Lie group analysis for thermophoretic and radiative augmentation of heat and mass transfer in a Brinkman-Darcy flow over a flat surface with heat generation

Abstract

A boundary layer analysis is presented to investigate numerically the effects of radiation, thermophoresis and the dimensionless heat generation or absorption on hydromagnetic flow with heat and mass transfer over a flat surface in a porous medium. The boundary layer equations are transformed to non-linear ordinary differential equations using scaling group of transformations and they are solved numerically by using the fourth order Runge-Kutta method with shooting technique for some values of physical parameters. Comparisons with previously published work are performed and the results are found to be in very good agreement. Many results are obtained and a representative set is displayed graphically to illustrate the influence of the various parameters on the dimensionless velocity, temperature and concentration profiles as well as the local skin-friction coefficient, wall heat transfer, particle deposition rate and wall thermophoretic deposition velocity. The results show that the magnetic field induces acceleration of the flow, rather than deceleration (as in classical magnetohydrodynamics (MHD) boundary layer flow) but to reduce temperature and increase concentration of particles in boundary layer. Also, there is a strong dependency of the concentration in the boundary layer on both the Schmidt number and mass transfer parameter.