Lie group analysis of thermophoresis on a vertical surface in a porous medium

The magnetohydrodynamic and thermophoretic effects on a vertical surface in a porous medium are investigated. The fascinating aspects of thermo diffusion and diffusion-thermo impacts are given. Mathematical modelling via Lie group method was applied. Thereafter, the infinitesimal generators of governing equations are computed. Using suitable similarity variables the existing system which was non-linear is converted into expressions having no dimensions. The resulting expressions were solved numerically using shooting method and the characteristics of embedded parameters such as temperature, velocity, concentration profiles have been displayed graphically. We have compared our findings with those of previous ones to assure the affirmity of our analysis. The change in Sherwood number for progressive Dufour solutal values are also analyzed.