A 2-m × 1.5-m section of wall of an industrial furnace burning natural gas is not
insulated, and the temperature at the outer surface of this section is measured to be 80°C.
The temperature of the furnace room is 30°C, and the combined convection and
radiation heat transfer coefficient at the surface of the outer furnace is 10 W/m2 ⋅ °C. It
is proposed to insulate this section of the furnace wall with glass wool insulation (k =
0.038 W/m ⋅ °C) in order to reduce the heat loss by 90 percent. Assuming the outer
surface temperature of the metal section still remains at about 80°C, determine the
thickness of the insulation that needs to be used.
The furnace operates continuously and has an efficiency of 78 percent. The price
of the natural gas is $0.55/therm (1 therm = 105,500 kJ of energy content). If the
installation of the insulation will cost $250 for materials and labor, determine how long
it will take for the insulation to pay for itself from the energy it saves.