Similarity analysis of a nonlinear fin equation

Pakdemirli M., Sahin A. Z.

APPLIED MATHEMATICS LETTERS, vol.19, no.4, pp.378-384, 2006 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 19 Issue: 4
  • Publication Date: 2006
  • Doi Number: 10.1016/j.aml.2005.04.017
  • Journal Name: APPLIED MATHEMATICS LETTERS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.378-384
  • Keywords: heat transfer, fins, similarity transformations, BOUNDARY-LAYER EQUATIONS, HEAT-TRANSFER COEFFICIENT, NON-NEWTONIAN FLUIDS, CONDUCTION, DESIGN
  • Istanbul Technical University Affiliated: Yes

Abstract

A nonlinear fin equation in which the thermal conductivity is an arbitrary function of the temperature and the heat transfer coefficient is an arbitrary function of a spatial variable is considered. Scaling, translational and spiral group symmetries of the equations are determined. Classification of the functions for which these symmetries exist is performed. In general, no useful symmetries exist for arbitrary thermal conductivity and heat transfer coefficients. However, for some restricted forms of the functions, useful symmetries exist. A similarity transformation is used to reduce the partial differential equation to an ordinary differential equation as an example. (C) 2005 Elsevier Ltd. All rights reserved.