Abstract—This work deals with heat and mass transfer by steady laminar boundary layer flow of a Newtonian, viscous fluid over a vertical flat plate with variable surface heat flux embedded in a fluid saturated porous medium in the presence of thermophoresis particle deposition effect. The governing partial differential equations are transformed into no-similar form by using special transformation and solved numerically by using an implicit finite difference method. Many results are obtained and a representative set is displaced graphically to illustrate the influence of the various physical parameters on the wall thermophoresis deposition velocity and concentration profiles. It is found that the increasing of thermophoresis constant or temperature differences enhances heat transfer rates from vertical surfaces and increase wall thermophoresis velocities; this is due to favorable temperature gradients or buoyancy forces. It is also found that the effect of thermophoresis phenomena is more pronounced near pure natural convection heat transfer limit; because this phenomenon is directly a temperature gradient or buoyancy forces dependent. Comparisons with previously published work in the limits are performed and the results are found to be in excellent agreement. Keywords—Thermophoresis, porous medium, variable surface heat flux. I.INTRODUCTION HERMOPHORESIS is a phenomenon, which causes small particles to be driven away from a hot surface and toward a cold one. Dust particles when suspended in a gas temperature gradient; experience a force in the direction opposite to the temperature gradient. This phenomenon has many practical applications in removing small particles from gas streams, in determining exhaust gas particles trajectories from combustion devices, and in studding the particulate material deposition on turbine blades. Goren [1] studied the effect of thermophoresis on a viscous and incompressible fluid, the classical problem of flow over a flat plate is used to calculate deposition rates and it is found that the increasing of difference between the surface and free stream temperatures causes substantial changes in surface deposition. Gokoglu and Rosner [2] obtained a set of similarity solutions for the two dimensional laminar boundary layers, Park and Rosner [3] obtained a set of similarity solutions for the stagnation point flows. Chio [4] obtained the similarity solutions for the problem of a continuously moving surface in a stationary incompressible fluid, including the Rebhi A. Damseh and Benbella A. Shannak are with the Mechanical Department, Al-Husun University College, Albalqa Applied University, Irbid, Jordan (e-mail: rdamseh@yahoo.com). H. M. Duwairi is with the Mechanical Engineering Department, Faculty of Engineering and Technology, The University of Jordan, 11942 Amman, Jordan. combined effects of convection, diffusion, wall velocity and thermophoresis. Grag and Jayaraj [5] discussed the thermophoresis of small particles in forced convection laminar flow over inclined plates embedded in a plain medium; Epstein et al. [6] have studied the thermophoresis transport of small particles through a free convection boundary layer adjacent to a cold, vertical deposition surface in a viscous and incompressible fluid. Chiou [7] has considered the particle deposition from natural convection boundary layer flow onto an isothermal vertical cylinder. Convective flows in porous media have been extensively investigated during the last several decades, due to many practical applications, which can be modeled or approximated as transport phenomena in porous media. Comprehensive literature surveys concerning the subject of porous media can be found in the most recent books by Ingham and Pop [8], Nield and Bejan [9]. In this work, the problem selected for study is the pure forced, pure natural and mixed convection heat and mass transfer problems from vertical surfaces embedded in a fluid saturated porous media with variable surface heat and mass fluxes. Full inclusion of the thermophoresis phenomena is done in the formulations. II. MATHEMATICAL FORMULATION Consider mixed convection from an impermeable vertical surface embedded in saturated porous medium. The analysis is carried out for the power-law variation of the surface heat flux m w bx q = (x) and the power law variation of the surface mass flux n Lx q = (x) 0 , where b and L are constants and m and n are the exponents. The x coordinate is measured from the leading edge of the plate and the y coordinate is measured normal to the plate. The gravitational acceleration g is acting downward in the direction opposite to the x coordinate. The Darcy model which is valid under the conditions of low velocities and small pores of porous matrix is used in the analysis. Also the properties of the fluid are assumed to be constant and the porous medium is treated as isotropic. Allowing for both Brownian motion of particles and thermophoresis transport, the governing equations can be written as Lai and Kulacki [11]: 0 = ∂ ∂ + ∂ ∂ y v x u (1) ( ) ) ( ) ( ∞ ∞ − + − = C C T T Kg u c T β β υ (2) Thermophoresis Particle Precipitate on Heated Surfaces Rebhi A. Damseh, H. M. Duwairi, Benbella A. Shannak T World Academy of Science, Engineering and Technology International Journal of Mechanical and Mechatronics Engineering Vol:8, No:4, 2014 682 International Scholarly and Scientific Research & Innovation 8(4) 2014 scholar.waset.org/1307-6892/9997933 International Science Index, Mechanical and Mechatronics Engineering Vol:8, No:4, 2014 waset.org/Publication/9997933