Question

A spherical shaped vessel of 2 m 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 0.09 W/m°C.

Answer 1

Solution.

$r_2=2m;$

$r_1=1.91m;$

$\Delta t=220^oC;$

$k=0.09W/m^oC;$

$Q=\dfrac{\Delta t}{R};$

$R=\dfrac{r_2-r_1}{4\pi k r_1r_2};$

$R=\dfrac{2-1.91}{4\sdot3.14\sdot0.09\sdot2\sdot1.91}=\dfrac{0.09}{4.32}=0.021^oC/W;$

$Q=\dfrac{220}{0.021}=10476W=10.476kW;$

Answer: $Q=10.476kW.$