## 1 Introduction  
Thermophoresis is a physical phenomenon of mass transfer, subjected to a temperature gradient, which moves from higher to lower temperature zones of the gas fluid. It plays a significant role in laminar boundary layer flow and is well researched through theoretical and experimental procedures. Additionally, the thermophoretic driving force occurring in convection flow through a porous medium has attracted significant attention because of widely practical application cases, such as in aerosol particles sampling, vehicle air cleaning, filtration process, scale formation inside tube systems of heat exchangers, particle deposition on gas turbine blades, the semiconductor manufacturing process, and wasted gas exhaust systems from combustion. [PERSON] and [PERSON] [1] first studied coupled diffusiophoresis and thermophoresis in a simple one-dimensional water vapor system for the measurement of thermophoretic velocity. Another earlier study on the role of thermophoresis in the laminar flow of viscous and incompressible fluids over a horizontal plate, with analysis on cold and hot wall surface conditions, was proposed by [PERSON] [2]. He adopted the classical problem of flow over a flat plate to calculate the deposition rates and stated that significant changes in surface depositions could be obtained by increasing the surface and free stream temperature difference. Some studies [3; 4; 5; 6] have also been presented to discuss the coupled diffusion and thermophoresis interactive effect phenomena based on fundamental research. [PERSON] et al. [7] established the numerical solution for the velocity and temperature fields in the laminar boundary layer adjacent to a heated plate. They proposed several available theoretical expressions for the thermophoretic force. [PERSON] and [PERSON] [8] investigated heat and mass transfer through a steady laminar boundary layer flow of a Newtonian, viscous fluid over a vertical flat plate embedded in a porous medium in the presence of the thermophoresis particle deposition effect and obtained the wall concentration profiles. [PERSON] [9] investigated the mixed convection flow, heat, and mass transfer about an isothermal vertical flat plate embedded in a fluid-saturated porous medium with the effects of thermophoresis and viscous dissipation in aiding and opposing flows and obtained the results in terms of the local Nusselt and Sherwood number. Subsequently, he proposed a mathematical model to analyze the local similarity boundary layer to investigate the effects of thermophoresis and variable thermal conductivity on heat and mass transfer over an accelerating surface with a heat source in the presence of suction and blowing [10]. [PERSON]'s law was applied to fluid flow through a porous medium to prove that the pressure drop produced by the frictional drag is proportional to the velocity of low-speed flow. For high flow velocity with Reynolds numbers based on a mean pore diameter greater than 1, [PERSON]'s law should be corrected to incorporate non-Darcian effects, including inertia and boundary effects. [PERSON] and [PERSON] [11] described the effects of stable thermal stratification for free convection of two conjugate boundary layers on both sides of an impermeable vertical partition embedded in a porous medium. Afterward, [PERSON] and [PERSON] [12] proposed a fundamental study of natural convection heat and mass transfer near a vertical surface embedded in a fluid-saturated porous medium. They used scale analysis to show that the physical phenomenon of natural convection heat and mass transfer was a function of the buoyancy ratios and Lewis numbers. [PERSON] and [PERSON] [13; 14] obtained the similarity and integral solutions for the problem of the free convection boundary layer along a vertical plate immersed in a thermally stratified, fluid-saturated porous medium with variable wall temperature. Studies on mass transfer due to thermophoresis in laminar convective flow have also been presented. [PERSON] et al.