Group analysis of nonlinear fin equations

Group classification of a class of nonlinear fin equations is carried out exhaustively. Additional equivalence transformations and conditional equivalence groups are also found. These enable us to simplify the classification results and their further applications. 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 complete and essentially generalize recent works on the subject [M. Pakdemirli and A.Z. Sahin, Similarity analysis of a nonlinear fin equation, Appl. Math. Lett. 19 (2006) 378–384; A.H. Bokhari, A.H. Kara and F.D. Zaman, A note on a symmetry analysis and exact solutions of a nonlinear fin equation, Appl. Math. Lett. 19 (2006) 1356–1360].