Magnetic effect on thermally stratified nanofluid saturated non-Darcy porous medium under convective boundary condition

Abstract

The flow, heat and nanoparticle mass transfer characteristics in the free convection from a vertical plate in a thermally linearly stratified nanofluid saturated non-Darcy porous medium under convective boundary condition is investigated. In addition, the magnetic field effect under convective boundary condition is incorporated in the nanofluid model. The transformed non-similar non-linear coupled partial differential equations representing the transport of mass, momentum, thermal energy, and the nanoparticles volume fraction are solved numerically by the Blottner [18] scheme, which is modified to accommodate the effect of the convective boundary condition. 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. It is observed that the thermal transport is significantly affected due to the stratification of the medium and it is more significant with varying values of the parameters related to the nanofluid in the medium as well as the Biot number due to the convective boundary condition. The effects of thermal stratification, non-Darcy, convection and magnetic field parameters on the velocity, temperature, nanoparticle volume fraction, heat and nanoparticle mass transfer rates are illustrated graphically.