A roof-cooling system, which operates by maintain-ing a

Chapter 12, Problem 12.144

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A roof-cooling system, which operates by maintain-ing a thin film of water on the roof surface, may beused to reduce air-conditioning costs or to maintain acooler environment in nonconditioned buildings. Todetermine the effectiveness of such a system, con-sider a sheet metal roof for which the solar absorptiv-ity ?Sis 0.50 and the hemispherical emissivity ?is0.3. Representative conditions correspond to a sur-face convection coefficient hof 20 W/m2?K, a solarirradiation GSof 700 W/m2, a sky temperature of?10C, an atmospheric temperature of 30C, and arelative humidity of 65%. The roof may be assumedto be well insulated from below. Determine the roofsurface temperature without the water film. Assum-ing the film and roof surface temperatures to beequal, determine the surface temperature with the ilm. The solar absorptivity and the hemisphericalemissivity of the filmsurface combination are ?S?0.8 and ??0.9, respectively