Lattice Boltzmann Method for simulation of mixed convection of a Bingham fluid in a lid-driven cavity

In this paper, a two-dimensional simulation of steady mixed convection in a square enclosure with differentially heated sidewalls has been performed when the enclosure is filled with a Bingham fluid. The problem has been solved by the Bingham model without any regularisations and also by applying the regularised Papanatasiou model. An innovative approach based on a modification of the Lattice Boltzmann Method (LBM) has been applied to solve the problem. Yield stress effects on heat and momentum transport using the Papanatasiou model are investigated for certain pertinent parameters of the Reynolds number (Re = 100, 500, and 1000), the Prandtl number (Pr = 0.1, 1, and 10) and the Bingham number (Bn = 0, 1, 5 and 10), when the Grashof number is fixed at Gr = 10,000. Results show that a rise in the Reynolds number augments the heat transfer and changes the extent of the unyielded section. Furthermore, for fixed Reynolds and Prandtl numbers, an increase in the Bingham number decreases the heat transfer while enlarging the unyielded section. Although an increase in the Prandtl number enhances heat transfer, it does not affect the proportions of the unyielded/yielded regions in the cavity. Finally, the results of the Bingham and Papanatasiou models are compared and it is found that there is a visible difference between the two models especially in the yielded/unyielded sections.