UNSTEADY FREE CONVECTION IN A SQUARE POROUS CAVITY SATURATED WITH NANOFLUID: THE CASE OF LOCAL THERMAL NONEQUILIBRIUM AND BUONGIORNO'S MATHEMATICAL MODELS

Considering Buongiorno's model, the unsteady free convection in a porous enclosure filled with a nanofluid is studied while the nanoparticles, the base fluid, and the solid porous matrix are in local thermal nonequilibrium. It is assumed that the left and right vertical walls are suddenly heated and cooled. Moreover, the movement of the nanoparticles is affected by Brownian and thermophoresis forces. The influence of multifarious thermophysical variables, such as solid-fluid and nanoparticle-fluid interaction heat transfer parameters, buoyancy ratio parameter, and Rayleigh number, on the transient average Nusselt number for the solid matrix, the base fluid, and the nanoparticles is investigated. It is found that the increase of solid-fluid and nanoparticle-fluid interaction heat transfer parameters would majorly augment the solid and nanoparticle average Nusselt numbers, respectively. Furthermore, the decrease of the buoyancy ratio and the increase of Rayleigh number would boost the average Nusselt number for all of the three phases. Eventually, the period of reaching to steady state shows a direct proportion to buoyancy ratio and a reverse proportion to Rayleigh number.