Find the temperature as a function of radius r in case of a cylindrical shell whose inner surface temperature and outer surface temperature are $ \theta_1$ and $ \theta_2$. The inner and outer radii of the cylindrical shell are $r_1$ and $r_2$.

Question

$\begin {array} {1 1} (A)\;\theta_1 - (\theta_1 + \theta_2)\: ln\: (r_1/r_2) / ln(r_2/r_1) & \quad (B)\;\theta_1 + (\theta_1 - \theta_2)\: ln\: (r/r_1) / ln(r_2/r_1) \\ (C)\;\theta_1 - (\theta_1 - \theta_2)\: ln\: (r/r_1) / ln(r_1/r_2) & \quad (D)\;\theta_1 - (\theta_1 - \theta_2)\: ln\: (r/r_1) / ln(r_2/r_1) \end {array}$