Calculate the temperature of the greenhouse ambient air


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Q: A thin sheet of glass is used on the roof of a greenhouse and is irradiated as shown. The irradiation comprises the total solar flux GS, the flux G aim due to atmospheric emission (sky radiation), and the flux Gi due to emission from interior surfaces. The fluxes G aim and G; are concentrated in the far IR region (? > 8µm). The glass may also exchange energy by convection with the outside and inside atmospheres. The glass may be assumed to be totally transparent for ? < 1µm="" (t?="1.0" for="" ?="">< 1µm)="" and="" opaque,="" with="" a?="1.0" for="" ?=""> 1µm.

(a) Assuming steady-state conditions, with all radiative fluxes uniformly distributed over the surfaces and the glass characterized by a uniform temperature Tg, write an appropriate energy balance for a unit area of the glass.

(b) For Tg = 27°C, hi = 10 W/m2 · K, GS = 1100 W/m2, T8,o = 24°C, ho = 55 W/m2 · K, G aim = 250 W/m2, and G; = 440 W/m2, calculate the temperature of the greenhouse ambient air, T8,i.

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Mechanical Engineering: Calculate the temperature of the greenhouse ambient air
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