Numerical investigation of viscoplastic fluids on natural convection in open cavities with solid obstacles

This study investigates the natural convection process within open cavities filled with viscoplastic fluid following the Bingham model with solid square conductive blocks uniformly distributed throughout the cavity. The problem is modeled as a two-dimensional laminar in a steady state with the heated surface parallel to the cavity opening and the other adiabatic surfaces. Three geometries are analyzed: the downward-facing cavity, side-facing cavity, and upward-facing cavity. Parametric analysis is performed in terms of Rayleigh number and Bingham number. The solid-fluid thermal conductivity ratio, the number of blocks, the Prandtl number, and the solid volume fraction within the cavity are fixed, with values of 10, 16, 500, and 0.36, respectively. The results are presented in streamlines, isotherms, unyielded regions, dimensionless velocity, dimensionless temperature, and Nusselt number on the heated surface. A comparison with the closed square cavity is performed, and it is noted that the natural convection has a greater magnitude in the open cavity. Rayleigh and Bingham's numbers have opposite effects on heat transfer. Effects of block interference and channeling of flow within the cavity are observed. For a given value of the Bingham number, there is an abrupt transition from the advective to conductive regime inside the cavity and a critical Bingham number (Bnmax) in which unyielded regions fill the entire geometry, i.e., without flow. Finally, average Nusselt number correlations for each geometry and flow, and no-flow diagrams are presented.