Free convection in a porous wavy cavity filled with a nanofluid using Buongiorno's mathematical model with thermal dispersion effect

Abstract A numerical study of natural convection inside a porous wavy cavity filled with a nanofluid under the effect of thermal dispersion has been carried out using the Forchheimer–Buongiorno approach. The left boundary of the cavity is a wavy isothermal wall while the rest are flat isothermal walls. All boundaries are assumed to be impermeable to the base fluid and nanoparticles. The governing equations formulated in dimensionless stream function, temperature and nanoparticle volume fraction variables have been solved using implicit finite difference schemes of the second order accuracy. The effects of the Rayleigh number, undulation number, thermal dispersion parameter and flow inertia parameter on the average Nusselt number along the hot bottom wall, as well as on the streamlines, isotherms and isoconcentrations have been analyzed. It has been revealed the heat transfer enhancement with Rayleigh number, undulation number and dispersion parameter. While convective flow is attenuated with a growth of undulation number, dispersion parameter and flow inertia parameter. More essential homogenization of nanoparticles distribution inside the cavity occurs with an increase in Rayleigh number and a decrease in undulation number.