International Journal of Engineering Research ISSN:2319-6890)(online),2347-5013(print) Volume No.5 Issue: Special 4, pp: 790-991 20 May 2016 ICCIT16 @ CiTech, Bengaluru doi : 10.17950/ijer/v5i4/039 971 | Page Effect of Thermophoresis on Heat and Mass Transfer by Convective Flow along a Sinusoidal Wavy Surface B. Mallikarjuna* 1 , S.V.S.S.N.V.G. Krishna Murthy 2 and Ali. J. Chamkha 3 1 Department of Mathematics, BMS College of Engineering, Bangalore, Karnataka -560019 2 Department of Applied Mathematics, Defense Institute of Advanced Technology, Deemed University, Pune, India-411025 3 Manufacturing Engineering Department, Public Authority for Applied Education and Training, Shuweikh, Saudi Arabia, 70654 Kuwait Corresponding author e-mail: mallikarjunab.maths@bmsce.ac.in Abstract - A mathematical model has been developed for multi-physical transport of free and mixed convective heat and mass transfer flow of a viscous fluid near sinusoidal wavy surface in a fluid saturated porous medium by taking into account of thermophoresis effect. The Darcy’s law can be used to describe the saturated porous medium. The governing nonlinear coupled equations representing transport of mass, momentum, energy and species are transformed into a smooth surface by using a suitable transformation. Then the transformed partial differential equations are converted into coupled nonlinear ordinary differential equations and then solved numerically by using shooting technique. The numerical results compared with previously published work and the results are approximately found to be a very good agreement. It is noted that concentration distribution is more pronounced due to the effect of thermophoresis and it is more significant with varying values of the parameters in both cases of assisting flow and opposing flow. The numerical results reported for fluid velocity, temperature and concentration profiles and the local Nusselt number and Sherwood number reveal interesting phenomenon, and some of these qualitative results are illustrated through graphs. Keywords - Vertical wavy surface; thermophoresis effect; free and mixed convection; Darcy porous media I. INTRODUCTION The prediction of heat transfer from irregular surfaces is a topic of fundamental importance. Irregular geometries in manufacturing frequently occur in practice. Irregular surfaces are encountered in many practical applications for which convective heat transfer is of interest. For instance: condensation process, heat transfer devices such as flat plate solar collectors and flat plate condensers in refrigerators, grain storage container where walls are buckled. The presence of roughness elements disturb the flow and alter the heat transfer rate. At first, Yao [1]-[2] investigated free and mixed convection along a vertical wavy surface with uniform wall temperature and heat flux and he proposed a simple coordinate transformation to transform the effect of wavy surface on governing equations. Recently, Lakshminarayana and Sibanda [3] and Rathish Kumar and Krishna Murthy [4] considered Darcy and non-Darcy principle respectively to investigate Soret and Dufour effects on free convection along a vertical wavy surface. Siddiqa and Anwar [5] studied natural convective boundary layer flow over a wavy horizontal surface. Bhuvanavijaya and Mallikarjuna [6] investigated double dispersion effects on double diffusive flow along a vertical wavy surface in a porous medium. Srinivasacharya et.al [7] investigated radiation effect on convective flow of a viscous fluid over a wavy surface in a Darcy porous medium. The study of thermophoresis plays a vital role in the species transport mechanism of several devices consists of small micron sized particles and large temperature gradient. The effect of the thermophoresis is so widespread in many practical applications in removing small particles from gas streams, in studying particulate material deposition on turbine blades and in determining exhaust gas particle trajectories from combustion devices. This shows that the thermophoresis is the dominant mass transfer mechanism in the modified chemical vapor deposition process which is utilized in germanium dioxide optical fiber performs and graded index silicon dioxide. Bakier and Reddy [8] considered the effects of thermophoresis and radiation on laminar flow along a semi-infinite vertical plate. Das [9] studied thermophoresis and chemical reaction effects on MHD micropolar fluid flow with variable properties. Kameswaran et.al [10] studied thermophoresis and non-linear effects on convective flow in a non-Darcy porous medium. Rashad et.al [11] studied thermophoresis effect on heat and mass transfer over a rotating cone in a porous medium. In view of above applications, the authors envisage to investigate combined free and forced convection along a vertical wavy surface embedded in a fluid saturated porous medium under the influence of thermophoresis. II. FORMULATION OF THE PROBLEM We consider laminar, incompressible, steady-state two dimensional, boundary layer free and mixed convective flows over a vertical wavy surface embedded in a viscous fluid saturated porous medium. The wavy surface configuration along the vertical plate is defined as         l x a x y   sin ) (