The paper deals with numerical methods to solve the nonlinear unsteady heat transfer equation in 2D square plate with temperature-dependent thermal conductibility, subject to Dirichlet boundary conditions. The adopted strategy of resolution is the combination of three techniques using firstly, the implicit Euler time discretization method, leading to steady second order nonlinear partial equation in two variables. Then, the Finite Difference Method (FDM) with central difference approximation which is second order accurate, fully discretize the 2D partial equation and give a set of nonlinear algebraic equations. Finally, the approximate solution is obtained by the iteration of Newton method.

two dimensional nonlinear heat transfer modeling, Dirichlet boundary conditions, implicit Euler discretization, FDM, Newton method.

Received: October 14, 2023; Revised: December 9, 2023; Accepted: December 23, 2023

How to cite this article: Djibet Mbainguesse, Djerayom Luc, Bakari Abbo and Youssouf Paré, Numerical solutions of nonlinear heat transfer modelling in a two-dimensional space, International Journal of Numerical Methods and Applications 24(1) (2024), 63-77. http://dx.doi.org/10.17654/0975045224005

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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