2112 −ΠΠRR4 KRR4K2112IES-28. A SOLID SPHERE AND A HOLLOW SPHERE OF...
2
)
2
1
2
−
π
r
4
kr
r
4
k
IES-28. A solid sphere and a hollow sphere of the same material and size are
heated to the same temperature and allowed to cool in the same
surroundings. If the temperature difference between the body and that
of the surroundings is T, then
[IES-1992]
(a) Both spheres will cool at the same rate for small values of T
(b) Both spheres will cool at the same reactor small values of T
(c) The hollow sphere will cool at a faster rate for all the values of T
(d) The solid sphere will cool a faster rate for all the values of T
Logarithmic Mean Area for the Hollow SphereIES-29. What will be the geometric radius of heat transfer for a hollow sphere
of inner and outer radii r
1
and r
2
? [IES-2004]
(a)
r r
1 2
(b)
r r
2 1
(c)
r
2
/
r
1
(d)
(
r
2
−
r
1
)
Heat Condition through a Composite SphereIES-30. A composite hollow sphere with steady internal heating is made of 2
layers of materials of equal thickness with thermal conductivities in
the ratio of 1 : 2 for inner to outer layers. Ratio of inside to outside
diameter is 0.8. What is ratio of temperature drop across the inner and
outer layers?
[IES-2005]
(a) 0.4
(b) 1.6
(c) 2 ln (0.8)
(d) 2.5
Page 17 of 97
IES-31. Match List-I (Governing Equations of Heat Transfer) with List-II
(Specific Cases of Heat Transfer) and select the correct answer using
the code given below:
[IES-2005]
List-I
List-II
2
0
d T
dT
A.
dr
+
r dr
=
1. Pin fin 1–D case
∂
=
∂
T
T
B.
∂
∂
2. 1–D conduction in cylinder
x
α
t
1
0
C.
dr
+
r dr
=
3. 1–D conduction in sphere
θ
−
θ
=
4. Plane slab
d
m
D.
dx
(Symbols have their usual meaning)
Codes:
A
B
C
D
A
B
C
D
(a)
2
4
3
1
(b)
3
1
2
4
(c)
2
1
3
4
(d)
3
4
2
1
Previous 20-Years IAS QuestionsIAS-1.
A hollow sphere has inner and outer surface areas of 2 m
2
and 8 m
2
respectively. For a given temperature difference across the surfaces,
the heat flow is to be calculated considering the material of the sphere
as a plane wall of the same thickness. What is the equivalent mean area
normal to the direction of heat flow?
[IAS-2007]
(a) 6 m
2
(b) 5 m
2
(c) 4 m
2
(d) None of the above
Page 18 of 97
Answers with Explanation (Objective) Previous 20-Years GATE AnswersGATE-1. Ans. (d) One dimensional, Unsteady state, without internal heat generation
t
∂
x
α
GATE-2. Ans. (b)
GATE-3. Ans. (b)
GATE-4. Ans. (d)
Q
=
+
=
GATE-5. Ans. (c)
20 2
250
1
0.30 0.15
1
+
+
+
20
20
50
50
or 250
20
or
3.75 C
=
−
=
°
1
0.30
+
20
20
GATE-6.
Ans. (d)
int
1
2
T
=
+
er
2
T
T
T
T
+
+
⎛
−
⎞
⎛
−
⎞
1
2
1
2
⎜
⎟
⎜
⎟
1
2
2
2
⎝
⎠
⎝
⎠
Heat flow must be same( )
Q
k A
k
= −
= −
b
b
=
or
2
k
k
GATE-7. Ans. (c) Electrical circuit
Use this formula
R
L
=
+
1
1
eq
K A
L
L
2
3
K A
K A
2
2
3
3
GATE-8. Ans. (d) Lower the thermal conductivity greater will be the slope of the
temperature distribution curve (The curve shown here is temperature
distribution curve).
π
−
π
× ×
2
2
1
600
L t
t
i
f