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 a cylinder is $2\pi rL$, so we find:
$ \frac{H}{2\pi R} dr = -kLdT $
Applying the integral on both sides, it follows:
$ \frac{HlnR_2 - HlnR_1}{2\pi}= -kL(T_1-T_2)$
$H = \frac{2\pi kL(T_1-T_2)}{ln(R_2/R_1)}$
