Consider a tube $($diameter $=2cm,$ length $=13m)$ of which a uniform heat flux is applied from all surfaces. The volumetric flow rate of water flowing in the tube is $5\frac{L}{m}in.$ Inlet and outlet temperatures of water are $10C$ and $80C,$ respectively. Determine the $($a$)$ rate of convection heat transfer, $($b$)$ inner surface temperature of the pipe at the exit.