The Effectiveness of Variable Properties on Thermophoresis Particle Deposition at The Levels of 1st and 4th Orders of Chemical Reaction of Buoyancy-driven Flows of Second Grade Fluid

This article presents the analytic solution to a steady, incompressible, free convective flow of an electrically conducting second grade fluid past a vertical surface with variable properties namely: variable viscosity; variable thermal conductivity and variable concentration diffusivity in the presence of thermophoresis, chemical reaction and convective boundary condition. The impact of different orders of chemical reaction on thermophoresis and the transport process of flow, heat and mass transfer in the boundary layer for assisting and opposing flow cases are properly examined and discussed. The governing equations associated with the fluid model are transformed and parameterized to a system of coupled nonlinear ordinary differential equations using similarity transformations. The resulting coupled ordinary differential equations (ODEs) were solved by adopting the Optimal Homotopy Analysis Method (OHAM).  The results indicate that velocity and temperature distributions are decreasing functions of second grade parameter for both cases of assisting and opposing flows.  Also, concentration distribution is a decreasing function of thermophoretic parameter for low and high orders of chemical reaction.