Thin electrical heater is wrapped around the outer surface of a long cylindrical tube whose inner surface is maintained at a temperature of 5°c. the tube wall has inner and outer radii of 40 and 90 mm, respectively, and a thermal conductivity of 10 w/m·k. the thermal contact resistance between the heater and the outer surface of the tube (per unit length of the tube) is 0.01 m·k/w. the outer surface of the heater is exposed to a fluid with [infinity] -10°c and a convection coefficient of 100 w/m2·k. determine the heater power per unit length of tube required to maintain the heater at 25°c.