A flat roof is modeled as a flat plate insulated on the bottom and placed in the sunlight. If the radiant heat that the roof receives from the sun is 600 W/m2 , the convection heat transfer coefficient between the roof and the air is 12 W/(m2 K), and the air temperature is 27°C, determine the roof temperature for the following two cases: (a) Radiative heat loss to space is negligible. (b) The roof is black (? = 1.0) and radiates to space, which is assumed to be a black-body at 0 K.
GIVEN
FIND
ASSUMPTIONS
- Steady state prevails
- No heat is lost from the bottom of the plate
SKETCH
(a) For this case steady state and the conservation of energy require the heat lost by convection, from
Equation (1.10), to be equal to the heat gained from the sun
(b) In this case, the solar gain must be equal to the sum of the convective loss, from Equation (1.10),
and radiative loss,
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