Chapter 12, Problem 12.120P

A thin sheet of glass is used on the roof of a green- house and is irradiated as shown

The irradiation comprises the total solar flux $G_s$ , the flux $G_{atm}$ due to atmospheric emission (sky radiation), and the flux Gi due to emission from interior surfaces. The fluxes $G_{atm}\text{ and }{G}_i$ are concentrated in the far IR region $\lambda \ge 8\mu m$ .The glass may also exchange energy by convection with the outside and inside atmospheres. The glass may be assumed to be totally transparentfor $\lambda <1\mu \text{m}\left({\tau }_{\lambda }=1.0\text{ for }\lambda <1\mu \text{m}\right)$ and opaque,with ${\alpha }_{\lambda }=1.0\text{ for }\lambda \ge 1\mu \text{m}$ .

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

(b) For $T_g={27}^{\circ }C,{\text{ h}}_o=10{\text{ W/m}}^2\cdot K,{\text{ G}}_s=1100{\text{W/m}}^2,{\text{ T}}_{\infty ,o}={24}^{\circ }C,{\text{h}}_o=55{\text{ W/m}}^2\cdot K,{\text{ G}}_{atm}=250{\text{W/m}}^2,{\text{ and G}}_i=440{\text{W/m}}^2$ , calculate the temperature of the greenhouse ambient air, ${\text{T}}_{\infty ,i}$ .