Lie group analysis of heat and mass transfer effects on steady MHD free convection dissipative flow past an inclined porous surface

An analysis has been carried out to study heat and mass transfer effects on steady two-dimensional flow of an electrically conducting incompressible dissipating fluid past an inclined semi-infinite porous surface. The flow is permeated by a uniform transverse magnetic field. A scaling group of transformations is applied to the governing equations. The system remains invariant due to some relations among the parameters of the transformations. After finding three absolute invariants, a third-order ordinary differential equation corresponding to the momentum equation, and two second-order ordinary differential equations corresponding to energy and diffusion equations are derived. The coupled ordinary differential equations along with the boundary conditions are solved numerically. 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. It is observed that the velocity decreases with an increase in the magnetic field parameter and permeability parameter. It is found that the velocity increases with an increase in the thermal and solutal Grashof numbers. Also, the velocity and concentration of the fluid decreases with an increase in the Schmidt number. The results, thus, obtained are presented graphically and discussed. (author)