A Numerical Solution of Three-Dimensional Unsteady State Heat Equation

International Journal of Mathematical Modelling & Computations

مقاله 4، دوره 11، 1 (WINTER) - شماره پیاپی 41، خرداد 2021، صفحه 49-60   

نوع مقاله: Full Length Article

شناسه دیجیتال (DOI): 10.30495/ijm2c.2021.684809

نویسنده

Endalew Getnet Tsega^*

Department of Mathematics, College of Science, Bahir Dar University, Bahir Dar, Ethiopia

چکیده

Heat equation is a partial differential equation that describes the distribution of temperature (heat) in a given body over time. In this study, a finite volume based method is used to solve three-dimensional heat equation. A MATLAB code is developed to implement the numerical method in a unit cube. The stability of the numerical scheme is analysed using the Von Neumann method. An example is provided in order to demonstrate the method. The numerical solution by the method is in an excellent agreement with the exact solution for the example considered. The computational procedures used in this study can provide good insights to solve a three dimensional diffusion equation arising in many physical phenomena.

کلیدواژه‌ها

Heat Equation؛ Unsteady؛ Three-dimensional؛ Finite volume method؛ MATLAB code