Frontiers in Heat and Mass Transfer (FHMT), 5, 11 (2014) DOI: 10.5098/hmt.5.11 Global Digital Central ISSN: 2151-8629 1 EFFECTS OF THERMAL AND SOLUTAL STRATIFICATION ON MIXED CONVECTION FLOW ALONG A VERTICAL PLATE SATURATED WITH COUPLE STRESS FLUID K. Kaladhar a , D. Srinivasacharya b a Department of Mathematics, National Institute of Technology Puducherry, Karaikal-609605, India b Department of Mathematics, National Institute of Technology, Warangal-506004, India ABSTRACT The effect of heat and mass stratification on mixed convection along a vertical plate embedded in a couple stress fluid has been presented. The nonlinear system of equations with appropriate boundary conditions is primarily reduced to non-dimensional form by pseudo-similarity transformations. Keller-box implicit finite difference scheme is employed to solve the resultant system of dimensionless equations. The validation of this scheme is shown through the comparison between the present and available literature under special case of the present problem. The couple stress parameter, mixed convection parameter and the double stratification parameter effects on the rates of heat and mass transfer for diverse values of the emerging flow parameters are illustrated in tabular form. The present results show that the couple stress parameter, mixed convection parameter, thermal and the solutal stratification parameters influences the flow significantly. Keywords: Mixed convection, couple stress fluid, double stratification. 1. INTRODUCTION A flow with free and forced convection is of considerable interest due to its wide range in manufacturing and practical applications that consist of, metallurgical processes, nuclear reactors, heat exchangers, geothermal systems, geothermal systems, crystal growth, nuclear waste materials, and many. In literature, convection in heat and mass transfer flow along a non-isothermal vertical plane for Newtonian fluids with boundary layer estimates have been studied by many authors. The theoretical results for heat and solutal transfer from a vertical flat plate have been presented by Somers (1956). Szewczyk (1964) analyzed the effects of mixed convection laminar flow. Mixed convection flow along a flat plate with local similarity method was studied by Lloyd and Sparrow (1970). It has been produced the solutions through pure to mixed convection. Detailed explanation of many works can be found in Bejan (1994). Most recently, The effect on homogeneous chemical reaction on mixed convection in a porous medium saturated with polar fluid have been studied numerically by Patil and Chamkha (2013). Analysis of non-Newtonian fluids with heat and mass transfer is momentous in practical situations. For instance, slurries, foodstuffs, polymeric liquids, thermal design of industrial equipment dealing with molten plastics, etc. The examples of such fluids are blood at low shear rate, lubricants containing small amount of polymer additives, electro- rheological fluids, paints, fiber solutions and synthetic fluids, etc. The nonlinear relationship between the rate of strain and stress can be found in non-Newtonian fluid models. Stokes (1966) introduced this model, in which body couples, non-symmetric tensors and couple stresses exist. The classical viscous theories fails to describe the size dependant effect but which can be found with the effect of couple stresses. The free and mixed convection flow of couple stress fluid in a vertical channel have been presented by Srinivasacharya and Kaladhar (2012a,b). The magnetohydrodynamics, viscous dissipation and heat mass transfer effects on horizontal wavy channel in a porous channel saturated with couple stress fluid have been discussed by Muthuraj et al. (2013). The couple stress fluid with melting heat transfer under stagnation point flow was offered by Hayat et al. (2013). Srinivasacharya and Kaladhar (2013) described the analytical solution for mixed convection flow of couple stress fluid with MHD, Hall and ion-slip effects between circular rotating parallel disks. Makinde and Eegunjobi (2013) studied the nature of couple stress fluid in a vertical channel with entropy generation and porous medium. Najeeb et al. (2013) reported the flow of couple stress fluid in an contracting and expanding porous channel with an approximate solutions. Most recently, the size-dependent and consisting creeping flow of couple stress fluid was presented by Hadjesfandiari et al. (2013). The presence of different fluids or variations in temperature/ concentration leads to the stratification of a fluid. Although there is minute literature and in view of applications, Prandtl (1952), Jaluria and Himasekhar (1983), Murthy et al. (2004), Srinivasacharya et al. (2011) and few more are presented the stratification effects in different cases. It is the objective of the present work to consider the mixed convection flow of couple stress fluid along a vertical plate with solutal and thermal stratification effects. The medium is linearly stratified and the wall concentration and wall temperature are constants. The present boundary conditions are close realistic to the practical interest, like the heat mass transfer characteristics around a cooling magmatic intrusion or around a hot radioactive subsurface storage site where the theory of convection is involved. The governing nonlinear system of equations are solved by using the Keller box method (Cebeci and Bradshaw (1984)). The effects of the couple stress parameter, mixed convection, and the stratification parameters are examined and are presented graphically. 2. ANALYSIS The geometry of the problem and the coordinate system are shown in Fig. 1, in which x-axis and y-axis are along and normal to the vertical plate respectively. Steady and incompressible couple stress fluid along a plat plate is considered. Stratification and mixed convection are also taken into consideration. Density change in the fluid is neglected Frontiers in Heat and Mass Transfer Available at www.ThermalFluidsCentral.org * Corresponding author. Email: kkr.nitpy@gmail.com