Abstract: Natural convection for a Herschel-Bulkely fluid, inside a differentially heated square cavity, is studied numerically using Fluent/Ansys 15.0 code. The cavity is heated from the vertical sides and insulated from the horizontal ones. We have studied the effect of Bingham-number (Bn) at a fixed Rayleigh-number (Ra), then the effect of Rayleigh-number at fixed Bn and finally the effect of the rheological index n at fixed Bn and Ra. Prandtl-number (Pr) is taken equal 1.0 for the whole study. Results showed that an increasing Bn leads to a flow-intensity decrease, and hence its perturbation. Therefore, temperature field becomes less perturbed and the Nusselt decreases. The opposite happens if Bn decreases. Increasing Ra, leads to similar results as those known for the Newtonian-case, but with a lower intensity because of Bn effect. The decrease of n has an opposite effect of that of increasing Bn, and inversely. A rapid tendency toward the conductive problem (Ra=0.0) is registered if Bn>0 particularly when n>1.0.

Key words: Natural convection, square cavity, Bingham fluid, Herschel-Bulkely fluid.