Assume the roof of a room in a typical house is 12 cm thick concrete slab with a

Question

Assume the roof of a room in a typical house is 12 cm thick concrete slab with a thermal conductivity k=2.0 W/m C. The roof of the room is 4.0 m wide and 4.5 m long. Assume convection heat transfer coefficient on the inner and outter surfaces of the roof are 6 and 10 W/m^2 C, respectively. At noon, when the sun is "hotter" the solar irradiation is estimated to be q=750 W/m^2 and the solar absorptivity of the roof surface is %u03B1=0.85 (this means that the slab absorbs 85% of the solar irradiation). The ambient air outside is reported to be 30 C (due to the high humidity, you can neglect radiation to the sky). The room of the house has an air conditioner system that removes heat at a rate of 4100 Watts (14000 BTU/h). If you can neglect gains from the walls of the room and consider only gains from the roof of the room. Which is going to be the inner temperature of the room?

Explanation / Answer

Let the inner temperature of the room be T

heat absorbed by the roof due to sun = area of roof * irradiance * 0.85 = 0.85 * 750 * 4 * 4.5 = 11,475 Watt

net heat transfer inside the room = heat removed by the air condictionar = 4100 Watt

so heat reflected by the roof = 11,475 - 4100 = 7,375 Watt

so... for the outer suface of the roof ..

10 * 4*4.5 * ( T_outer - 30 ) = 7,375

so.. T_outer = 70.9722 Celcius

Let inner temp be T_inner..

net thermal reistance = 0.12 / ( 2 * 4 *4.5 ) + ( 1 / (6 * 4*4.5 ) ) = 0.0125926

so.. 70.9722 - T_innet = 4100 * 0.0125926

so T_inner = 19.3426 Celcius...

so the inner temp of the room = 19.3426 Celcius...

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects