A theoretical investigation has been made for a radiating and chemically reacting viscous-fluid of a conducting gas over a vertical porous surface immerse in a saturated porous medium for the impact of magnetic drag-force, buoyancy forces and thermal-diffusion (Soret) order under oscillatory suction and heat absorption. The analytical solutions have been derived for the physical variables related to the governing equations under the appropriate boundary conditions. It is found that the velocity profiles increase with the increasing values of Soret number (S0) and higher Soret number (S0 = 5) shows the large temperature difference. It is noticed that increasing radiation parameter (R) elevated the velocity profiles near the plate. In the effects of Soret number (S0) the velocity profiles are an increasing function for both the cases of  M = 0 and M = 10. The validity and accuracy of the flow model is presented and found suitable to proceed the work. In this study, the findings would be useful in many practical areas such as diffusion operations, which involved molecular diffusion of species with molar concentration.

The novelty of thermal conductivity is the transmission of warmth from warmer to cooler portions of a body ensuing in balancing of temperature. Owing to importance of thermal conductivity in engineering technologies, a finite difference scheme is developed to study the originality of thermal conductivity in a two-dimensional fluid motion in assembly with thermophoretic forces, variable thermal conductivity and viscous dissipative heat over a permeable horizontal surface. The thermophoretic effect is included in the concentration boundary layer equation and the formulation has adopted by Talbot-Cheng-Scheffer-Willis (1980). A suitable similarity transformation is adapted to convert the leading PDEs to non-linear ordinary differential equations in non-dimensional form. A well-tested, numerically stable finite difference scheme in connection with Bvp4c is employed via MATLAB code for the conservation of equations under the appropriate transformed boundary conditions. The impact of thermophoretic forces and thermal conductivity in presence of suction/blowing over the fluid velocity and temperature are significant. The thermal conductivity of a substantial is an important property that assistances in the growth of active boiler/refrigerating machineries. In this study, thermophoretic forces (TP) and thermal conductivity (β) enhances the fluid velocity in presence of blowing, while they declines the velocity due to suction. The validity and accuracy of the present model have been checked and found adequate agreement with the previous studies. The importance of such analysis over a horizontal surface have numerous manufacturing, industrial and engineering applications in plastic sheets extrusion, polymer extraction, blowing of glass, manufacture of paper, thermo-electronics and rubber sheets.

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