1. 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
Explanation: 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.
2. 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
Explanation: The temperature distribution is parabolic.
3. 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
Explanation: 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.
4. 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
Explanation: t – t w/t MAX – t w = 1 – (r/R) ½.
5. 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
Explanation: In this range, the conduction region must be perfectly insulated.
6. 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
Explanation: q g 4 π (R 3 – r 3)/3 = h 0 4 π r 2 (t 2 – t a).
7. Consider the above problem, also calculate the temperature at the inside surfaces of the sphere
a) 138.3 degree Celsius
b) 327.8 degree Celsius
c) 254.7 degree Celsius
d) 984.9 degree Celsius
Explanation: t = t 2 + q g (R 2 – r 2)/6 k – q g r 3 (1/r – 1/R)/3 k.
8. Which one is true regarding rectangular fin?
a) A C = b δ and P = 2(b + δ)
b) A C = 2 b δ and P = 2(b + δ)
c) A C = 3 b δ and P = 2(b + δ)
d) A C = 4 b δ and P = 2(b + δ)
Explanation: For rectangle, A = (length) (breadth). Where, b = width and δ = thickness
9. Analysis of heat flow from the finned surface is made with the following assumptions
(i) Uniform heat transfer coefficient, h over the entire fin surface
(ii) No heat generation within the fin generation
(iii) Homogenous material
Identify the correct option
a) i only
b) i and ii only
c) i, ii and iii
d) ii only
Explanation: The knowledge of temperature distribution is necessary for their optimum design with regard to size and weight.
10. If heat conducted into the element at plane x is Q X = – k A C (d t/d x) X. Then heat conducted out of the element at plane (x + d x) is
a) – 2k A C d/d x (t + d t/d x (d x))
b) – k A C d/d x (t + d t/d x (d x))
c) – 3k A C d/d x (t + d t/d x (d x))
d) – 4k A C d/d x (t + d t/d x (d x))
Explanation: Heat conducted out of the element is – [k A C (d t/d x) X + d x].