whose inner surface is maintained at a temperature of $5C.$ The tube wall has inner and outer radii of $25$ and $75$ mm $,$ respectively, and a thermal conductivity of $10=\frac{W}{m}K.$ The thermal contact resistance between the heater and the outer surface of the tube $($per unit length of the tube$)$ is $Rt,c=0\mathrm{.}01m\frac{K}{W}.$ The outer surface of the heater is exposed to a fluid with $T=10C$ and a convection coefficient of $h=100\frac{W}{m}2K.$ Determine the heater power per unit length of tube required to maintain the heater at $T_o=20C.$