Modelling of the solar heating of a multi-layered spherical cone

Abstract

In this paper, the solar heating of a multi-layered spherical body with azimuthal symmetry is considered. The mathematical model is related to the determination of the steady state of the temperature distribution in the spherical cone consisting of concentric spherical layers. The solar heating is composed of two parts of the heat flux: direct and diffusion. Also, the simultaneous cooling of the cone by its outer surface (as convective heat flow to the environment) is taken into account. The proposed system of the partial differential equations supplemented by the adequate boundary conditions is solved in the analytical way by using, among others, the Legendre functions of the first kind. The sample results of temperature distribution in the cross-section of the cone with different polar angles are also presented.