Question

A spherical shaped vessel of 1.4 m outer diameter is 90 mm thick. Find the rate of heat leakage, if the temperature difference between the inner and outer surfaces is 220°C. Thermal conductivity of the material of the sphere is 0.083 W/m K.
1. 0.2 kW
2. 0.5 kW
3. 1.08 kW
4. 1.6 kW

Answer 1

Correct Answer - Option 3 : 1.08 kW

r₂ = 0.7 m

r₁ = 0.7 – 0.09 = 0.61 m

dT = 220°C, k = 0.083 W/mK

rate of heat leakage:

\(Q = \frac{{dT}}{R}\)

\(R = \frac{{{r_2} - {r_1}}}{{4\pi k{r_1}{r_2}}} = \frac{{0.09}}{{4 \times 3.14 \times 0.083 \times 0.7 \times 0.61}}\)

R = 0.20218

\(Q = \frac{{220}}{{2020}} = 1.088kW\)