Question

A point source of heat of power $P$ is placed at the centre of a spherical shell of mean radius $R$. The material of the shell has thermal conductivity $K$. If the temperature difference between the outer and inner surface of the shell is not to exceed $T$, the thickness of the shell should not be less than ______.

Answer 1

When the spherical shell is thin, $t<<R$

In this case, the rate of flow of heat from the sphere to the surroundings

$P=\frac{K\left(4\pi R^2\right)T}{t}$

where $T$ is the temperature difference and $t$ is the thickness of steel.

$t=\frac{4\pi R^{2}KT}{P}$.