2D Thermal Modeling of a Square Solar Still Glass Cover Using the Poisson Equation and the Finite Difference Method

Nacer Eddine Benhissen, Asma Khelassi-Sefaoui

Abstract

The aim of this study is to model and solve the two-dimensional Poisson equation using the Finite Difference Method (FDM) in order to approximate the steady-state thermal distribution on a square glass cover of a solar still. The glass surface is represented as a square computational domain subjected to various Dirichlet boundary conditions, enabling the simulation of different thermal loading scenarios. The mathematical formulation is discretized on a uniform mesh, and the resulting linear system is solved efficiently using the Thomas algorithm adapted for block tridiagonal matrices. The numerical results illustrate the influence of boundary temperatures, imposed heat fluxes, and grid resolution on the internal temperature distribution. Although the model is based on conduction-dominated heat transfer and assumes a homogeneous thin glass layer, it provides meaningful insight into the thermal response of solar still glazing. This approach offers a simple and effective framework that can be extended in future work to three-dimensional geometries and to fully coupled radiative–convective heat transfer models.

Keywords

Heat transfer, solar still, Poisson equation, finite difference method, glass cover.

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References

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DOI: http://dx.doi.org/10.47238/ijeca.v10i2.284

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