Approximate symmetries of hyperbolic heat conduction equation with temperature dependent thermal properties


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Pakdemirli M., Şahin A. Z.

Mathematical and Computational Applications, vol.10, no.1, pp.139-145, 2005 (Journal Indexed in SCI Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 1
  • Publication Date: 2005
  • Doi Number: 10.3390/mca10010139
  • Title of Journal : Mathematical and Computational Applications
  • Page Numbers: pp.139-145
  • Keywords: Approximate Symmetries, Hyperbolic Heat Equation, Perturbation Methods, Similarity Solutions, Variable Thermal Properties

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.