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 differentiallyheated sidewalls has been performed when the enclosure is filled with a Bingham fluid. Theproblem has been solved by the Bingham model without any regularisations and also by applying the regularisedPapanatasiou model. An innovative approach based on a modification of the Lattice BoltzmannMethod (LBM) has been applied to solve the problem. Yield stress effects on heat and momentum transportusing the Papanatasiou model are investigated for certain pertinent parameters of the Reynoldsnumber (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 theReynolds 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 decreasesthe heat transfer while enlarging the unyielded section. Although an increase in the Prandtl numberenhances 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 avisible difference between the two models especially in the yielded/unyielded sections