Chapter 3, Problem 3.48P

A thin electrical heater is wrapped around the outer surface of a long cylindrical tube whose inner surface is maintained at a temperature of $5°\text{C}\text{.}$ The tube wall has inner and outer radii of 25 and 75 mm. respectively. and a thermal conductivity of $10\text{W/m}\cdot \text{K}\text{.}$ The thermal contact resistance between the heater and the outer surface of the tube (per unit length of the tube) is $R_{t,c}^{\text{'}}=0.01\text{m}\cdot \text{K/W}\text{.}$ The outer surface of the heater is exposed to a fluid with $T_{\infty }=-10°\text{C}$ and a convection coefficient of $h=100\text{}{\text{W/m}}^{\text{2}}\cdot \text{K}\text{.}$ Determine the heater power per unit length of tube required to maintain the heater at $T_o=25°\text{C}\text{.}$