A semi-cylindrical greenhouse is being designed for a botanical garden. The inner radius of the greenhouse is r inner = 2 meters and it is L= 30 meters long. It is to be made of a new revolutionary mulch material that has a thermal conductivity of k soil = 0.05 W/m-K. The thickness of the soil shell is 2 cm. On a clear night, the air temperature is Tinf,o = 200 K and the temperature of the night sky is Tsurr = 30 K. A breeze blows over the greenhouse, resulting in a convective heat transfer coefficient of ho = 15 W/m2-K. The emissivity of soil to longwave radiation is 0.8. A fan located within the greenhouse circulates conditioned and breathable air; the breeze sets up a convective heat transfer coefficient of hi = 20 W/m2-K.

TIPS!: Neglect heat loss from the semi-circular end faces of the greenhouse. Also neglect the heat loss from the greenhouse to the ground below. The soil and mylar surfaces can be assumed to be diffuse and gray to longwave irradiation from the surroundings and emission.

1. Determine the heating load needed to maintain the interior of the greenhouse at a temperature of Tinf,I = 293 K at steady state.
2. A thin film of mylar is proposed to be adhered to the shell on the outer surface. The emissivity of Mylar to longwave radiation is 0.044 and the thickness of the film can be neglected. Since it is hard to adhere the film to the porous surface, there is a contact resistance of R''tc = 0.5 m2-K/W between the outer surface and mylar. Determine the new heating load needed to maintain the same interior steady state air temperature. 3. Compare the convective and radiative heat loss in both cases above. Provide a brief analysis of the result