%0 Journal Article
%T Lie Group Analysis of Mixed Convection Flow with Mass Transfer over a Stretching Surface with Suction or Injection
%A Mudassar Jalil
%A Saleem Asghar
%A Muhammad Mushtaq
%J Mathematical Problems in Engineering
%D 2010
%I Hindawi Publishing Corporation
%R 10.1155/2010/264901
%X The mixed convection flow with mass transfer over a stretching surface with suction or injection is examined. By using Lie group analysis, the symmetries of the equations are calculated. A four-finite parameter and one infinite parameter Lie group transformations are obtained. Two different cases are discussed, one for the scaling symmetry and the other for spiral symmetry. The governing partial differential equations are transformed into ordinary differential equations using these symmetries. It has been noted that the similarity variables and functions available in the literature become special cases of the similarity variables and functions discussed in this paper. 1. Introduction The study of continuously stretching sheets has many applications in manufacturing industries. Application of stretching sheets can be found in the areas like paper production, hot rolling, glass blowing, continuous casting of metals, and wire drawing. First of all Sakiadis [1, 2] investigated the boundary layer behavior on stretching surfaces and presented numerical solution for the sheet having constant speed. Extension to this problem where velocity is proportional to the distance from the slit was given by Crane [3]. Flow and heat transfer in the boundary layer on stretching surface was studied by Tsou et al. [4]. Fox et al. [5] presented different methods (analytical or numerical) for solving problems of stretching sheet with suction and injection. Heat and mass transfer on stretched surface with suction and injection was introduced by Erickson et al. [6]. P. S. Gupta and A. S. Gupta [7] studied the same problem for linearly stretching sheet. Heat transfer past a moving continuous plate with variable temperature was studied by Soundalgekar and Murty [8] and Grubka et al. [9]. Ali [10] presented similarity solutions for stretched surface with suction and injection. Hayat et al. [11] investigated the effect of heat and mass transfer for Soret and Dufour's effect on mixed convection boundary layer flow over a stretching vertical surface in a porous medium filled with a viscoelastic fluid. Lie group analysis is a classical method discovered by Norwegian mathematician Sophus Lie for finding invariant and similarity solutions [12¨C15]. Y¨ır¨ısoy and Pakdemirli [16] presented exact solution of boundary layer equations of a special non-Newtonian fluid over a stretching sheet by the method of Lie group analysis. They extended their work to creeping flow of second-grade fluid [17]. Sivasankaran et al. [18, 19] studied the problem of natural convection heat and mass transfer flow
%U http://www.hindawi.com/journals/mpe/2010/264901/