QN$3.$ Consider the system in figure $3,$ involving $1-$D radial heat conduction through the wall of a cylindrical pipe. The pipe is either insulated at both ends or is long enough $($length$,L)$ that end effects are negligible. Assume that there are no internal heat sources within the pipe wall. Given that the inner surface temperature $T_1$ is greater than the outer surface temperature $T_2,$ heat will flow radially outward from the inner radius $R_1$ to the outer radius $R_2.($a$)$ Derive the expression for heat flow, $Q.$ Show that the thermal resistance $R,$ is expressed as

$R=\frac{ln(\frac{r_2}{r_1})}{2kL}$

Hint: The differential equation governing heat diffusion is

$\frac{1}{r}*\frac{d}{dr}(r*\frac{dT}{dr})=0$