How to solve

A thin electricat heater is fitted between two long, concentric cylinders having inner

and outer radii of $20$ and $40$ mm ; respectively: The inner solid cylinder $($A$)-$has a thenmal

conductivity of $0\mathrm{.}15\frac{W}{m}*K.$ The outer cylinder $($B$)$ has a thermal conductivity of $1\mathrm{.}5$

W$/$m K and its surface is subjected to convection with a fluid of temperature $T_{}=-15C$

and heat transfer coefficient of $50\frac{W}{m^2}*K.$ The thermal resistances between the

cylindrical surfaces and the heater are negligible.

a$)$ Determine the electricat power per unit length of the cylinders $($W$/$m$)$ that is required

to maintain the outer surface of the cylinder $($B$)$ at $5C.$

b$)$ What is the temperature at the center of cylinder $($A$)?$