A Numerical Solution of Three-Dimensional Unsteady State Heat Equation

محورهای موضوعی : فصلنامه ریاضی

Endalew Tsega ¹ (Department of Mathematics, College of Science, Bahir Dar University, Bahir Dar, Ethiopia)

تاریخ دریافت : 1399/05/26 تاریخ پذیرش : 1399/08/02 تاریخ انتشار : 1399/12/11

کلید واژه: Finite volume method, Heat Equation, Three-dimensional, Unsteady, MATLAB code,

چکیده مقاله :

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.