MHD natural convection in a heat generating porous medium-filled wavy enclosures using Buongiorno's nanofluid model

Abstract

A numerical simulation of magnetohydrodynamic free convection and heat transfer of nanofluids flow inside wavy enclosures filled with a heat generating porous medium has been carried out. The Buongiorno's model with effects of Brownian motion and thermophoresis is used for the nanofluid and Darcy model with a slow motion is applied for the porous medium. The enclosure is considered under effects of an inclined magnetic field with constant strength and a source of a heat generation with constant volumetric rate is taken into account. The governing equations is presented in dimensional form and converted to dimensionless before it is transformed to a rectangular domain using a suitable transformation. The resulting system is solved numerically using an implicit finite difference method and comparisons with previously published data are performed. A set of figures is plotted for streamlines, isotherms and nanoparticles contours as well as local Nusselt number at the heated wall. The key parameters in this study are the undulation number 1≤k≤4, the wavy contraction 0.1≤b≤0.25, the Hartmann number 0≤Ha≤100, the magnetic field inclination angle 0≤α≤π/2, the Darcy number 10−2≤Da≤10−5, the thermophoresis parameter 0.1≤Nt≤0.5, the nanofluid buoyancy ratio 0.1≤Nr≤0.5, the Brownian motion parameter 0.1≤Nb≤0.5 and the heat generation parameter 0≤Qm≤5. It is found that the heat transfer rate is an increasing function in both the undulation number and the wavy contraction ratio.