Combined internal and external natural convection of Bingham plastics in a cavity using a lattice Boltzmann method

Natural convection of Bingham plastics in a cavity with differentially heated walls and an internal heat source is investigated numerically. The governing dimensional non-dimensional macroscopic equations are presented, the constitutive equation written based on exact model. implemented lattice Boltzmann method explained showed how to derive presented equations. code validated verified against previous studies exhibited good agreement. results demonstrated discussed for various parameters Rayleigh (R = 102–104), Rayleigh–Roberts (RR 102–106), Prandtl (Pr 0.1–100), (Bn), Yield (Y) numbers. effects depicted isotherms, yielded/unyielded zones, streamlines, lines temperatures velocities middle cavity. maximum (or critical) number (Ym) found studied reported. independent numbers fixed ratio R RR (Δ RR/R), like external convection. However, alteration Δ changes unique value number. We considered three ratios 1, 10, 100 single zero inclined angles (θ=0°) were observed at Ym=0.038,0.073, 0.38, respectively. increase angle counter-clockwise expands unyielded zones declines