Local thermal nonequilibrium conjugate natural convection heat transfer of nanofluids in a cavity partially filled with porous media using Buongiorno's model

The natural convection heat transfer in a cavity filled with three layers of solid, porous medium, and free fluid is addressed. The porous medium and free fluid layers are filled with a nanofluid. The porous layer is modeled using the local thermal nonequilibrium (LTNE) model, considering the temperature difference between the solid porous matrix and the nanofluid phases. The nanofluid is modeled using the Buongiorno's model incorporating the thermophoresis and Brownian motion effects. The governing equations are transformed into a set of nondimensional partial differential equations, and then solved using finite element method in a nonuniform grid. The effects of various nondimensional parameters are discussed. The results showed that the Brownian motion and thermophoresis effects result in significant concentration gradients of nanoparticles in the porous and free fluid layers. The increase in Rayleigh (Ra), Darcy (Da), the thermal conductivity ratios for the solid wall and solid porous matrix, i.e., K-r and R-k, enhanced the average Nusselt number. The increase in the convection interaction heat transfer parameter between the solid porous matrix and the nanofluid in the pores (H) increases the average Nusselt number in the solid porous matrix but decreases the average Nusselt number in the nanofluid phase of the porous layer.