Similarity analysis of a nonlinear fin equation

AbstractA 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

Group classification of fin equation with variable thermal properties

A nonlinear fin equation in which thermal conductivity is an arbitrary function of temperature and, heat transfer coefficient is an arbitrary function of spatial variable is considered. Lie Group theory is applied to the equation. Group classification with respect to the thermal conductivity and heat transfer coefficient is performed. Results are summarized in a table for convenience. Some similarity transformations are used to convert the partial differential equation into an ordinary differential equation. © 2004 Elsevier Ltd. All rights reserved