For more information log on
Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)
Copyright by Brij Bhooshan @ 2013
Page 1
Solution of UPSC Papers
Of
Heat Transfer
Steady State Heat Conduction
Prepared By
Brij Bhooshan
Asst. Professor
B. S. A. College of Engg. And Technology
Mathura, Uttar Pradesh, (India)
Supported By:
Purvi Bhooshan
Please welcome for any correction or misprint in the entire manuscript and your
valuable suggestions kindly mail us [email protected]
1985
Problem:
Develop an expression for the heat flux passing radially through a long
composite cylinder of length
L
made up of three concentric layers of different materials
and thicknesses in terms of
r
1
the inside radius of the inner cylinder;
r
2
,
r
3
and
r
4
, the
outside radii of the inner, middle and the outer cylinders respectively; their
corresponding thermal conductivities
k
l
,
k
2
and
k
3
; the temperature
T
1
at the inner
surface of the inner cylinder and the temperature
T
4
at the outer surface of the outer,
cylinder,
T
1
being greater than
T
4
. If the inside heat transfer coefficient of a fluid at
temperature
T
1
flowing through this cylinder is
h
i
and the outside heat transfer
coefficient of another fluid at temperature
T
2
flow in the outside is
h
0
, determine the
overall heat transfer coefficient referred to the inside surface.
[Engg. Services-1985]
Solution:
Now according to problem electrical network as shown in diagram.
Now thermal resistance due to fluid is
T
2
T
1
R
ci
R
1
R
2
R
3
R
c0

For more information log on
Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)
Copyright by Brij Bhooshan @ 2013
Page 2
2
Solution of UPSC Papers of Steady State Heat Conduction
Now thermal resistance due to conduction is
Now net thermal resistance is
R
th
=
R
ci
+ R
1
+ R
2
+ R
3
+ R
c0
Now we know that heat flux
Also we know that
Using equation (1) and (2), we have
where
U
0
is overall heat transfer
Then overall heat transfer is
1991
Problem:
Starting from basic differential equation, derive an expression for the
temperature distribution in a cylindrical rod in which a uniform heat generation occurs
and the surface temperature of the rod is
T
S
. Mention the assumptions.
[IAS-1991]
Solution:
Let us consider a long solid cylinder of radius
R
with internal heat generation
as shown in above diagram, such as an electric coil in which heat is generated as a
result of the electric current in the wire or a cylindrical nuclear fuel element in which
heat is generated by nuclear fission.
The one-dimensional heat conduction equation in cylindrical coordinates is
On integration
0

For more information log on
Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)
Copyright by Brij Bhooshan @ 2013
Page 3
3
Solution of UPSC Papers of Heat Transfer By Brij Bhooshan
Again integration
where
A
and
B
are the arbitrary constants.

#### You've reached the end of your free preview.

Want to read all 23 pages?

- Fall '15