Group Analysis of Nonlinear Fin Equations

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].