Meccanica (2006) 41:681–691 DOI 10.1007/s11012-006-9014-x Lie-group method of solution for steady two-dimensional boundary-layer stagnation-point flow towards a heated stretching sheet placed in a porous medium Youssef Z. Boutros · Mina B. Abd-el-Malek · Nagwa A. Badran · Hossam S. Hassan Received: 12 February 2005 / Accepted: 17 June 2006 / Published online: 31 October 2006 © Springer Science+Business Media B.V. 2006 Abstract The boundary-layer equations for two- dimensional steady flow of an incompressible, viscous fluid near a stagnation point at a heated stretching sheet placed in a porous medium are considered. We apply Lie-group method for deter- mining symmetry reductions of partial differential equations. Lie-group method starts out with a gen- eral infinitesimal group of transformations under which the given partial differential equations are invariant. The determining equations are a set of linear differential equations, the solution of which gives the transformation function or the infinitesi- mals of the dependent and independent variables. After the group has been determined, a solution to the given partial differential equations may be found from the invariant surface condition such that its solution leads to similarity variables that reduce the number of independent variables of the sys- tem. The effect of the velocity parameter λ, which is Y. Z. Boutros · M. B. Abd-el-Malek (B ) · N. A. Badran Department of Engineering Mathematics and Physics, Faculty of Engineering, Alexandria University, Alexandria 21544, Egypt e-mail: minab@aucegypt.edu H. S. Hassan Department of Basic and Applied Science, Arab Academy for Science and Technology and Maritime Transport, P.O. BOX1029 Alexandria, Egypt. e-mail: hossams@aast.edu M. B. Abd-el-Malek Present address: Department of Mathematics, The American University in Cairo, Cairo 11511, Egypt the ratio of the external free stream velocity to the stretching surface velocity, permeability parameter of the porous medium k 1 , and Prandtl number Pr on the horizontal and transverse velocities, temper- ature profiles, surface heat flux and the wall shear stress, has been studied. Keywords Boundary layer · Stagnation point flow · Porous medium · Lie-group · Mechanics of fluids 1 Introduction Flow and heat transfer of an incompressible vis- cous fluid over a stretching sheet appear in sev- eral manufacturing processes of industry such as the extrusion of polymers, the cooling of metallic plates, the aerodynamic extrusion of plastic sheets, etc. In the glass industry, blowing, floating or spin- ning of fibres are processes, which involve the flow due to a stretching surface [12]. Mahapatra and Gupta [7] studied the steady two-dimensional stagnation-point flow of an incom- pressible viscous fluid over a flat deformable sheet when the sheet is stretched in its own plane with a velocity proportional to the distance from the stagnation-point. They concluded that, for a fluid of small kinematic viscosity, a boundary layer is formed when the stretching velocity is less than the free stream velocity and an inverted boundary