Simulation of natural convection in a solar collector

Abstract

The process of natural convection in a flat solar collector, which was designed by the authors, was mathematically modeled using experimental data. Stones were used as storage means. The inclined collector is expressed as a two-dimensional plate for modeling. The initial and boundary conditions were formulated. It was assumed that the flow in this region is laminar. To simulate the flow of natural air convection, a system of non-stationary partial differential equations was chosen based on the laws of conservation of mass, momentum and energy in the Boussinesq approximation. The equations were solved in a dimensionless form using the finite difference method and an explicit scheme. The picture of the temperature fields and the appearance of convection was obtained on the basis of experimental temperature data in the inlet and outlet zones of the collector, as well as on the surface of the heat accumulator during the day. To evaluate the effectiveness of the resulting model an average approximation error (approximation) of 7.7% was established. The results obtained in specific values of the Grashof and Prandtl numbers are presented in the form of graphs.