Heat Transfer Multiple Choice Questions & Answers (MCQs) on “Heat Generation Through Sphere”.
1. Consider heat conduction through a solid sphere of radius R. There are certain assumptions
(i) Unsteady state conditions
(ii) One-dimensional radial conduction
(iii) Constant thermal conductivity
Identify the correct statements
a) i and iii
b) ii and iii
c) i, ii and iii
d) i and ii
Answer: b
Clarification: Statement 1 should be steady state condition.
2. An 8 cm diameter orange, approximately spherical in shape, undergoes ripening process and generates 18000 k J/m3 hr of energy. If external surface of the orange is at 6.5 degree Celsius, find out the temperature at the center of the orange. Take thermal conductivity = 0.8 k J/ m hr degree for the orange material
a) 13.5 degree Celsius
b) 12.5 degree Celsius
c) 11.5 degree Celsius
d) 10.5 degree Celsius
Answer: b
Clarification: q g = 5000 W/m3, k = 0.222 W/m K and t = t W + q g R 2/6K = 12.5 degree Celsius.
3. Consider the above problem, calculate the heat flow from the outer surface of the orange
a) 4.82 k J/hr
b) 5.82 k J/hr
c) 6.82 k J/hr
d) 7.82 k J/hr
Answer: a
Clarification: Q = 4/3 (π R 3 q g) = 1.34 J/s.
4. What is the heat flow for steady state conduction for sphere?
a) 4 Q R + Q G = Q R + d R
b) 3 Q R + Q G = Q R + d R
c) 2 Q R + Q G = Q R + d R
d) Q R + Q G = Q R + d R
Answer: d
Clarification: Q R + Q G = Q R + d (Q R) d R/d R.
Where, Q R = Heat conducted in at radius R
Q G = Heat conducted in the element
Q R + d R = Heat conducted out at radius R + d R.
5. The general solution for temperature distribution in case of solid sphere is
a) t = t W + q g (R 2 – r 2)/4 k
b) t = t W + q g (R 2 – r 2)/8 k
c) t = t W + q g (R 2 – r 2)/6 k
d) t = t W + q g (R 2 – r 2)/2 k
Answer: c
Clarification: The temperature distribution is parabolic.
6. A solid sphere of 8 cm radius has a uniform heat generation 0f 4000000 W/m3. The outside surface is exposed to a fluid at 150 degree Celsius with convective heat transfer coefficient of 750 W/m2 K. If thermal conductivity of the solid material is 30 W/m K, determine maximum temperature
a) 444.45 degree Celsius
b) 434.45 degree Celsius
c) 424.45 degree Celsius
d) 414.45 degree Celsius
Answer: b
Clarification: q g (4 π R3/3) = h 4 π R2 (t W – t a), t w = 292.22 degree Celsius
T MAX = t w + q g R 2/6 k.
7. Consider the above problem, find the temperature at 5 cm radius
a) 348.9 degree Celsius
b) 358.9 degree Celsius
c) 368.9 degree Celsius
d) 378.9 degree Celsius
Answer: d
Clarification: t – t w/t MAX – t w = 1 – (r/R) ½.
8. Identify the correct boundary condition for a hollow sphere with inside surface insulated
a) At r = r 1, the conduction region is perfectly insulated
b) At r = r 1, the conduction region is partially insulated
c) Heat flow is infinity
d) Heat flow is negative
Answer: a
Clarification: In this range, the conduction region must be perfectly insulated.
9. A hollow sphere (k = 30 W/m K) of inner radius 6 cm and outside radius 8 cm has a heat generation rate of 4000000 W/m3. The inside surface is insulated and heat is removed by convection over the outside surface by a fluid at 100 degree Celsius with surface conductance 300 W/m2 K. Make calculations for the temperature at the outside surfaces of the sphere
a) 105.6 degree Celsius
b) 205.6 degree Celsius
c) 305.6 degree Celsius
d) 405.6 degree Celsius