Question

A solid cylinder, 0 ≤ r ≤ b, is initially at zero temperature. For times t > 0, internal energy is generated in the solid at a rate of g(t) per unit volume (W/m3), whereas the boundary surface at r = b dissipates heat by convection into a medium at zero temperature. Obtain an expression for the temperature distribution T(r,t) in the cylinder for times t > 0.

Answer 1

At $t>0$ $r=0,T(r,t)=\frac{g(t)}{v}$

At $t>0$ $r=b,T(r,t)=-g(t)$

$\therefore\ T(r,t)=\frac{g(t,)}{v}-g(t)$