Rayleigh–Bénard convection of nanofluids based on the pseudo-single-phase continuum model

• A pseudo-single-phase model is derived based on continuum mechanics.
• The presence of nanoparticles retards onset of thermal convection.
• The Nusselt number is almost independent of nanoparticle mass fraction.
• The heat transfer coefficient increases with respect to nanoparticle mass fraction.

Nanofluids are composed of fluids and dispersed submicron solid particles. The presence of nanoparticles in the fluids enhances the effective thermal conductivity. In order to predict the enhancement of heat transfer in the nanofluids, it is necessary to model the nanofluid systems rigorously from the viewpoint of fluid dynamics. In the present investigation, we suggest a fluid mechanical model of nanofluids based on a rigorous theory of continuum mechanics. Starting from a two-fluid model, a pseudo-single-phase model is derived exploiting the fact that the velocity and temperature of nanoparticles follow tightly those of base fluid. The resulting pseudo-single-phase model of nanofluids is employed to investigate the Rayleigh–Bénard convection of nanofluids. It is revealed that the presence of nanoparticles retards onset of convection and reduces convective fluid motion. Although the Nusselt number Nu and the heat transfer coefficient h are increasing functions of the Rayleigh number Ra for all values of particle mass fraction ωp, Nu is almost independent of ωp while h increases with respect to ωp because the thermal conductivity increases as ωp increases. The present pseudo-single-phase model of nanofluids may be adopted to predict heat and mass transfer as well as fluid dynamic characteristics in various nanofluid systems.