Suppose you build a wooden cubic shed with a large window for a roof. The wood w

Question

Suppose you build a wooden cubic shed with a large window for a roof.  The wood walls and floor have thickness 5cm, and the window has thickness 1cm.  The walls have thermal conductivity k = 0.12 W/mK, and the windows have k = 0.95 W/mK.  Sunlight is directed on the window directly overhead with intensity 1200 W/m^2, but 10% is reflected.  If the surrounding air and ground temperature is 20C, what temperature would the shed equilibrate to?  You may consider only solar radiation and conduction as heat transfer mechanisms.  

Explanation / Answer

we know that

R = R1 + R2

R = L1/K1A + L2/K2A

we know that

P = delta T /R

P/A = delta T /(l1/K1 +L2/K2)

P/A = 0.9 x1200 = 1080 W/m^2

1080 = delta T /0.427

461.368 = delta T

T-20= 461

T = 481.368 degree

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