Simple models for the operation of partially transparent radiative windows and their comparison to the radiative coolers

Abstract

In this work we solve approximately the radiative heat transfer problem in one dimension to perform a comparative analysis of the time averaged performance of the partially transparent radiative windows and radiative coolers. Our physical model includes the atmosphere, the window, and the backwall that are all in the thermal equilibrium with each other, and that can exchange energy via radiative heat transfer or convection. Moreover, we use a simplified two-state model for the optical properties of an atmosphere and a window material which assumes two distinct sets of the optical reflection/absorption/transmission parameters in the visible/near-IR versus mid-IR spectral ranges. Furthermore, we have distinguished the design goals for the partially transparent windows and radiative coolers and provided optimal choice for the material parameters to realize these goals. Thus, radiative coolers are normally non-transparent in the visible, and the main goal is to design a cooler with the temperature of its dark side as low as possible compared to that of the atmosphere. For the radiative windows, however, their surfaces are necessarily partially transparent in the visible. In the cooling mode, therefore, the main question is about the maximal visible light transmission through the window at which the temperature on the window somber side does not exceed that of the atmosphere. We believe that our simple physical models complimented with an in-depth comparative analysis of the radiative windows and coolers can be of interest to a number of scientists and engineers pursuing research in these disciplines.