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

1. “All the factors relating to the geometry of the sections are grouped together into a multiple constant called the shape factor”.

a) True

b) False

View Answer

Explanation: They are grouped together into a single constant instead of multiple one.

2. Shape factor for a plane wall is equal to

a) A/δ

b) 2A/δ

c) 3A/δ

d) 4A/δ

View Answer

Explanation: It should be obtained by dividing area with respect to length.

3. For a prescribed temperature difference, bodies with the same shape factor will allow heat conduction proportional to

a) k/2

b) 2k

c) k

d) k/4

View Answer

Explanation: It is proportional to material thermal conductivity irrespective of size and configuration.

4. Shape factor for cylinder is

a) 6 π l/log _{e} (r _{2}/r _{1})

b) 4 π l/log _{e} (r _{2}/r _{1})

c) π l/log _{e} (r _{2}/r _{1})

d) 2 π l/log _{e} (r _{2}/r _{1})

View Answer

Explanation: It is two times the rest of the product.

5. The annealing furnace for continuous bar stock is open at the ends and has interior dimensions of 0.6 m * 0.6 m * 1.5 m long with a wall 0.3 m thick all around. Calculate the shape factor for the furnace?

a) 15.24 m

b) 16.34 m

c) 14.54 m

d) 13.76 m

View Answer

Explanation: Shape factor for 4 walls = 4 (area of wall)/ (thickness) = 4 (1.5) (0.6)/0.3 = 12 m. Shape factor for 4 edges = 4 (0.54) (1.5) = 3.24 m. Total = 15.24 m.

6. Shape factor for sphere is

a) 4 π r _{1} r _{2}

b) 4 π r _{1} r _{2}/r _{2 }– r _{1}

c) 4 π /r _{2 }– r _{1}

d) r _{1} r _{2}/r _{2 }– r _{1}

View Answer

Explanation: In case of sphere it is given in option b. Area of sphere is 4 π r

^{2}.

7. Which is true regarding a complete rectangular furnace?

a) 6 walls, 12 edges and 6 corners

b) 0 walls, 2 edges and 4 corners

c) 6 walls, 12 edges and 8 corners

d) 2 walls, 6 edges and 8 corners

View Answer

Explanation: It has 6 walls, 12 edges and 8 corners.

8. The shape factor for complete rectangular furnace is

Where a, b and c are the inside dimensions and d x is the wall thickness

a) 2/ d x (a b + b c + c a) + 4 (0.64) (a + b +c) + 8 (0.45) d x

b) 2/ d x (a b + b c + c a) + 4 (0.44) (a + b +c) + 8 (0.35) d x

c) 2/ d x (a b + b c + c a) + 4 (0.34) (a + b +c) + 8 (0.25) d x

d) 2/ d x (a b + b c + c a) + 4 (0.54) (a + b +c) + 8 (0.15) d x

View Answer

Explanation: S

_{edge}= 0.54 times length of edge. S

_{corner }= 0.15 d x.

9. For the same material and same temperature difference, the heat flow in terms of shape factor is given by

a) S k d t

b) k d t/S

c) 2S k/d t

d) 2S/3

View Answer

Explanation: The heat flow is proportional to the shape factor.

10. For the same amount of fabrication material and same inside capacity, the heat loss is lowest in

a) Sphere

b) Cylinder

c) Rectangle

d) Cube

View Answer

Explanation: For cylinder, it is 0.439 i.e. lowest.

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