Heat Transfer
Exam Duration: 45 Mins Total Questions : 25
Heat transfer takes place according to
- (a)
zeroth law of thermodynamics
- (b)
first law of thermodynamics
- (c)
second law of thermodynamics
- (d)
third law of thermodynamics
Using thermal electrical analogy in heat transfer, match List I (Electrical quantities) with List" (Thermal quantities) and select the correct answer using the codes given below the lists.
List I | List II |
P. Voltage | 1. Thermal resistance |
Q. Current | 2. Thermal capacity |
R. Resistance | 3. Heat flow |
S. Capacitance | 4. Temperature |
- (a)
P Q R S 2 3 1 4 - (b)
P Q R S 4 1 3 2 - (c)
P Q R S 2 1 3 4 - (d)
P Q R S 4 3 1 2
The equivalent thermal conductivity of the wall as shown in the figure below is
- (a)
\(\frac { { K }_{ 1 }+{ K }_{ 2 } }{ 2 } \)
- (b)
\(\frac { { K }_{ 1 }{ K }_{ 2 } }{ { K }_{ 1 }+{ K }_{ 2 } } \)
- (c)
\(\frac { 2{ K }_{ 1 }{ K }_{ 2 } }{ { K }_{ 1 }+{ K }_{ 2 } } \)
- (d)
\(\sqrt { { K }_{ 1 }{ K }_{ 2 } } \)
Heat flows through a composite slab, as shown in the figure given below. The depth of the slab is 1 m. The values of K are in W/m-K. The overall thermal resistance in K/W is
- (a)
17.2
- (b)
21.9
- (c)
28.6
- (d)
39.2
In the given figure, consider one-dimensional heat conduction in Y- direction. Temperature of point Pis 80 0C and Q = 1 W/m2. If K = 1 W/m-K, then at steady state, the temperature of point Q is
- (a)
zero
- (b)
77 0C
- (c)
80 0C
- (d)
Data insufficient
A flat plate has thickness 5 cm, thermal conductivity 1 W/m-K, convective heat transfer coefficients on its two flat faces of 10 W/m2-K and 20 W/m2-K. The overall heat transfer coefficient for such a flat plate is
- (a)
5 W/m2-K
- (b)
6.33 W/m2-K
- (c)
20 W/m2-K
- (d)
30 W/m2-K
A steady two-dimensional heat conduction takes place in the body shown in the figure below. The normal temperature gradients over surfaces P and Q can be considered to be uniform. The temperature gradient \(\frac { \partial T }{ \partial x } \) at surface Q is equal to 10 K/m. Surfaces P and Q are maintained at constant temperatures as shown in the figure, while the remaining part of the boundary is insulated. The body has a constant thermal conductivity of 0.1 W/m-K. The values of \(\frac { \partial T }{ \partial y } \) and \(\frac { \partial T }{ \partial x } \) at surface P are
- (a)
\(\frac { \partial T }{ \partial x } =20K/m,\frac { \partial T }{ \partial y } =0\)
- (b)
\(\frac { \partial T }{ \partial x } =0,\frac { \partial T }{ \partial y } =10K/m\)
- (c)
\(\frac { \partial T }{ \partial x } =10K/m,\frac { \partial T }{ \partial y } =10K/m\)
- (d)
\(\frac { \partial T }{ \partial x } =0,\frac { \partial T }{ \partial y } =20K/m\)
There is a steady one-dimensional heat conduction through a slab. If T1 = 70 °C and T2 =30 °C, then temperature of point P is
- (a)
40 0C
- (b)
43.3 0C
- (c)
45 0C
- (d)
47 0C
Upto the critical radius of insulation
- (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
Water jacketed copper rod of D m diameter is used to carry the current. The water, which flows continuously maintains the rod temperature at T10C during normal operation at I A. The electrical resistance of the rod is known to be R Ω/m. If the coolant water ceased to be available and the heat removal diminished greatly, the rod would eventually melt. What is the time required for melting if the melting point of the rod material is Tmp? (CP is specific heat, p is density of the rod material an L is the length of the rod.)
- (a)
\(\rho \left( \frac { \pi { D }^{ 2 } }{ 4 } \right) { C }_{ P }\frac { \left( { T }_{ mp }-{ T }_{ l } \right) }{ { l }^{ 2 }R } \)
- (b)
\(\frac { \left( { T }_{ mp }-{ T }_{ l } \right) }{ \rho l^{ 2 }R } \)
- (c)
\(\frac { \rho \left( { T }_{ mp }-{ T }_{ l } \right) }{ { l }^{ 2 } } \)
- (d)
\(\frac { { C }_{ p }\left( { T }_{ mp }-{ T }_{ l } \right) }{ { l }^{ 2 }R } \)
The net resistance of given system is (given, h1 = 1W/m2- 0C, h2 = 2 W/m2-0C, K = 4 W/m-0C, A = 3 m2, l =1 m)
- (a)
\(\frac { 5 }{ 32 } \) 0C / W
- (b)
\(\frac { 12 }{ 5 } \) 0C / W
- (c)
\(\frac { 5 }{ 24 } \) 0C / W
- (d)
\(\frac { 24 }{ 5 } \) 0C / W
In compound cylinder, heat flows longitudinally, thermal conductivities for inner cylinder and outer cylinder are 1 W/m-K and 4 W/m-K respectively. The net resistance of given system (in K/W) is
- (a)
\(\frac { 17 }{ 4\pi } \)
- (b)
\(\frac { 4 }{ 17\pi } \)
- (c)
\(\frac { 8 }{ \pi } \)
- (d)
\(\frac { 2\pi }{ ln2 } \)
A composite hollow sphere with steady internal heating is made of 2 layers of materials of equal thicknesses with thermal conductivities in the ratio of 1 : 2 for inner to outer layers. Ratio of inside to outside diameters is 0.8. What is the ratio of temperature drop across the inner and outer layers?
- (a)
0.4
- (b)
1.6
- (c)
2 ln 0.8
- (d)
2.5
In given figure, there is a hollow cylinder which contains a liquid at 25 °C and outer surface is exposed to gas having temperature 225°C. If thermal conductivity of cylinder is 1 W/m-K and hi = ho = 2 W/m2-K, r1 = 1cm, r2 = 2 cm, then heat transfer rate (assume radial heat transfer) in W/m is
- (a)
13
- (b)
9.52
- (c)
11.25
- (d)
16.59
A cylinder made of a metal of conductivity 40 W/m-K is to be insulated with a material of conductivity 0.1 W/m-K. If the convective heat transfer coefficient with the ambient atmosphere is 5 W/m2-K, the critical radius of insulation is
- (a)
2 cm
- (b)
4 cm
- (c)
8 cm
- (d)
50 cm
Thermal conductivity of hollow cylinder varies as K = K0r, where r is radial distance from centre. Thermal resistance of cylinder (L = 1m) if T1 > T2, is
- (a)
\(\frac { { r }_{ 2 }-{ r }_{ 1 } }{ 4\pi { K }_{ 0 }{ r }_{ 1 }{ r }_{ 2 } } \)
- (b)
\(\frac { { r }_{ 2 }-{ r }_{ 1 } }{ 2\pi { K }_{ 0 }{ r }_{ 1 }{ r }_{ 2 } } \)
- (c)
\(\frac { ln\left( { r }_{ 2 }/{ r }_{ 1 } \right) }{ 2\pi { K }_{ 0 } } \)
- (d)
\(\frac { 2\pi { K }_{ 0 } }{ ln\left( { r }_{ 2 }/{ r }_{ 1 } \right) } \)
A wire is kept in a hollow tube having radius 8 cm and thermal conductivity 0.2 W/m-K. (L = 1m). Diameter of wire is 1 cm and electric current flows through it I0 = 0.5 A, V, = 10 V, V2 = 4 V. Heat transfer across the cylinder (radial) is
- (a)
10 W
- (b)
4 W
- (c)
3 W
- (d)
6 W
A wire is kept in a hollow tube having radius 8 cm and thermal conductivity 0.2 W/m-K. (L = 1m). Diameter of wire is 1 cm and electric current flows through it l0 = 0.5 A, V1 = 10 V, V2 = 4 V. Temperature of wire, if To = 20°C, is
- (a)
22.37 0C
- (b)
24.96 0C
- (c)
39.87 0C
- (d)
26.64 0C
A copper tube with 8 cm outer diameter, 6 cm inner diameter and K = 15 W/m-K is covered with an insulation covering of thickness 2 cm and K = 0.2 W/m-K. A hot gas at 300 0C with h = 400 W/m2-K flows inside the tube. The outer surface of insulation is exposed to cool air at 30 "C with ha = 50 W/m2-K. Overall heat transfer coefficient based on outer surface of insulation is
- (a)
6.75 W/m2-K
- (b)
10 W/m2-K
- (c)
5.6 W/m2-K
- (d)
7.25 W/m2-K
A copper tube with 8 cm outer diameter, 6 cm inner diameter and K = 15 W/m-K is covered with an insulation covering of thickness 2 cm and K = 0.2 W/m-K. A hot gas at 300 0C with h = 400 W/m2-K flows inside the tube. The outer surface of insulation is exposed to cool air at 30 "C with ha = 50 W/m2 -K. If tube length is 25 m, then heat loss from tube is (in kW)
- (a)
20
- (b)
17.19
- (c)
18
- (d)
15.27
An electrical conductor of 10 mm diameter, insulated by asbestos (K = 0.18 W/m-K), is installed in air at 30°C having convective heat transfer coefficient of 7.8 W/m2-K. If the surface temperature of base conductor is 85 0C, a 2 mm thick insulation is provided and resistivity of conductor is 70 μΩ-cm.Current flowing through the conductor is
- (a)
40 A
- (b)
45 A
- (c)
43.8 A
- (d)
50 A
An electrical conductor of 10 mm diameter, insulated by asbestos (K = 0.18 W/m-K), is installed in air at 30°C having convective heat transfer coefficient of 7.8 W/m2-K. If the surface temperature of base conductor is 85 0C, a 2 mm thick insulation is provided and resistivity of conductor is 70 μΩ-cm. Critical thickness of insulation is
- (a)
23 mm
- (b)
5 mm
- (c)
18 mm
- (d)
28 mm
An electrical conductor of 10 mm diameter, insulated by asbestos (K = 0.18 W/m-K), is installed in air at 30°C having convective heat transfer coefficient of 7.8 W/m2-K. If the surface temperature of base conductor is 85 0C, a 2 mm thick insulation is provided and resistivity of conductor is 70 μΩ-cm. Maximum current which can flow through the wire, is
- (a)
43.8 A
- (b)
52.48 A
- (c)
55 A
- (d)
60.72 A
Consider steady one-dimensional heat flow in a plate of 20 mm thickness with a uniform heat generation of 80 MW/m2 . The left and right faces are kept at constant temperatures of 160°C and 120 °C respectively. (Kplate = 200 W/m-K). The location of maximum temperature within the plate from its left face is
- (a)
15 mm
- (b)
10 mm
- (c)
5 mm
- (d)
zero
Consider steady one-dimensional heat flow in a plate of 20 mm thickness with a uniform heat generation of 80 MW/m2 . The left and right faces are kept at constant temperatures of 160°C and 120 °C respectively. (Kplate = 200 W/m-K). The maximum temperature within the plate in 0C, is
- (a)
160
- (b)
165
- (c)
200
- (d)
250