THERMAL SCIENCE

International Scientific Journal

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Yi Tian

,

Zai-Zai Yan

,

Zhi-Min Hong

A NEW METHOD FOR SOLVING A CLASS OF HEAT CONDUCTION EQUATIONS

ABSTRACT
A numerical method for solving a class of heat conduction equations with variable coefficients in one dimensional space is demonstrated. This method combines the Crank-Nicolson and Monte Carlo methods. Using Crank-Nicolson method, the governing equations are discretized into a large sparse system of linear algebraic equations, which are solved by Monte Carlo method. To illustrate the usefulness of this technique, we apply it to two problems. Numerical results show the performance of the present work.
KEYWORDS
heat conduction equation, Crank-Nicolson method, Monte Carlo method
PAPER SUBMITTED: 2014-01-16
PAPER REVISED: 2015-05-25
PAPER ACCEPTED: 2015-04-15
PUBLISHED ONLINE: 2015-10-25
DOI REFERENCE: https://doi.org/10.2298/TSCI1504205T
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2015, VOLUME 19, ISSUE Issue 4, PAGES [1205 - 1210]
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A NEW METHOD FOR SOLVING A CLASS OF HEAT CONDUCTION EQUATIONS

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence