Ahmed A. Afify

Similarity analysis in magnetohydrodynamics: effects of hall and ion-slip currents on free convection flow and mass transfer of a gas past a semi-infinite vertical plate

SummaryThe effects of Hall and ion-slip currents on a steady free convection flow and mass transfer past a semi-infinite vertical plate in a viscous incompressible electrically conducting fluid are investigated when the fluid is subjected to a strong non-uniform magnetic field. The similarity solutions are obtained using a scaling group of transformations. These are the only symmetry transformations admitted by the field equations. The derived fundamental equations under the assumption of a small magnetic Reynolds number are solved numerically by employing the shooting method. The axial and transverse components of the velocity function profiles are computed for various values of magnetic parameters, Hall and ionslip current parameters.

Lie group analysis of hydromagnetic flow and heat transfer of a power-law fluid over stretching surface with temperature-dependent viscosity and thermal conductivity

The symmetry group of MHD boundary layer flow and heat transfer of a non-Newtonian power-law fluid over a stretching surface under the effects of variable fluid properties is investigated. The similarity equations with the corresponding boundary conditions are solved numerically by using a shooting method with the fourth order Runge–Kutta integration scheme. Comparisons of the numerical method with the existing results in the literature are made and obtained an excellent agreement. It is observed that the heat transfer rate diminishes with an increase in magnetic parameter and variable thermal conductivity parameter. Further, the opposite influence is found with an increase in variable viscosity parameter.