2022 Numerical Solution of Three-Dimensional Transient Heat Conduction Equation in Cylindrical Coordinates
Endalew Getnet Tsega
J. Appl. Math. 2022: 1-8 (2022). DOI: 10.1155/2022/1993151

## Abstract

Heat equation is a partial differential equation used to describe the temperature distribution in a heat-conducting body. The implementation of a numerical solution method for heat equation can vary with the geometry of the body. In this study, a three-dimensional transient heat conduction equation was solved by approximating second-order spatial derivatives by five-point central differences in cylindrical coordinates. The stability condition of the numerical method was discussed. A MATLAB code was developed to implement the numerical method. An example was provided in order to demonstrate the method. The numerical solution by the method was in a good agreement with the exact solution for the example considered. The accuracy of the five-point central difference method was compared with that of the three-point central difference method in solving the heat equation in cylindrical coordinates. The solutions obtained by the numerical method in cylindrical coordinates were displayed in the Cartesian coordinate system graphically. The method requires relatively very small time steps for a given mesh spacing to avoid computational instability. The result of this study can provide insights to use appropriate coordinates and more accurate computational methods in solving physical problems described by partial differential equations.

## Citation

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Endalew Getnet Tsega. "Numerical Solution of Three-Dimensional Transient Heat Conduction Equation in Cylindrical Coordinates." J. Appl. Math. 2022 1 - 8, 2022. https://doi.org/10.1155/2022/1993151

## Information

Received: 28 July 2021; Revised: 3 October 2021; Accepted: 7 December 2021; Published: 2022
First available in Project Euclid: 28 July 2022

zbMATH: 1499.65437
Digital Object Identifier: 10.1155/2022/1993151

Rights: Copyright © 2022 Hindawi

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