The roof of a house consists of a 22-cm-thick concrete slab (k = 2 W/m∙K) that is 15 m wi...

The roof of a house consists of a 22-cm-thick concrete slab (k = 2 W/m∙K) that is 15 m wide and 20 m long. The emissivity of the outer surface of the 1roof is 0.9, and the convection heat transfer coefficient on that surface is estimated to be 15 W/m2∙K. The inner surface of the roof is maintained at 15°C. On a clear winter night, the ambient air is reported to be at 10°C while the night sky temperature for radiation heat transfer is 255 K. Considering both radiation and convection heat transfer, determine the outer surface temperature and the rate of heat transfer through the roof.

If the house is heated by a furnace burning natural gas with an efficiency of 85 percent, and the unit cost of natural gas is $1.20/therm (1 therm = 105.500 kJ of energy content), determine the money lost through the roof that night during a 14-hour period.