Linear and Non-Linear Analysis of Rayleigh-Bénard Convection in a Micropolar Fluid Occupying Enclosures With Realistic Boundaries

Abstract

The linear and non-linear analysis of Rayleigh-Bénard convection (RBC) in a micropolar fluid (MPF) occupying enclosures are analyzed for realistic boundaries. The different enclosures considered are shallow enclosure (h < b), square enclosure (h = b) and tall enclosure (h > b). Linear analysis is conducted to study the on-set-of-convection, using the Fourier series representation. The different boundaries taken into consideration are Free-Free (F-F), Rigid-Free (R-F) and Rigid-Rigid (R-R). Using the Fourier-series representation, the fourth order Lorenz model is derived to quantify the heat transport. The effect of various MPF parameters has been analyzed. The rate of heat transfer is calculated from average Nusselt number, (Nu(t)).