Abstract
In order to obtain the temperature of the evaporation-cooled outer surface of a building, which is exposed to solar radiation, by wetting the surface with water as in the case of spraying water onto the roof, it was necessary to set up a thermal equilibrium equation for the wet surface and conduct convergent calculation because the saturated water vapor pressure is nonlinear with regard to temperature. In this report, a method is proposed which enables easy calculation of the temperature of an evaporation-cooled surface by taking into account the similarity between the evaporation-cooled surface temperature and the wet-bulb temperature closely related to the wet surface. In this method, the temperature of the dry surface exposed to solar radiation is calculated, and based on the surface temperature and the absolute humidity of ambient outdoor air, the temperature is calculated by using a wet-bulb temperature calculation method. The obtained value is defined as a surface wet-bulb temperature. The relation between the surface wet-bulb temperature and the evaporation-cooled surface temperature is deductively expressed in Equation 11 based on the similarity to the wet-bulb temperature calculation equation. This relational expression consists of four terms: the first and second terms indicate the relation of the wet-bulb temperature while the third and fourth terms indicate the difference between the evaporation-cooled surface temperature and the surface wet-bulb temperature. This difference is relatively small and can be obtained as a solution of the quadratic equation by using a differential coefficient of the saturated water vapor pressure curve. We verified that the accuracy of the solution that uses Equation 11 is almost identical to the accurate solution. Next, we clarified relations among the evaporation-cooled surface temperature, surface wet-bulb temperature, and elements that determine those temperatures. We verified that, specifically in the circumstances of an ordinary building, the temperature of an evaporation-cooled surface is not easily influenced by thermal conductance and ambient temperature of the outer surface of the building. Furthermore, we indicated the range of difference between the surface wet-bulb temperature and the evaporation-cooled surface temperature. Furthermore, according to the calculation method, we showed the calculation procedure for obtaining the temperature of an evaporation-cooled surface by using a commonly-used psychrometric chart for wet air, thereby verifying that intuitive expression and understanding are possible.
