Viscous dissipation and magnetic field effects in a non-darcy porous medium saturated with a nanofluid under convective boundary condition

Abstract

This paper investigates the influence of viscous dissipation and magnetic field on natural convection from a vertical plate in a non-Darcy porous medium saturated with a nanofluid. In addition, a convective boundary condition is incorporated in the nanofluid model. A nonsimilarity transformation is used to reduce the mass, momentum, thermal energy, and the nanoparticle concentration equations into a set of nonlinear partial differential equations. The obtained equations are solved numerically by an accurate implicit finite-difference method. The accuracy of the numerical results is validated by a quantitative comparison of the heat transfer rates with previously published results for a special case and the results are found to be in good agreement. The effects of magnetic field, viscous dissipation, and non-Darcy and the convection parameters on the velocity, temperature, nanoparticle volume fraction, and heat and nanoparticle mass transfer rates are illustrated graphically