A solid-liquid local thermal non-equilibrium lattice Boltzmann model for heat transfer in nanofluids. Part II: Natural convection of nanofluids in a square enclosure

The novel solid-liquid local thermal non-equilibrium lattice Boltzmann model, developed in Part I of this paper series [1], is applied to the classical problem of natural convection of nanofluids in a square enclosure with vertical walls at differential temperatures. Effects of Rayleigh numbers, nanoparticles random motion, nanoparticles volume fraction and nanoparticles non-uniform distribution in natural convection of nanofluids are studied. Because random motions of nanoparticles are intensified with temperature, vertical velocity and temperature profiles in the nanofluid are asymmetric with respect to the hot and cold vertical walls. Distribution of nanoparticles in the nanofluid inside the enclosure is affected by both the Rayleigh number and random motion of nanoparticles, and nanoparticles' distribution become relatively non-uniform at relatively high Rayleigh numbers. The non-uniform distribution of nanoparticles also affect local vertical velocity distribution, local temperature distribution, and the average Nusselt numbers. The effect of random motion of nanoparticles is shown to be responsible for enhanced convection at small Rayleigh numbers, the increasing viscosity of nanofluids is shown to be responsible for the deteriorating effects on heat transfer at intermediate Rayleigh numbers and non-uniform distribution of nanoparticles is shown to be responsible for ascending trend of Nusselt numbers at high Rayleigh numbers. The non-monotonous variation of the Nusselt number with respect to the Rayleigh number are in qualitative agreement with existing experimental data. (C) 2018 Published by Elsevier Ltd.