Question set 150
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
Answer: b
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
Answer: a
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
Answer: c
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)
Answer: d
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
Answer: a
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
Answer: b
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
Answer: c
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
Answer: d
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
Answer: a
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
Answer: b
Explanation: For cylinder, it is 0.439 i.e. lowest.