Group Analysis of Nonlinear Fin Equations

TL;DR

This paper performs an exhaustive group classification of nonlinear fin equations, identifies symmetries and transformations, and constructs exact solutions, thereby extending and generalizing previous research in the field.

Contribution

It provides a comprehensive classification of symmetries and solutions for nonlinear fin equations, including new equivalence transformations and nonclassical symmetries.

Findings

Lie symmetries used to derive exact solutions

Additional equivalence transformations identified

Results extend and generalize prior studies

Abstract

Group classification of a class of nonlinear fin equations is carried out exhaustively. Additional equivalence transformations and conditional equivalence groups are also found. They allow to simplify results of classification and further applications of them. The derived Lie symmetries are used to construct exact solutions of truly nonlinear equations for the class under consideration. Nonclassical symmetries of the fin equations are discussed. Adduced results amend and essentially generalize recent works on the subject [M. Pakdemirli and A.Z. Sahin, Appl. Math. Lett., 2006, V.19, 378-384; A.H. Bokhari, A.H. Kara and F.D. Zaman, Appl. Math. Lett., 2006, V.19, 1356-1340].