Reduced equations for a thin liquid film subjected to solar radiation

A thin fluid film flowing on the surface of a photovoltaic (PV) cell can significantly reduce its operating temperature, resulting in increased electrical output, extended lifetime, and reduced surface soiling. Moreover, as studies have indicated that the heat transfer across a wavy liquid film can be up to 10 −100% larger than it for a flat film, investigating the complex relationship between the irradiated wavy film and the temperature profile across it is critical for optimizing this system. However, the numerical solution of this complex hydrothermal problem is prohibitively expensive for parametric studies, and thus, we attempt to investigate it by developing appropriate low-order models. We employ the Weighted Integral Boundary Layer (WIBL) methodology for the hydrodynamics of the film in conjunction with an asymptotic decomposition of the temperature variable such that the system of equations governing the temperature field is truncated consistently in line with the least-degeneracy principle retaining all the fundamental physical effects at leading order. Our derivation produces a hierarchy of models of increasing sophistication from which the overall temperature field can be reconstructed, enabling a parametric study of this complicated problem.