Mathematical Modelling Using the Finite Element Method (FEM) And Numerical Simulations of the Performance of Parabolic and Flat-Plate Solar Collectors Incorporating an Energy Storage System in the Batna Region, Algeria.

Abstract

This study introduces a finite element method (FEM) for the mathematical modelling and numerical simulation of heat transmission in two types of solar thermal collectors: a parabolic trough collector (PTC) and a flat plate collector (FPC) — coupled to a hot water storage tank, under the climatic conditions of Batna, Algeria (35.6°N). The governing equations of heat transfer (conduction, convection, radiation) are discretised using Q4 quadrilateral elements on structured meshes. The 1D, 2D, and 3D temperature fields, heat fluxes, thermal and exergetic efficiencies, and stratified storage performance are determined and deeply interpreted. Two complete simulation codes (MATLAB and Python) were developed and validated. Results show that the parabolic collector achieves an average thermal efficiency of 68% versus 62% for the flat plate, with annual useful energy outputs of 5,430 kWh/yr and 2,847 kWh/yr respectively. Payback periods are estimated at 7 years (FPC) and 11 years (PTC), with annual CO₂ reductions of 330 and 629 kg.