A non-Newtonian thermal lattice Boltzmann method for simulation of Rayleigh-Benard convection of power-law fluids

Despite the widespread popularity of the Bhatnagar-Gross-Krook lattice Boltzmann (BGK-LB) model due to its simplicity and efficiency, its application in heat transfer involving non-Newtonian fluids (NNFs) has been limited by inherent constraints. This paper proposes a numerically stable BGK-LB model for the thermal flow of NNFs. The modified model incorporates the local shear rate into the equilibrium distribution function of the velocity field and addresses the numerical instability problems encountered in the traditional BGK-LB model under low viscosity conditions by introducing an additional parameter. In addition, a temperature evolution equation that can accurately recover the convective diffusion equation is adopted. The accuracy of the current method is validated by performing simulations of Rayleigh-B & eacute;nard convection (RBC) in a square cavity filled with Newtonian fluids and NNFs. Subsequently, simulations are conducted to investigate the behavior of RBC in power-law fluids. The analysis focuses on examining the impact of the Rayleigh number (Ra = 5 x 10(3) - 10(5)) and the power-law index (n = 0.8-1.3) on the convective structure and heat transfer characteristics while maintaining a fixed Prandtl number (Pr = 7) and aspect ratio (L/H = 2). It is discovered that, for a given n value, the convection intensity and heat transfer rate increase with increasing Ra, which is supported by the increasing trend of the mean Nusselt number (Nu) with Ra. Furthermore, compared to NFs, pseudo-plastic fluids display a higher Nu value due to an augmented heat transfer rate, while dilatant fluids exhibit a lower Nu value owing to a diminished heat transfer rate.(c) 2023 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).