Laminar Natural Convection of Bingham Fluids in a Square Enclosure with Vertical Walls Subjected to Constant Heat Flux

Abstract

In this study, two-dimensional steady-state simulations of laminar natural convection in square enclosures with vertical sidewalls subjected to constant heat flux have been carried out, where the enclosures are considered to be completely filled with a yield-stress fluid obeying the Bingham model. Yield stress effects on heat and momentum transport are investigated for nominal values of Rayleigh number (Ra) in the range 10³–10⁶ and a Prandtl number (Pr) range of 0.1–100. It is found that the mean Nusselt number Nu increases with increasing values of Rayleigh number for both Newtonian and Bingham fluids. However, Nu values obtained for Bingham fluids are smaller than that obtained in the case of Newtonian fluids with the same nominal value of Rayleigh number Ra due to weakening of convective transport. The mean Nusselt number Nu in the case of Bingham fluids is found to decrease with increasing Bingham number, and for large values of Bingham number Bn, the value settles to unity (Nu = 1.0) as heat transfer takes place principally due to thermal conduction. The Nu values for the vertical walls subjected to constant heat flux are smaller than the corresponding values in the same configuration with constant vertical wall temperatures (for identical values of nominal Rayleigh, Prandtl, and Bingham numbers). However, the value of Bingham number at which Nu approaches to unity remains the same for both constant wall temperature and constant wall heat flux configurations. It is demonstrated that for small values of Bingham number Nu increases with increasing Prandtl number, but the opposite behavior occurs for large values of Bingham number. New correlations are proposed for the mean Nusselt number Nu for both Newtonian and Bingham fluids for square enclosures with vertical walls subjected to constant heat flux, which are shown to satisfactorily capture the correct qualitative and quantitative behavior of Nu in response to changes in Ra, Pr, and Bn.

Acknowledgments

The visit of O.T. to Liverpool was funded by the European Union's Erasmus Lifelong Learning Programme and is hereby gratefully acknowledged.