This set of Heat Transfer Multiple Choice Questions & Answers (MCQs) focuses on “Shape Factor”.

1. Which of the following is a wrong statement according to the shape factor is equal to one?

a) For any surface completely enclosed by another surface

b) For infinite parallel planes radiating only to each other

c) For a flat or convex surface with respect to itself

d) Inside cylinder to outer cylinder of a long co-axial cylinder

View Answer

Explanation: For a flat or convex surface, the shape factor with respect to itself is zero. This aspect stems from the fact that for any part of flat or convex surface, one cannot see any other part of the same surface.

2. Establish a relation for the shape factor of cylindrical cavity with respect to itself of depth h and diameter d. The cavity is closed on its outer surface with a flat plate

a) 4 h/4 h + d

b) 4 h + d/h

c) 4 h + d/4 h

d) h/4 h + d

View Answer

Explanation: F

_{11}+ F

_{ 12}= 1 and F

_{21}+ F

_{ 22}= 1. But F

_{ 22}= 0, so F

_{11}= 1 – A

_{2 }/ A

_{1}.

3. The reciprocity theorem states that

a) F _{12} = F _{21}

b) A _{1 }F _{12 }= A_{ 2} F _{21}

c) A _{1 }F _{21 }= A_{ 2} F _{12}

d) A _{2 }F _{21 }= A_{ 1} F _{12}

View Answer

Explanation: It indicates the net radiation exchange can be calculated by computing one way configuration factor from either surface to the other.

4. Two radiating surface A _{1} = 6 m^{2} and A _{2} = 4 m^{2} have shape factor F _{12} = 0.1. Then the shape factor F _{21} will be

a) 0.12

b) 0.18

c) 0.15

d) 0.10

View Answer

Explanation: A

_{1 }F

_{12 }= A

_{ 2}F

_{21}.

5. What is the value of shape factor for two infinite parallel surfaces separated by a distance x?

a) 0

b) 1

c) x

d) Infinity

View Answer

Explanation: All the radiation emitted by one falls on the other so shape factor is unity.

6. What is the shape factor of a sphere of diameter d inside a cubical box of length l = d?

a) π/6

b) 2 π/6

c) π/3

d) π/4

View Answer

Explanation: F

_{11}+ F

_{ 12}= 1 or F

_{12}= 1. So, F

_{21 }= π/6.

7. What is the shape factor of hemispherical surface closed by a plane surface of diameter d?

a) 0

b) 1.5

c) 1

d) 0.5

View Answer

Explanation: F

_{11}+ F

_{ 12}= 1 and F

_{21}= 1. Therefore, F

_{11}= 0.5.

8. Establish a relation for shape factor for a conical cavity with respect to itself of depth h and diameter d. The cavity is closed on its outer surface with a flat plate

a) 1 – d/ (4 h ^{2} + d) ^{1/2}

b) 1 – d/ (4 h ^{2} + d ^{2}) ^{1/2}

c) 1 – d/ (4 h + d ^{2}) ^{1/2}

d) 1 – d/ (h ^{2} + d ^{2}) ^{1/2}

View Answer

Explanation: F

_{11}= 1 – A

_{2 }/ A

_{1}= 1 – 2 sin α = 1 – d/ (4 h

^{2}+ d

^{2})

^{½}.

9. What is the shape factor for a hemispherical bowl with respect to itself of diameter d? The cavity is closed on its outer surface with a flat plate

a) 1.5

b) 1

c) 0.5

d) 2.5

View Answer

Explanation: F

_{11}= 1 – A

_{2 }/ A

_{1 }= 0.5.

10. Consider a system of concentric spheres of radius r_{ 1} and r_{ 2} (r_{ 2} is greater than r_{ 1}). If r_{ 1} = 5 cm, determine the radius r_{ 2} if it is desired to have the value of shape factor F _{21} equal to 0.6

a) 6.45 cm

b) 7.45 cm

c) 8.45 cm

d) 9.45 cm

View Answer

Explanation: From reciprocity theorem, A

_{1 }F

_{12 }= A

_{ 2}F

_{21}.

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

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