Lattice Boltzmann method for natural convection of a Bingham fluid in a porous cavity

In this paper, natural convection in a porous cavity filled with Bingham fluids has been simulated numerically. In order to study the problem, an innovative Lattice Boltzmann method for porous media of Bingham fluid is introduced. In this study, the Papanastasiou regularisation of the Bingham constitutive model has been applied for the studied Bingham fluid and moreover the Darcy-Brinkman-Forchheimer model has been employed for the porous media. Fluid flow, heat transfer, and yielded/unyielded parts have been conducted for certain pertinent parameters of Rayleigh number (Ra = 10⁴ - 10⁷), Darcy number (Da = 10^-2, 10^-4, 10^-6), and porosity (𝜖 = 0.1 - 0.9). Moreover, the Bingham number (Bn) is studied in a wide range of different studied parameters. Results indicate that the heat transfer increases and the unyielded section diminishes as Rayleigh number rises. For specific Rayleigh and Darcy numbers, the increase in the Bingham number decreases the heat transfer. Furthermore, the growth of the Bingham number expands the unyielded sections in the cavity. Finally, for fixed Rayleigh and Bingham numbers, the unyielded region is decreased by the augmentation of the porosity. In addition, heat transfer augments gradually as the porosity increases.