A thin electrical heates is inserted between a long circular sod and a concentric tube with inner and

outer radii of $25$ and $50$ mun $.$ The rad $($A$)$ has a thermal conductivity of K A $=0.1\frac{W}{m}.$ K $,$ while the

tabe $($B$)$ has a thermal conductivity of $k=2\mathrm{.}0\frac{W}{m}.K$ and its outer surfece is subjected to

convection with a fluid of temperature $T_{os}=-15C$ and heat transfor coefficiont $100\frac{W}{m^2}.$ K $.$

Neglect any contact resistinne.

$($a$)$ Determine the electrical power fer unit length of the cylinders $($W$/$m$)$ that is required to maintain

the outer surferee of cylinder B at $5C.$

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