Lattice Boltzmann simulation of cavity flows driven by shear and internal heat generation for both Newtonian and viscoplastic fluids

Abstract

Following our recent investigation [G. Kefayati, “Internally heated convection of viscoplastic fluids in enclosures using a lattice Boltzmann method,” Phys. Fluids 35, 013108 (2023)], this paper centers on exploring the influence of shear on internally heated convection and its flow within a square cavity. The study delves into the behavior of both Newtonian and viscoplastic fluids within this setup. The cavity features two vertical side walls that consistently maintain low temperatures, serving as isotherms. Meanwhile, the horizontal walls are adiabatic and provide thermal insulation. In this work, we present dimensional macroscopic equations and introduce innovative non-dimensional macroscopic equations. To generate shear, the top lid is continuously translated, and we quantify its intensity using the corresponding Richardson number. For investigating the viscoplastic behavior and defining the yielded (fluid) and unyielded (solid) zones, we employ an exact Bingham model, which relies on a unique tensor. To tackle the problem effectively, we develop a dimensionless lattice Boltzmann method to derive the specified macroscopic non-dimensional equations and subsequently solve the fluid motion scenario. Throughout the study, we introduce modified non-dimensional parameters, including the introduced yield number (Y), Reynolds number (R) ranging from 0 to 400, Prandtl number (Pr) ranging from 0 to 100, and the modified Grashof number (G) within the range of 104–106. By varying these parameters, we analyze their influence on streamlines, isotherms, and the regions of yield and unyielded zones. The obtained results revealed that shear plays a significant role in influencing fluid flow, heat transfer, and the behavior of the unyielded section within the enclosure.