derive the logarithmic velocity
distribution for turbulent flow. [For both near the wall and far away from
wall].
2.
[a]
Explain with a neat sketch, the velocity distribution for turbulent flow in
tubes.
[b] Write down the equations for the three regions of
turbulent flow.
3. Explain The following : (a) Reynolds stresses, (b) Eddy Viscosity,
(c) Creeping flow (d) Drag coefficient.
4. What do you know about Boundary Layer
theory? Illustrate with flow near a wall suddenly set in motion.
5. Discuss the laminar and turbulent hydrodynamic,
thermal and concentration boundary layer thicknesses.
6. Obtain a description of the
incompressible flow pattern near the leading edge of a flat plate immersed in a
fluid stream.
7. Write short notes on the following:
(i) Boundary layer thickness; (ii) Displacement thickness; (iii) Momentum
thickness and (iv) Energy thickness.
8.
Water
is flowing through a long straight smooth pipe of 15 cm inside diameter at a
temperature of 20^{0}C. The pressure gradient along the length
of the pipe is 50 mm Hg/kilometer. What is the volumetric rate of flow assuming
the flow is turbulent.
9. Write short notes on the following:
(i) Boundary layer thickness; (ii) Displacement thickness; (iii) Momentum
thickness and (iv) Energy thickness.
10. Explain in detail, the following: (a)
Flow through packed bed & (b) Von Karman’s similarity hypothesis.
UNIT V
ANALOGIES BETWEEN
TRANSPORT PROCESSES
PART
A (2 MARK)
(1) State
the usefulness of analogy.


(2) Define
J_{D } factor


(3) Write
down the j_{D} factor.


(4) Define jH factor.


(5) State Colburn analogy.


(6) State the Reynold’s analogy


(7)Define Soret coefficient s
.


(8) What is Soret effect?


(9) Write down Schmidt number
and compare with Prandtl number.


(10) Write down the expression
for D=dC/d for the situation when D< 1


(11) Compare the temperature,
pressure and composition dependence of mass diffusivity.thermal conductivity
and viscosity.


PART
B
(1)

Write
what you know about Reynolds Analogy in detail.



(2)

Describe
the Von Karman hypothesis in respect of analogy between the different
transport operations.



(3)

Write an account of Colburn analogy



(4)

Write an
essay about analogy that exists amongst the three transports Momentum, Heat
and Mass.



(5)

Write in
detail about Prandtl Analogy.

(6) Write Short notes on:
(i) Reynolds analogy
(ii) Prnndtl analogy
(iii) Colburn analogy
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