Effect of nonhomogeneous nanofluid model on transient natural convection in a non-Darcy porous cavity containing an inner solid body

Transient natural convection of an alumina-water nanofluid saturated in non-Darcy porous media is investigated in this paper. The domain of the nanofluid is an annulus composed from a square cavity confining a solid conductive body. The nanoparticles are assumed to be slipping in the base fluid according to Buongiorno model. The Brinkman-Forchheimer-extended Darcy formulation has been adopted for the porous medium. The dimensionless governing equations are solved by implementing the finite difference method. In this study, a special focus is given on the following model parameters; porosity of the porous medium, Darcy number and the nanoparticles average volume fraction. The results show that the nanoparticles possess high uniformity in the base fluid and the Nusselt number augments with increasing values of the Darcy number. The porosity increases the average Nusselt number at a higher Darcy number while its influence remains negligible at a low Darcy number. For the given porosity, there is a critical value of the nanoparticles volume fraction when the average Nusselt number is maximal.