Chapter 12, Problem 12.144P

A roof-cooling system, which operates by maintaining a thin film of water on the roof surface, may be used to reduce air-conditioning costs or to maintain a cooler environment in nonconditioned buildings. To determine the effectiveness of such a system, con- sider a sheet metal roof for which the solar absorptivity ${\alpha }_s$ is 0.50 and the hemispherical emissivity ◰ is 0.3. Representative conditions correspond to a sur- face convection coefficient $h$ of ${\text{20 W/m}}^2\cdot K$ , a solar irradiation $G_s$ of ${\text{700 W/m}}^2$ , a sky temperature of $-{10}^{\circ }C$ , an atmospheric temperature of ${30}^{\circ }C$ , and a relative humidity of 65%. The roof may be assumed to be well insulated from below. Determine the roof surface temperature without the water film. Assuming the film and roof surface temperatures to be equal, determine the surface temperature with thefilm. The solar absorptivity and the hemispherical emissivity of the film−surface combination are ${\alpha }_s=0.8\text{ and }\epsilon =0.9$ , respectively.