CRITICAL THICKNESS OF INSULATION OBJECTIVE QUESTIONS (GATE, IES, IA...
3. Critical Thickness of Insulation
O
BJECTIVEQ
UESTIONS(GATE, IES, IAS)
Previous 20-Years GATE Questions Critical Thickness of InsulationGATE-1. A steel steam pipe 10 cm inner diameter and 11 cm outer diameter is
covered with insulation having the thermal conductivity of 1 W/mK. If
the convective heat transfer coefficient between the surface of
insulation and the surrounding air is 8 W / m
2
K, then critical radius of
insulation is:
[GATE-2000]
(a) 10 cm
(b) 11 cm
(c) 12.5 cm
(d) 15 cm
GATE-2. It is proposed to coat a 1 mm diameter wire with enamel paint (k = 0.1
W/mK) to increase heat transfer with air. If the air side heat transfer
coefficient is 100 W/m
2
K, then optimum thickness of enamel paint
should be:
[GATE-1999]
(a) 0.25 mm
(b) 0.5 mm
(c) 1 mm
(d) 2 mm
GATE-3. For a current wire of 20 mm diameter exposed to air (h = 20 W/m
2
K),
maximum heat dissipation occurs when thickness of insulation (k = 0.5
W/mK) is:
[GATE-1993; 1996]
(a) 20 mm
(b) 25 mm
(c) 20 mm
(d) 10 mm
Heat Conduction with Heat Generation in the Nuclear Cylindrical Fuel RodGATE-4. Two rods, one of length L and the other of length 2L are made of the
same material and have the same diameter. The two ends of the longer
rod are maintained at 100°C. One end of the shorter rod Is maintained
at 100°C while the other end is insulated. Both the rods are exposed to
the same environment at 40°C. The temperature at the insulated end of
the shorter rod is measured to be 55°C. The temperature at the mid-
point of the longer rod would be:
[GATE-1992]
(a) 40°C
(b) 50°C
(c) 55°C
(d) 100°C
Previous 20-Years IES QuestionsIES-1.
Upto the critical radius of insulation:
[IES-1993; 2005]
(a) Added insulation increases heat loss
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(b) Added insulation decreases heat loss
(c) Convection heat loss is less than conduction heat loss
(d) Heat flux decreases
IES-2.
Upto the critical radius of insulation
[IES-2010]
(a) Convection heat loss will be less than conduction heat loss
(b) Heat flux will decrease
(c) Added insulation will increase heat loss
(d) Added insulation will decrease heat loss
IES-3.
The value of thermal conductivity of thermal insulation applied to a
hollow spherical vessel containing very hot material is 0·5 W/mK. The
convective heat transfer coefficient at the outer surface of insulation is
10 W/m
2
K.
What is the critical radius of the sphere?
[IES-2008]
(a) 0·1 m
(b) 0·2 m
(c) 1·0 m
(d) 2·0 m
IES-4.
A hollow pipe of 1 cm outer diameter is to be insulated by thick
cylindrical insulation having thermal conductivity 1 W/mK. The surface
heat transfer coefficient on the insulation surface is 5 W/m
2
K. What is
the minimum effective thickness of insulation for causing the
reduction in heat leakage from the insulated pipe?
[IES-2004]
(a) 10 cm
(b) 15 cm
(c) 19.5 cm
(d) 20 cm
IES-5.
A metal rod of 2 cm diameter has a conductivity of 40W/mK, which is to
be insulated with an insulating material of conductivity of 0.1 W/m K. If
the convective heat transfer coefficient with the ambient atmosphere is
5 W/m
2
K, the critical thickness of insulation will be:
[IES-2001; 2003]
(a) 1 cm
(b) 2 cm
(c) 7 cm
(d) 8 cm
IES-6. A copper wire of radius 0.5 mm is insulated with a sheathing of
thickness 1 mm having a thermal conductivity of 0.5 W/m – K. The
outside surface convective heat transfer coefficient is 10 W/m
2
– K. If
the thickness of insulation sheathing is raised by 10 mm, then the
electrical current-carrying capacity of the wire will:
[IES-2000]
(a) Increase
(b) Decrease
(c) Remain the same
(d) Vary
depending
upon
the
electrical conductivity of the wire
IES-7.
In current carrying conductors, if the radius of the conductor is less
than the critical radius, then addition of electrical insulation is
desirable, as
[IES-1995]
(a) It reduces the heat loss from the conductor and thereby enables the
conductor to carry a higher current.
(b) It increases the heat loss from the conductor and thereby enables the
(c) It increases the thermal resistance of the insulation and thereby enables the
(d) It reduces the thermal resistance of the insulation and thereby enables the
IES-8.
It is desired to increase the heat dissipation rate over the surface of an
electronic device of spherical shape of 5 mm radius exposed to
convection with h = 10 W/m
2
K by encasing it in a spherical sheath of
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conductivity 0.04 W/mK, For maximum heat flow, the diameter of the
sheath should be:
[IES-1996]
(a) 18 mm
(b) 16 mm
(c) 12 mm
(d) 8 mm
IES-9.
What is the critical radius of insulation for a sphere equal to?
k = thermal conductivity in W/m-K
[IES-2008]
h = heat transfer coefficient in W/m
2
K
(a) 2kh
(b) 2k/h
(c) k/h
(d) 2kh
IES-10. Assertion (A): Addition of insulation to the inside surface of a pipe
always reduces heat transfer rate and critical radius concept has no
significance. [IES-1995]
Reason (R): If insulation is added to the inside surface, both surface
resistance and internal resistance increase.
(a) Both A and R are individually true and R is the correct explanation of A
(b) Both A and R are individually true but R is not the correct explanation of A
(c) A is true but R is false
(d) A is false but R is true
IES-11. Match List-I (Parameter) with List-II (Definition) and select the correct
answer using the codes given below the lists:
[IES-1995]
List-I
List-II
A. Time constant of a thermometer of radius r
o
1.
hr
o
/k
fluid
B. Biot number for a sphere of radius r
o
2.
k/h
C. Critical thickness of insulation for a wire of radius r
o
3.
hr
o
/k
solid
D. Nusselt number for a sphere of radius r
o
4.
h r l cV
2
π
o
ρ
Nomenclature
:
h: Film heat transfer coefficient, k
solid
: Thermal
conductivity of solid, k
fluid
: Thermal conductivity of fluid, ρ: Density,
c: Specific heat, V: Volume, l: Length.
Codes:
A
B
C
D
A
B
C
D
(a)
4
3
2
1
(b)
1
2
3
4
(c)
2
3
4
1
(d)
4
1
2
3
IES-12. An electric cable of aluminium conductor (k = 240 W/mK) is to be
insulated with rubber (k = 0.15 W/mK). The cable is to be located in air
(h = 6W/m
2
). The critical thickness of insulation will be:
[IES-1992]
(a) 25mm
(b) 40 mm
(c) 160 mm
(d) 800 mm
IES-13. Consider the following statements:
[IES-1996]