# Thermal Engineering Questions and Answers – Heat Transfer by Conduction

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This set of Thermal Engineering Objective Questions & Answers focuses on “Heat Transfer by Conduction”.

1. If the radius of any current carrying conductor is less than the critical radius, then why the addition of electrical insulation will enable the wire to carry a higher current?
a) The heat loss from the wire would decrease
b) The heat loss from the wire would increase
c) The thermal resistance of the insulation is reduced
d) The thermal resistance of the conductor is increased

Explanation: If the radius of any current carrying conductor is less than the critical radius, then the addition of electrical insulation will enable the wire to carry a higher current because heat loss from the wire would increase. Radius of wire is inversely proportional to heat loss.

2. Which of the following substance has the minimum value of thermal conductivity?
a) Air
b) Water
c) Plastic
d) Rubber

Explanation: Among the given options air has the minimum value of thermal conductivity. Thermal conductivity of air is approximately Kair=0.02.

3. In MLTθ system (T time and θ temperature), what is the dimension of thermal conductivity?
a) ML-1T-1θ-3
b) MLT-1θ-3
c) MLT-3θ-1
d) MLT-2θ-1

Explanation: Q=-KA(dT/dx)
(ML2T-3) = k (L2) (θ)
K = ML2T-3/Lθ , K=MLT-3θ-1.

4. For conduction through a spherical wall with constant thermal conductivity and with inner side temperature greater than outer wall temperature in 1-D heat transfer, what is the type of temperature
distribution?
a) Linear
b) Parabolic
c) Hyperbolic
d) Logarithmic

Explanation: For one dimensional steady heat flow-
i. Temperature distribution in slab is linear
ii. Temperature distribution in cylinder is logarithmic
iii. Temperature distribution in sphere is hyperbolic.

5. Which of the following expresses the thermal diffusivity of a substance in terms of thermal conductivity of a substance (k), mass density (ρ) and specific heat (c)?
a) k2ρc
b) 1/ρkc
c) k/ρc
d) ρc/k2

Explanation: Thermal diffusivity indicates the ease at which energy get diffused in the volume of the substances. It is defined as the ratio of the thermal conductivity to the heat capacity of the substance.
Therefore, α = k/ρc.

6. A copper block and an air mass block having similar dimensions are subjected to symmetrical heat transfer from one face of the each block. The other face of the block will be reaching to the same temperature at a rate?
a) Faster in air block
b) Faster in copper block
c) Equal in air as well as copper block
d) Data in sufficient

Explanation: Thermal conductivity is minimum in gases and maximum in solids. Thermal conductivity of copper is higher than air. Hence heat flow will be in copper block rather than air block.

7. The outer surface of a long cylinder is maintained at constant temperature. The cylinder does not have any heat source. The temperatures in the cylinder will _________

Explanation: The temperature distribution will vary logarithmically with radius for cylinder.
α = $$\frac{2πLk(T1-T2)}{(ln⁡(\frac{r1}{r2})}$$.

8. A steam pipe is covered with two layers of insulating materials, with the better insulating material forming the outer. What is the effect on heat conducted if the two layers are interchanged?
a) Will increase
b) Will decrease
c) Will remain unaffected
d) May increase or decrease depending upon the thickness of each layer

Explanation: Let k1 and k2 be the thermal conductivity of the two insulators, k1 being the better insulator.
Q = $$\frac{A∆T}{\frac{ln⁡(\frac{r2}{r1})}{k1}+\frac{ln⁡(\frac{r3}{r2})}{k2}}$$
If we interchange the insulators, the value of Q might increase or decrease depending upon the thickness of each layer.

9. A plane wall is 20cm thick with an area perpendicular to heat flow of 1m2 and has a thermal conductivity of 0.5W/mK. A temperature difference of 100°C is imposed across it. What is the ratio of heat flow?
a) 0.10 kW
b) 0.15 kW
c) 0.20 kW
d) 0.25 kW

Explanation: Thermal resistance, Rth = $$\frac{L}{KA}=\frac{0.2}{0.5×1}=0.5\frac{K}{W}$$

Heat transfer, Q = $$\frac{(T1-T2)}{R_{th}}=\frac{100}{0.5}$$=200W=0.2kW.

10. An insulating material with a thermal conductivity k = 0.12W/mK is used for a pipe carrying steam. The local coefficient of heat transfer to the surrounding h = 4 W/m2K. In order to provide effective insulation, what should be the minimum outer diameter of the pipe?
a) 45mm
b) 60mm
c) 75mm
d) 90mm

rc = $$\frac{k}{h}=\frac{0.12}{4}$$=0.03m=30mm
Hence, outer diameter = rc = (2×30) mm = 60mm.

11. In a long cylindrical rod of radius R and a surface heat flux of q0, what is the uniform internal heat generation rate?
a) 2q0/R
b) 2q0
c) q0/R
d) 2q0/3R

Explanation: In steady state, Heat generated = Heat conducted at surface
qg × πR2L = q0 × 2πRL
qg = 2q0/R.

12. A plane slab of 100mm thickness generates heat. It is observed that the temperature drop between the center and its surface to be 50°C. If the thickness is increased to 200mm the temperature difference will be ___________
a) 100°C
b) 200°C
c) 400°C
d) 600°C

Explanation: Tmax = Twall + qgL2/2k
(Tmax – Twall) = qgL2/2k
(Tmax – Twall) α L2
$$\frac{(Tmax – Twall)2}{(Tmax – Twall)1}=\frac{L_2}{L_1}$$
(Tmax – Twall)2/50 = $$(\frac{200}{100})$$2
(Tmax – Twall)2 = 400°C.

13. As the temperature increases, the thermal conductivity of a gas ____________
a) Increases
b) Decreases
c) Remain constant
d) Increases up to a certain temperature and then decreases