Conjugate natural convection of nanofluids inside an enclosure filled by three layers of solid, porous medium and free nanofluid using Buongiorno's and local thermal non-equilibrium models

The natural convective heat transfer of nanofluids was addressed inside a square enclosure filled by three different layers: solid, porous medium and free fluid. The behavior of the porous layer has been simulated using local thermal non-equilibrium model. The Buongiorno's model was utilized to evaluate the distribution of nanoparticles inside the enclosure that arose from the thermophoresis and Brownian motion. The governing equations were solved by the Galerkin finite element method in a non-uniform grid. The governing parameters are Rayleigh number Ra=10(3)-10(6), porosity epsilon=0.3-0.9, Darcy number Da=10(-5)-10(-2), interface parameter K-r=0.1-10, H=0.1-1000; ratio of wall thermal conductivity to that of the nanofluid, R-k=0.1-10, dimensionless length of the heater B=0.2-0.8; dimensionless centre position height of the heater Z=0.3-0.7 and Lewis number Le=10-100. A considerable concentration gradient of nanoparticles was found inside the enclosure. In some studied cases, the non-dimensional volume fraction of nanoparticles is about 10% higher than the average volume fraction of nanoparticles at the region near the cold wall. The variability of Darcy and the Rayleigh numbers indicated significant effects on heat transfer rate and the concentration patterns of the nanoparticles and inward the cavity. The increase in Le and Nr amplifies and decreases the heat transfer rates through fluid and solid phases, respectively. In addition, it can be seen that the increment in heat transfer rates with Le increases as Nr increases.