Blackbody Rooftop Homework | Emissivity 0.9, Absorbtivity 0.8

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The discussion revolves around calculating the equilibrium temperature of a black rooftop with given emissivity and absorptivity values, under specific conditions. The roof receives solar radiation at an intensity of 300 BTU/hr ft², while the surrounding air temperature is 68 °F and the effective sky temperature is -10 °F. The rate of heat loss due to conduction and convection is modeled using a specific equation. Participants are assessing the accuracy of their approaches, including the use of computational tools like WolframAlpha for solving the equations. The key focus is on understanding the heat balance and radiation loss from the roof.
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Homework Statement


The black roof of a building has an emissivity of 0.9 and an absorbtivity of 0.8 for solar radiation. The sun beats down at midday with an intensity of 300 BTU / hr ft2.

a) If the temperature of the air and the surroundings is 68 °F, if the wind velocity is negligible, and if no heat penetrates the roof, what is the equilibrium temperature of the roof ? For the rate of conduction / convection use q/A = 0.38 (T) 1.25, where T is the temperature drop between the roof and air in degrees F.

b) What fraction of the heat from the roof is lost to radiation.


Homework Equations





The Attempt at a Solution


For this problem, assume the effective sky temperature on that day is -10F. also, the "rate of conduction / convection" just means the overall rate of conduction + convection away from the roof.

I am wondering if I approached this correctly. I used wolframalpha to solve the equation.
 

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