Question $3$:

$[20$ mark:

The energy balance equation in spherical coordinates in the radial direction and with a constant heat generation $=$ constant $"K"$ independent of temperature $($equal to a constant $"K")$ can be written $($after some assumptions are made$)$ as:

$\frac{1}{r^2}\frac{d}{dr}(r^2\frac{dT}{dr})+k=0$

Where $$ is a constant $($thermal diffusivity$)$ and you can use ${}^2$ equal to $($K$/$a$),$ also a constant. With the given boundary condilions, find a complete solution for the temperature distribution. $T(r).$

CamScanner $$

Page $14$

p$,$ calculate all the appropriate constants $C_1$ and $C_2$ with the following boundary condition. at$,r=0,$

$(\frac{dT}{dr})=0$