Rayleigh-Bénard convection of Casson fluids

Abstract

This study aims at investigating numerically the Rayleigh-Bénard Convection (RBC) in viscoplastic fluids. A Casson fluid is considered in a bidimensional square cavity heated from below. The effects of the dimensionless yield stress, the Bingham number Bn, on the heat transfer and motion is investigated in the range 5.10^3 < Ra < 10^5 for the Rayleigh number and Pr = 10, 100, 1000 for the Prandtl number. One shows that the yield stress has a stabilizing effect, reducing the convection intensity. Above a certain value of Bnmax , the convection does not occur and the heat transfer is only due to conduction. For moderate Bn values, truly unyielded regions are located in the center of the cavity; their areas grow with increasing Bingham number and invade the whole cavity at the threshold value Bnmax .