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 5.103<Ra<105 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.