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Answer:
Total heat transfer rate is combined convection and radiation transfer rate, multiplied with absorptivity factor. From that equation you can find temperature of the roof using iteration method.
Explanation:
<u>Known:</u>
steel sheet roof emissivity ∈ = 0.13
steel sheet roof absorptivity _s = 0.65
air temperature T∞ = 16°C ...= 289K
heat transfer rate = 750 W/m2
natural convection h = 7W/m2K
Total heat transfer rate is combined heat transfer rate of convection and radiation, multiplied with absorptivity factor:
=
T∞-
)+∈σA(
-
T∞)-∈σ(
=0
2562-7-7.371*10^-9=0
Use iteration method to solve for
=350.17 K...=77.17°C
In this particular situation, cat would not be comfortable with walking on a roof since its surface temperature is 77.17°C which may even cause burns to its paws.