Question

The inner and outer surfaces of a spherical shell are maintained at 0t and 1t temperatures respectively. If the inner and outer radii of the shell are 0r and 1r respectively and thermal conductivity of the shell is k, find the amount of heat lost from the shell per unit time. Find also the temperature distribution through the shell.

Answer 1

To find the amount of heat lost from the shell per unit time, use the rate of heat transfer formula. The temperature distribution through the shell is linear from the inner to outer surfaces.

Step-by-step explanation:

To find the amount of heat lost from the shell per unit time, we need to calculate the rate of heat transfer. The rate of heat transfer through conduction is given by the equation Q/t = kA(T2-T1)/d, where Q/t is the rate of heat transfer, k is the thermal conductivity, A is the surface area, T2-T1 is the temperature difference, and d is the thickness of the shell.

By substituting the given values into the equation, we can find the rate of heat transfer. To determine the temperature distribution through the shell, we can use Fourier's Law of Heat Conduction which states that the temperature distribution is linear within a solid material with constant thermal conductivity. In this case, the temperature will vary from 0t on the inner surface to 1t on the outer surface of the shell.