Name
Reg No
APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
07 THRISSUR CLUSTER
FIRST SEMESTER M.TECH. DEGREE EXAMINATION DEC 2017
Mechanical Engineering Department
Internal Combustion Engines and Turbo Machinery
07ME6105 ADVANCED HEAT AND MASS TRANSFER
Time:3 hours Max.marks: 60
Answer all six questions. Part of each question is compulsory.
Answer either part or part of each question
Q.no. Module 1 Marks
1a Consider a cylindrical shell with inner and outer surfaces at r1 and r2
maintained at uniform temperatures T1 and T2, respectively. If there is a
uniform heat generation within the shell, obtain expressions for the steady
one dimensional radial distribution of the temperature, heat flux and heat
transfer rate.
4
Answer b or c
b Heat is generated within a wire of 3 mm in diameter by passing a current of
350A. The thermal conductivity and resistivity of the wire are 25 W/m K and
80×10-8 respectively, and the length of the wire is 2.2m. This wire is
immersed in a water bath maintained at 30oC. The heat transfer coefficient at
the outer surface of the wire is 4500 W/m2 K. Calculate the temperature at the
centre of the wire and at the surface of the wire.
5
c The thermal conductivity of a plane wall may be approximated by a linear
expression of the form k ko a where is a positive constant and is
a coefficient that may be positive or negative. Obtain an expression for the
heat flux across the plane wall whose inner and outer surfaces are maintained
at temperatures Ti and To, respectively.
5
Q.no. Module 2 Marks
2a What do you understand by lumped and distributed heat transfer models?
Elucidate your answer with examples.
4
Answer b or c
b A steel plate of 100 mm thick 7830 kg/m3, cp 550 J/kg.K, k 48
W/m. which is initially at a uniform temperature of Ti 200oC is to be
heated to a minimum temperature of 550oC. Heating is effected in a gas
fired furnace, where products of combustion at 800oC maintain a
convection coefficient of h 250 W/m2.K on both surfaces of the plate.
How long should the plate be left in the furnace?
5
c The density 2200 kg/m3) and specific heat (Cp 700 J/kg of a
material are known but its thermal conductivity is unknown. To determine
the thermal conductivity, an experiment is conducted on a thick sample of
the material in which a thermocouple is embedded 10 mm from a surface
that is suddenly brought to a temperature of 100oC by exposure to boiling
water. If the initial temperature of the slab was 30oC and the thermocouple
measures a temperature of 65oC, 2 minutes after the surface is brought to
100oC, what is its thermal conductivity?
5
Q.no. Module 3 Marks
3a Explain the physical significance of Nusselt number, Prandtl number,
Reynolds number and Eckert number in the heat transfer study.
4
Answer b or c
b Consider the laminar boundary layer flow of a liquid metal with velocity
and temperature along a flat plate kept at a uniform temperature Tw.
Derive expressions for the thermal boundary layer thickness t x )and the
local Nusselt number x Nu by using a linear profile for the temperature
distribution given in the form,
w
w t
T y T y
T T x





. Assume that the
flow velocity over the large portion of thermal boundary layer is uniform
and equal to
5
c A steady laminar boundary layer experiment was conducted on an
isothermal plate with a fluid of Prandtl number equals 0.72. The local wall
shear stress was given by the expression:
x
U
x U w

0.332 where the symbols have their usual notations.
Obtain an expression for local Nusselt number in terms of Reynolds
number and Prandtl number using Colburn analogy.
5
Q.no. Module 4 Marks
4a State and prove Kirchhoff's law of thermal radiation. 4
Answer b or c
b A long, thin walled horizontal tube 100 mm in diameter is maintained at
120oC by the passage of steam through its interior. A radiation shield
installed around the tube, providing an air gap of 10 mm between the tube
and the shield, reaches a surface temperature of 35oC. The tube and shield
are diffuse, gray surfaces with emissivities of 0.8 and 0.1 respectively.
What is the radiant heat transfer from the tube per unit length? Assume air
as a non-participating medium to radiation
5
c A furnace is of cylindrical shape with a diameter of 0.3 m and a length of
0.3 m. The two ends have diffuse, gray surfaces that are maintained at 400
and 500K with emissivities of 0.4 and 0.5 respectively. The lateral surface
is also diffuse and gray with an emissivity of 0.8 and a temperature of
800K. Determine the net irradiative heat transfer from each of the surfaces.
5
Q.no. Module 5 Marks
5a Explain the phenomenon of equimolar counter diffusion. Derive an
expression for equimolar counter diffusion between two gases.
5
Answer b or c
b Ammonia and air experience equimolar counter diffusion in a circular tube
of 3 mm diameter and 20 m long. The system is at a total pressure of 1 atm
and a temperature of 25oC. One end of the tube is connected to a large
reservoir of ammonia and the other end of the tube is open to atmosphere.
If the mass diffusivity of the mixture is 0.3×10-4 estimate the mass
transfer rate of ammonia and air through the tube.
7
c A pan of 40 mm deep is filled with water to a level of 20 mm and is
exposed to dry air at 30oC. Calculate the time required for all the water to
evaporate. Take, mass diffusivity as 0.25×10-4 m2/s.
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Q.no. Module 6 Marks
6a Explain the difference between diffusion and convective mass transfer. 5
Answer b or c
b
Air at 30oC and atmospheric pressure, containing small quantities of iodine
flows with a velocity of 5 m/s inside a 3 cm inner diameter tube. Determine
the mass transfer coefficient from the air stream to the wall surface. Take,
mass diffusivity as 0. 82×10-5 m2/s.
7
c Pure N2 gas at 1 atm and 25°C is flowing through a 10m long, 3 cm inner
diameter pipe made of 1mm-thick rubber. Determine the rate at which N2
leaks out of the pipe if the medium surrounding the pipe is a vacuum
and atmospheric air at 1 atm and 25°C with 21 percent O2 and 79
percent N2.
7