Chapter 13.2, Problem 11E

When there is heat transfer from the lateral side of an infinite circular cylinder of unit radius (see Figure 13.2.6) into a surrounding medium at temperature zero, the temperature u(r, t) inside the cylinder is determined from

$k\left(\frac{{\partial }^{2}u}{\partial r^2}+\frac{1}{r}\frac{\partial u}{\partial r}\right)=\frac{\partial u}{\partial t},0<r<1,t>0$

${\frac{\partial u}{\partial r}|}_{r-1}=-hu(1,t),h>0,t>0$

u(r, 0) = f(r), 0 < r < 1.

Solve for u(r, t).

Figure 13.2.6 Infinite cylinder in Problem 11