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Math. Comput. Appl. 2005, 10(1), 139-145; doi:10.3390/mca10010139

Approximate Symmetries of Hyperbolic Heat Conduction Equation with Temperature Dependent Thermal Properties

Department of Mechanical Engineering, King Fahd University of Petroleum & Minerals Dhahran, 31261, Saudi Arabia
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Published: 1 April 2005
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Abstract

Hyperbolic heat conduction equation with temperature dependent thermal properties is considered. The thermal conductivity, specific heat and density are assumed to be functions of temperature. The equation is cast into a non-dimensional form suitable for perturbation analysis. By employing a newly developed approximate symmetry theory, the approximate symmetries of the equation are calculated for the case of small variations in thermal properties. Various similarity solutions corresponding to the symmetries of first order equations are presented. For second order equations, the method of constructing approximate symmetries and similarity solutions are discussed. A linear functional variation is assumed for the thermal properties and a similarity solution is constructed using one of the first order solutions as an example.
Keywords: Approximate Symmetries; Hyperbolic Heat Equation; Similarity Solutions; Perturbation Methods; Variable Thermal Properties Approximate Symmetries; Hyperbolic Heat Equation; Similarity Solutions; Perturbation Methods; Variable Thermal Properties
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Pakdemirli, M.; Şahin, A.Z. Approximate Symmetries of Hyperbolic Heat Conduction Equation with Temperature Dependent Thermal Properties. Math. Comput. Appl. 2005, 10, 139-145.

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Math. Comput. Appl. EISSN 2297-8747 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
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