A very thin electric heater is wrapped around the outer surface of a long cylindrical tube to

maintain the temperature of the flowing fluid inside the tube at $5$ C $.$ The convection coefficient

between the flowing fluid and the inner wall of the tube is $10\frac{W}{m^2.K}.$ The tube wall has inner

and outer radii of $25$ mm and $75$ mm respectively and a thermal conductivity of $).$

Assume that there is no contact resistance between the heater and the outer surface of the tube. The

outer surface of the heater is exposed to a fluid with a temperature of $-10C$ and a convection

coefficient of $100W(m^2(K)).$ Answer the following guestions:$)$

$($a$)$ Draw the equivalent thermal circuit and mark the resistances

$[5$ points$]$

$($b$)$ Determine the heater power per unit length of the tube required to maintain the heater at $T_0=$

$25C.$

$[10$ points$]$