ORIGINAL Effects of thermal stratification on flow and heat transfer past a porous vertical stretching surface Swati Mukhopadhyay • Iswar Chandra Mondal • Rama Subba Reddy Gorla Received: 28 July 2011 / Accepted: 25 October 2011 / Published online: 24 November 2011 Ó Springer-Verlag 2011 Abstract The aim of this paper is to present the boundary layer flow of viscous incompressible fluid due to a porous vertical stretching surface with a power-law stretching velocity in a thermally stratified medium. Using a special form of Lie group transformations viz. scaling group of transformations, similarity solutions for this problem are obtained. The equations are then solved numerically. With increasing values of the stratification parameter, the velocity as well as temperature decreases. At a particular point of the porous stretching sheet, the velocity decreases with the increasing suction parameter. The dimensionless temperature at a point of the sheet decreases due to suction but increases due to injection. The findings of this study reveal that stratification and suction can be used as means of cooling the boundary layer flow region. List of symbols F Non-dimensional stream function F  Variable F 0 Streamwise velocity Pr Prandtl number St Stratification parameter T Temperature of the fluid T w Temperature of the wall of the surface T ? Free-stream temperature u, v Components of velocity in x and y directions z Variable Greek symbols a 1 ; a 2 ; a 3 ; a 4 ; a 5 ; a 6 Transformation parameters b 1 Volumetric coefficient of thermal expansion g Similarity variable C Lie-group transformations j The coefficient of thermal diffusivity l Dynamic viscosity m Kinematic viscosity w Stream function w  Variable q Density of the fluid h Non-dimensional temperature h  ;  h Variables 1 Introduction Off late, a considerable attention is laid on the study of laminar flow and heat transfer over a stretching sheet due to its various industrial applications and important bearings on several technological processes. Gupta [1], Emery [2] and Takhar [3] investigated the MHD free-convection boundary layer flow along a vertical heated plate. The effects of porous medium on free con- vective flow were studied by Cheng and Minkowycz [4] and Cheng [5]. The combined forced and free convection flow along a semi-infinite vertical plate was studied by Wilks [6]. The steady free convective boundary layer flow on a non-isothermal vertical plate was investigated by Boutros et al. [7]. Since then, many papers are available on the steady free convective boundary layer flow on moving S. Mukhopadhyay  I. C. Mondal Department of Mathematics, The University of Burdwan, Burdwan, West Bengal 713104, India R. S. R. Gorla (&) Department of Mechanical Engineering, Cleveland State University, Cleveland, OH 44115, USA e-mail: r.gorla@csuohio.edu 123 Heat Mass Transfer (2012) 48:915–921 DOI 10.1007/s00231-011-0930-5