(Solution) - A flat roof can be modeled as a flat plate -(2025 Original AI-Free Solution)

Paper Details

A flat roof can be 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
A flat plate in the sunlight
Radiant heat received from the sun (qr/A) = 600 W/m2
Air temperature (T?) = 27°C
Convective heat transfer coefficient ( hc ) = 12 W/(m2 K)
ASSUMPTIONS
Steady state prevails
No heat is lost from the bottom of theplate