A 2-m * 1.5-m section of wall of an industrial furnaceburning natural gas is not insulated, and the temperatureat the outer surface of this section is measured to be 80°C.The temperature of the furnace room is 30°C, and the combinedconvection and radiation heat transfer coefficient at thesurface of the outer furnace is 10 W/m2·K. It is proposed toinsulate this section of the furnace wall with glass wool insulation(k = 0.038 W/m·K) in order to reduce the heat lossby 90 percent. Assuming the outer surface temperature ofthe metal section still remains at about 110°C, determine thethickness of the insulation that needs to be used.The furnace operates continuously and has an efficiency of78 percent. The price of the natural gas is $1.10/therm (1 therm =105,500 kJ of energy content). If the installation of the insulationwill cost $250 for materials and labor, determine how long it willtake for the insulation to pay for itself from the energy it saves.

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·K. It is proposed to
insulate this section of the furnace wall with glass wool insulation
(k = 0.038 W/m·K) in order to reduce the heat loss
by 90 percent. Assuming the outer surface temperature of
the metal section still remains at about 110°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 $1.10/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.