NUMERICAL SOLUTIONS OF NONLINEAR HEAT TRANSFER MODELLING IN A TWO-DIMENSIONAL SPACE
Keywords:
two dimensional nonlinear heat transfer modeling, Dirichlet boundary conditions, implicit Euler discretization, FDM, Newton method.DOI:
https://doi.org/10.17654/0975045224005Abstract
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.
Received: October 14, 2023
Revised: December 9, 2023
Accepted: December 23, 2023
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