This set of Heat Transfer Multiple Choice Questions & Answers (MCQs) focuses on “Conduction Through A Sphere”.

1. The temperature distribution associated with radial conduction through a sphere is represented by

a) Parabola

b) Hyperbola

c) Linear

d) Ellipse

View Answer

Explanation: As conduction is radial i.e. in outward direction, so it follows the hyperbola equation..

2. The thermal resistance for heat conduction through a spherical wall is

a) (r_{2}-r_{1})/2πkr_{1}r_{2}

b) (r_{2}-r_{1})/3πkr_{1}r_{2}

c) (r_{2}-r_{1})/πkr_{1}r_{2}

d) (r_{2}-r_{1})/4πkr_{1}r_{2}

View Answer

Explanation: We get this on integrating the equation Q = -k A d t/ d r from limits r

_{1}to r

_{2}and T

_{1}to T

_{2}.

3. The rate of conduction heat flow in case of a composite sphere is given by

a) Q = t_{1 }– t_{2}/ (r_{2} – r_{1})/4πk_{1}r_{1}r_{2 }+_{ }(r_{3} – r_{2} )/4πk_{2}r_{2}r_{3}

b) Q = t_{1 }– t_{2}/ (r_{2} – r_{1})/4πk_{1}r_{1}r_{2 }+_{ }(r_{3} – r_{2} )/4πk_{2}r_{2}r_{3}

c) Q = t_{1 }– t_{2}/ (r_{2} – r_{1})/4πk_{1}r_{1}r_{2 }+_{ }(r_{3} – r_{2} )/4πk_{2}r_{2}r_{3}

d) Q = t_{1 }– t_{2}/ (r_{2} – r_{1})/4πk_{1}r_{1}r_{2 }+_{ }(r_{3} – r_{2} )/4πk_{2}r_{2}r_{3}

View Answer

Explanation: Here, convective film coefficient at the inner and outer surfaces are also considered.

4. The thermal resistance for heat conduction through a hollow sphere of inner radius r_{1} and outer radius r_{2} is

a) r _{2} – r _{1}/4πk_{ }r _{1}r _{2}

b) r _{2 }/4πk_{ }r _{1}r _{2}

c) r _{1}/4πk_{ }r _{1}r _{2}

d) 4πk_{ }r _{1}r _{2}

View Answer

Explanation: As Q = d t/ R

_{T}. Here R

_{T }is thermal resistance.

5. A spherical vessel of 0.5 m outside diameter is insulated with 0.2 m thickness of insulation of thermal conductivity 0.04 W/m degree. The surface temperature of the vessel is – 195 degree Celsius and outside air is at 10 degree Celsius. Determine heat flow per m^{2} based on inside area

a) – 63.79 W/m^{2}

b) – 73.79 W/m^{2}

c) – 83.79 W/m^{2}

d) – 93.79 W/m^{2}

View Answer

Explanation: Heat flow based on inside area = Q/4 π r

^{2 }= – 73.79 W/m

^{2}.

6. The quantity d t/Q for conduction of heat through a body i.e. spherical in shape is

a) ln (r_{2}/r_{1})/2πLk

b) ln (r_{2}/r_{1})/πLk

c) ln (r_{2}/r_{1})/2Lk

d) ln (r_{2}/r_{1})/2πk

View Answer

Explanation: We get this on integrating the equation Q = -k A d t/ d r from limits r

_{1}to r

_{2}and T

_{1}to T

_{2}.

7. A spherical vessel of 0.5 m outside diameter is insulated with 0.2 m thickness of insulation of thermal conductivity 0.04 W/m degree. The surface temperature of the vessel is – 195 degree Celsius and outside air is at 10 degree Celsius. Determine heat flow

a) – 47.93 W

b) – 57.93 W

c) – 67.93 W

d) – 77.93 W

View Answer

Explanation: Q = 4 π k r

_{1}r

_{2}(t

_{1}– t

_{2})/r

_{2 }– r

_{1}= -57.93 W.

8. If we increase the thickness of insulation of a circular rod, heat loss to surrounding due to

a) Convection and conduction increases

b) Convection and conduction decreases

c) Convection decreases while that due to conduction increases

d) Convection increases while that due to conduction decreases

View Answer

Explanation: In convection energy is transferred between solid and fluid but in conduction from T

_{ 1}to T

_{ 2}.

9. The following data pertains to a hollow cylinder and a hollow sphere made of same material and having the same temperature drop over the wall thickness

Inside radius = 0.1 m and outside surface area = 1 square meter

If the outside radius for both the geometrics is same, calculate the ratio of heat flow in the cylinder to that of sphere?

a) 0.056

b) 2.345

c) 1.756

d) 3.543

View Answer

Explanation: For sphere r

_{2 }= (1/4 π)

^{1/2}= 0.282 m, for cylinder, l = A

_{ 2}/2 r

_{2 }π = 0.565 m.

10. The oven of an electric store, of total outside surface area 2.9 m^{2} dissipates electric energy at the rate of 600 W. The surrounding room air is at 20 degree Celsius and the surface coefficient of heat transfer between the room air and the surface of the oven is estimated to be 11.35 W/m ^{2 }degree. Determine the average steady state temperature of the outside surface of the store

a) 38.22 degree Celsius

b) 48.22 degree Celsius

c) 58.22 degree Celsius

d) 68.22 degree Celsius

View Answer

Explanation: Q = h A (t

_{0 }– t

_{a}).

**Sanfoundry Global Education & Learning Series – Heat Transfer.**

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