MHD flow past a stretching permeable sheet V. Kumaran a, * , A.K. Banerjee a , A. Vanav Kumar a , K. Vajravelu b a Department of Mathematics, National Institute of Technology, Tiruchirappalli 620015, India b Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA article info Keywords: MHD flow Stretching permeable sheet Boundary layer flow Electrically conducting fluid abstract An exact solution is obtained for a boundary layer flow of an electrically conducting fluid past a quadratically stretching, and linearly permeable sheet. Effects of magnetic, suction/ injection, linear/nonlinear stretching parameters on the stream function and the skin fric- tion are shown graphically and are discussed. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phe- nomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress. Ó 2008 Elsevier Inc. All rights reserved. 1. Introduction The boundary layer flow over a stretching sheet has a variety of applications, in particular in cooling and extrusion pro- cesses and in paper production. Crane [1] obtained the analytical solution for a boundary layer flow of an incompressible viscous fluid over a stretching sheet. Followed by this, several investigators extended the problem and obtained closed form solutions (see [2–4]). A detailed literature survey for the flow past a stretching sheet can be seen in the recent paper by Liao [5]. Using the homotopy analysis method, series solutions were obtained by Hayat et al. for the stretching sheet problem with micropolar fluid (see [6]) and with mixed convection (see [7]). Thermal radiation effects on flow past a non-linearly stretching sheet were analysed by Sajid and Hayat [8] and also by Abbas and Hayat [9]. Ayub et al. studied the stagnation point flow of a viscoelastic fluid over a stretching surface (see [10]). Sajid et al. obtained the series solutions for unsteady flow and heat transfer over a radially stretching sheet (see [11]). The energy needed to overcome the frictional force on an airplane is a substantial part of the total energy consumed in flying the airplane. In a transport airplane flying at subsonic speeds and in cruise condition, approximately 50% of the energy (fuel) is used to overcome the skin friction of the boundary layer. The boundary layer is mostly turbulent on such airplanes. A turbulent boundary layer has more surface friction than a laminar boundary layer. Thus, we tend to keep the flow laminar on the surface. This reduces skin friction. Also, the separation of the boundary layer is associated with large energy losses and in most applications adversely affects the aerodynamic loads in the form of lift loss and drag increase. Therefore there is a strong tendency to delay or manipulate the occurrence of flow separation. Hence separation control is of great importance to most of the systems involving fluid flow, such as air, land or underwater vehicles and turbomachinery. In the case of an external flow, such as the flow on the exterior surface of an aircraft, the objective is to delay transition from laminar to tur- bulent, to suppress turbulence and to prevent separation. To do this we need to control the flow. The results include drag reduction, lift enhancement and flow-induced noise suppression. By controlling the flow, the fuel burned might be decreased almost 30% as reported by Braslow [12]. As a result, the pollutant emissions are reduced. To control the flow, passive or active devices are used. Passive control devices are those which are not energy consumptive. They mainly affect the flow by the geometry of the airfoil. In contrast, active control devices use energy such as surface suction or injection. 0096-3003/$ - see front matter Ó 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2008.10.025 * Corresponding author. E-mail address: kumaran@nitt.edu (V. Kumaran). Applied Mathematics and Computation 210 (2009) 26–32 Contents lists available at ScienceDirect Applied Mathematics and Computation journal homepage: www.elsevier.com/locate/amc