Aplicação do método das diferenças finitas implícito para obtenção da distribuição de temperaturas na seção transversal do tubo receptor de um coletor solar cilíndrico parabólico

Abstract

This paper consists of the application of the implicit, transient and two-dimensional finite difference method (FDM) for the heat equation in cylindrical coordinates in the receiver tube of a parabolic trough collector (PTC). The main objective is to find the steady state temperature distribution in the cross sectional area of the receiver. The boundary conditions and properties of materials are considered constant. The solar heat flux boundary condition around the receiver is determined by a two-dimensional numerical method based on the Monte Carlo Ray Tracing Method (MCRT) that takes into consideration the geometry of the PTC and the diameter of the receiver. Both methods are applied writing algorithms implemented in Python programming language. Mesh refinement and the time step size are studied. The validation of the FDM algorithm is carried out with comparisons to simplified analytical methods of heat transfer. The heat flux obtained is validated by comparisons with other references. The temperature distribution is obtained for three different types of materials, subject to the same boundary and initial conditions. The temperature distributions on the inner and outer surfaces of the receiver are also shown. It is observed that the thermal conductivity of the material strongly influences the behavior of the temperature distribution of the tube in the steady state.