Natural convection flow of a hybrid nanofluid in a square enclosure partially filled with a porous medium using a thermal non-equilibrium model

Abstract

Buoyancy-driven flow inside a superposed enclosure filled with composite porous-hybrid nanofluid layers was investigated numerically using a local thermal nonequilibrium model for the heat transfer between the fluid and the solid phases. The bottom wall of the enclosure was partly heated to provide a heat flux, while the other parts of the wall were thermally insulated. The top and vertical walls of the enclosure were maintained at constant cold temperatures. The Darcy-Brinkman model was adopted to model the flow inside the porous layer. The Galerkin finite element method was used to solve the governing equations using the semi-implicit method for pressure linked equations algorithm. The selected parameters are presented for the Rayleigh number (Ra), 103 ≤ Ra ≤ 107, the Darcy number (Da), 10−7 ≤ Da ≤ 1, the porous layer thickness (S), 0 ≤ S ≤ 1, the modified conductivity ratio (γ), 10−1 ≤ γ ≤ 104, the interphase heat transfer coefficient (H), 10−1 ≤ H ≤ 1000, the heat source length (B), 0.2, 0.4, 0.6, 0.8 and 1, and the nanoparticle volume fraction (ϕ), 0 ≤ ϕ ≤ 0.2. It has been concluded that the rate of heat transfer of hybrid nanofluid (Cu−Al2O3/water) is higher than with the pure fluid. Furthermore, at Ra ≤ 105, the heat transfer rate maintains its maximum value when S reaches the critical value (S = 0.3). The values of S, Da, and B were found to have a significant effect on the heat removal from the heat source. Increasing the values of γ and H can strongly enhance the heat transfer rate and satisfy the thermal equilibrium case.