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SYMMETRY REDUCTION A PROMISING METHOD FOR HEAT CONDUCTION EQUATIONS

ABSTRACT
Though there are many approximate methods, e. g., the variational iteration method and the homotopy perturbation, for non-linear heat conduction equations, exact solutions are needed in optimizing the heat problems. Here we show that the Lie symmetry and the similarity reduction provide a powerful mathematical tool to searching for the needed exact solutions. Lie algorithm is used to obtain the symmetry of the heat conduction equations and wave equations, then the studied equations are reduced by the similarity reduction method.
KEYWORDS
PAPER SUBMITTED: 2018-03-15
PAPER REVISED: 2018-08-08
PAPER ACCEPTED: 1970-01-01
PUBLISHED ONLINE: 2019-09-14
DOI REFERENCE: https://doi.org/10.2298/TSCI1904219T
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE 4, PAGES [2219 - 2227]
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© 2021 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, 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