The upper surface of a plywood roof is maintained at T(s)= 5 degrees centigrade
ID: 2993896 • Letter: T
Question
The upper surface of a plywood roof is maintained at T(s)= 5 degrees centigrade by blowing warm air over the lower surface of the roof. The emittance of the surface of the roof is epsilon=0.80 and it is losing heat to a night sky that acts like a black body at T(sky)=200K. The upper surface is also exposed to ambient air at T(out)= 10 degrees centigrade with a convection coefficient h(out)= 8 W/m^2K. The plywood roof is 12mm thick and k=0.12 W/mK for plywood. The convection coefficient for the warm air blowing over the lower surface of the roof is h(in)= 25 W/m^2K.
Find the net rate of heat loss from the upper surface of the roof to the surroundings and the temperature of the warm air blowing over the lower surface of the roof.
(ans: 158.4 W/m^2 and T(in)=27.2 degrees centigrade).
Explanation / Answer
HEAT LOSS BY RADIATION = SIGMA * E*(T1^4 - T2^4)
=(5.67 * 10^-8) 0.8 (278^4 - 200^4)
=198.4 W/m^2
HEAT GAIN BY CONVECTION = h(10-5) = 8 * (5) = 40W/m^2
NET HEAT LOSS= 198.4- 40 = 158.4W/m^2
LET TEMP OF AIR BE T
HEAT LOSS = 158.4 = (T-5) / {(1/25) + (0.012/0.12)}
T= 27.2
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