Natural Convection in Differentially Heated Partially Porous Layered Cavities Filled with a Nanofluid

Abstract

Natural convection heat transfer in a differentially heated and vertically partially layered porous cavity filled with a nanofluid is studied numerically based on double–domain formulation. The left wall, which is adjacent to the porous layer, is isothermally heated, while the right wall is isothermally cooled. The top and bottom walls of the cavity are thermally insulated. Impermeable cavity walls are considered except the interface between the porous layer and the nanofluid layer. The Darcy–Brinkman model is invoked for the porous layer which is saturated with the same nanofluid. Equations govern the conservation of mass, momentum, and energy with the entity of nanoparticles in the fluid filling the cavity and that are saturated in the porous layer are modeled and solved numerically using under successive relaxation upwind finite difference scheme. The contribution of five parameters are studied, these are; nanoparticle volume fraction ϕ (0–0.1), porous layer thickness Xp(0–0.9), Darcy number Da (10⁻⁷–1), aspect ratio A (1, 2, 4), and Rayleigh number Ra (10³–10⁶). The nanofluid is considered to be composed of copper nanoparticles and water as a base fluid. The results have shown that with the aid of a nanofluid, the convective heat transfer can be enhanced even at a low permeable porous medium. It is found that when Ra ≤ 10⁵, there is a critical porous layer thickness Xp at which the Nusselt number is maximum. Otherwise, the Nusselt number Nu decreases rapidly with Xp. Correlations of Nu with the other parameters are established and tested for A = 2.