Answer
The proof is below.
Work Step by Step
We start with the given equation:
$ H = -kA \frac{dT}{dr}$
We know that the area of the sides is $\pi R^2$, so we find:
$ \frac{H}{\pi R_1^2-\pi R_2^2} dr = -kLdT $
Applying the integral on both sides, it follows:
$H = \frac{\pi kR_1R_2(T_1-T_2)}{(L)}$
