# Heat Transfer MCQ’s – Shape Factor

1 - Question

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
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 - Question

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
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 - Question

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

4 - Question

Two radiating surface A 1 = 6 m2 and A 2 = 4 m2 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
Explanation: A 1 F 12 = A 2 F 21.

5 - Question

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

6 - Question

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
Explanation: F 11 + F 12 = 1 or F 12 = 1. So, F 21 = π/6.

7 - Question

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
Explanation: F 11 + F 12 = 1 and F 21 = 1. Therefore, F 11 = 0.5.

8 - Question

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
Explanation: F 11 = 1 – A 2 / A 1 = 1 – 2 sin α = 1 – d/ (4 h 2 + d 2) ½.

9 - Question

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
Explanation: F 11 = 1 – A 2 / A 1 = 0.5.

10 - Question

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