Hybrid lattice Boltzmann-TVD simulation of natural convection of nanofluids in a partially heated square cavity using Buongiorno's model

In this paper, the Buongiomo's two-phase model is adopted to study natural convection in a partially heated enclosure filled with nanofluids having temperature-dependent properties. In order to solve the governing equations, a hybrid lattice Boltzmann (LB) and total variation diminishing (TVD) scheme is proposed, in which the traditional LB method is employed to handle the flow and temperature fields, while the volume fraction equation is solved by a TVD method due to the fact that the corresponding equation is a type of convection dominated equation. Additionally, to improve the computational efficiency, the proposed algorithm is executed on the Graphics Processing Unit (GPU) by using Compute Unified Device Architecture (CUDA) programming. The effect of several parameters, such as Rayleigh number, nanoparticle diameter, temperature difference between the sidewalls, heating location and heater length on heat transfer rate and nanoparticle distribution are analyzed. It is observed that at low Rayleigh numbers, the heat transfer enhancement increases in nanoparticle volume fraction, while at high Rayleigh numbers, there exists an optimal volume fraction at which the heat transfer performance has a peak. Moreover, the average Nusselt number and the heat transfer enhancement are found to decrease with increasing heater length.