Athin 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.