PROBLEM $2(25$ points$)$

A portion of a long, hollow cylinder $arb,0$ is initially at temperature $T=rsin().$

For times $t>0,$ the boundaries at $r=a,r=b,=0,$ and $=$ are all kept at zero temperature.

Obtain an expression for the temperature distribution $T(r,,t)$ in the solid for times $t>0.$ Please

try to obtain the most simplified expression for the solution.