BUOYANCY-DRIVEN CAVITY FLOW OF A MICROPOLAR FLUID WITH VARIABLY HEATED BOTTOM WALL

This article explores the buoyancy-driven flow of a micropolar fluid in a square conduit. The flow is assumed to be steady, incompressible, and fully developed. The coupling between the energy and momentum equations is achieved using the Boussinesq approximation. A finite element scheme based on penalty formulation is implemented to simulate the governing equations. The simulations are carried out for both cases of constant and variable heating of the bottom wall. The contours of the temperature field and stream function are plotted for several values of involved physical parameters, namely, the Rayleigh number, Prandtl number, and micropolar parameters. The effects of these pertinent parameters on the average and local Nusselt numbers are also quantified. The study shows that the strength of recirculating zones decreases with increase in the micropolar parameter. Moreover, the expansion of isotherms toward the top boundary surface of an enclosure is noted for greater values of the micropolar parameter. The local and average Nusselt numbers decrease with change in the behavior of the fluid from Newtonian to micropolar. This article explores the buoyancy-driven flow of a micropolar fluid in a square conduit. The flow is assumed to be steady, incompressible, and fully developed. The coupling between the energy and momentum equations is achieved using the Boussinesq approximation. A finite element scheme based on penalty formulation is implemented to simulate the governing equations. The simulations are carried out for both cases of constant and variable heating of the bottom wall. The contours of the temperature field and stream function are plotted for several values of involved physical parameters, namely, the Rayleigh number, Prandtl number, and micropolar parameters. The effects of these pertinent parameters on the average and local Nusselt numbers are also quantified. The study shows that the strength of recirculating zones decreases with increase in the micropolar parameter. Moreover, the expansion of isotherms toward the top boundary surface of an enclosure is noted for greater values of the micropolar parameter. The local and average Nusselt numbers decrease with change in the behavior of the fluid from Newtonian to micropolar.