Laminar Rayleigh-Benard convection of yield stress fluids in a square enclosure

In this study, two-dimensional steady-state simulations of laminar natural convection in square enclosures with differentially heated horizontal walls with the bottom wall at higher temperature have been conducted for yield-stress fluids obeying the Bingham model. Heat and momentum transport are investigated for nominal values of Rayleigh number (Ra) in the range 10(3)-10(5) and a Prandtl number (Pr) range of 0.1-100. The mean Nusselt number (Nu) over bar is found to increase with increasing values of Rayleigh number for both Newtonian and Bingham fluids. However, weaker convective transport in Bingham fluids leads to smaller values of (Nu) over bar than that obtained in the case of Newtonian fluids with the same nominal value of Rayleigh number Ra. The mean Nusselt number (Nu) over bar decreases with increasing Bingham number in the case of yield stress fluids, and, for large values of Bingham number Bn, the value rapidly approaches to unity ((Nu) over bar = 1.0) as thermal conduction dominates the heat transfer. However, this variation in the present configuration is found to be markedly different from the corresponding variation of (Nu) over bar with Bn for the same nominal values of Ra and Pr in the differentially-heated vertical sidewall configuration. The effects of Prandtl number have also been investigated in detail and physical explanations are provided for the observed behaviour. Guided by a detailed scaling analysis, new correlations are proposed for the mean Nusselt number (Nu) over bar for both Newtonian and Bingham fluids which are demonstrated to satisfactorily capture the correct qualitative and quantitative behaviours of (Nu) over bar for the range of Ra, Pr and Bn considered in this analysis. (C) 2012 Elsevier B.V. All rights reserved.