Tallow is stored in a vertical tank 3 m in diameter and 9-m high. The tank is insulated with a 0.05-m layer of 85% magnesia. To prevent freezing, the tallow is maintained at a temperature of 50oC by condensing steam at 135.8 kPa (abs) in a heating coil of 3/4 inch 18-gauge (BWG) copper tubing. If the minimum outdoor temperature is -20oC and the tallow is always at a uniform temperature, compute the length of copper tubing needed to maintain the tank at 50oC in the coldest weather. Neglect heat losses from the top and bottom of the tank.
Heat-transfer coefficient h[W/(m2?K)]
Steam condensing inside coil 4540
Tubing wall to molten tallow 230
Molten tallow to tank wall 230
Outer surface of insulation 10