A thin electrical heater is wrapped around the outer surface of a long cylindrical tube whose inner surface is maintained at a temperature of 6°C. The tube wall has inner and outer radii of 24 and 78 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 R′t, c = 0.01 m ⋅ K/W. The outer surface of the heater is exposed to a fluid with T[infinity] = −10°C and a convection coefficient of h = 100 W/m2 ⋅ K. Determine the heater power per unit length of tube required to maintain the heater at To = 25°C.