Natural convection in a triangular cavity filled with a nanofluid-saturated porous medium using three heat equation model

The present study aims to examine the local thermal non-equilibrium natural convection heat and mass transfer of nanofluids in a triangular enclosure filled with a porous medium. The effect of the presence of nanoparticles and the thermal interaction between phases on the flow, temperature distribution of phases, the concentration distribution of nanoparticles as well as the Nusselt number of phases is theoretically studied. The interaction between the phases of nanoparticles and the base is taken into account by using a three thermal energy equation model while the concentration distribution of nanoparticles is modeled by Buongiorno's model. A hot flush element is mounted at the vertical wall of the triangle enclosure to provide a constant temperature of T-h while the inclined wall is at a constant temperature of T-c. A three heat equation model by considering the local thermal non-equilibrium model of nanoparticles, the porous medium, and the base fluid is developed and utilized for natural convection of nanofluids in an enclosure. The drift-flux of nanoparticles due to the nano-scale effects of thermophoresis and Brownian motion effects is addressed. The governing equations are represented in a non-dimensional form and solved by employing the finite element method. The results indicate that the increase of Rayleigh number shows a significant increase in the average Nusselt number for the base fluid phase, a less significant increase in the average Nusselt number for the solid matrix phase, and almost an insignificant effect in the average Nusselt number of the nanoparticle phase. Increasing the buoyancy ratio parameter (the ratio of mass transfer buoyancy forces to the thermal buoyancy forces) tends to reduce and increase the average Nusselt number in fluid and porous phases, respectively. An optimum value of buoyancy ratio parameter for the average Nusselt number of the nanoparticle phase is observed.