Convection of Viscoplastic Fluid in Square Cavity Heated from the Sidewalls

Abstract

Abstract The paper is devoted to the numerical study of two-dimensional convective motion of a viscoplastic fluid in a closed region under lateral heating. The problem is solved numerically using the ANSYS Fluent software. The Bulkeley-Herschel model describing viscoplastic behavior was chosen as a non-Newtonian fluid model. Under certain rheological parameters, this model is reduced to a Newtonian fluid model, the behavior of which is also investigated as a limit case. Based on the results of the calculations, the dependence of the maximum value of the stream function in the cavity on the Rayleigh number is plotted and the evolution of the unyielded zones with an increase in the Rayleigh number is traced. The threshold value of the Rayleigh number, at which a sharp growth of the flow intensity is observed, has been determined. The calculated threshold value of the Rayleigh number for the Bulkley-Herschel liquid was found to be very close to the threshold value of the Rayleigh number at which the flow of the Bingham liquid arises, which was obtained analytically.