Numerical investigation of natural convection of viscoplastic fluid in cavities filled by solid obstacles

Abstract

In the present study, three scientific papers on the natural convection of viscoplastic fluids in cavities are proposed to compose the thesis by a collection of articles. The first paper analyzes the natural convection process of a fluid modeled as a Bingham fluid in closed cavities with differentially heated vertical walls, adiabatic horizontal surfaces, and inserted square solid blocks representing a porous medium. It is observed that for high Bingham values and low Rayleigh values, the Nusselt number decreases, reaching a limiting value that depends on the ratio of thermal conductivities between the fluid and solid and the number of blocks near the heated surface. This limiting value characterizes heat transfer purely by conduction. With an increase in the number of blocks, a pattern emerges in forming unyielded regions within the cavity. Additionally, the fluid flow tends to migrate towards the path of least resistance, moving away from regions near the surfaces. The second paper analyzes three open geometries for different Rayleigh and Bingham numbers. The heated surface is parallel to the cavity opening, and a fixed number of solid blocks within the cavity represent the porous medium. The results indicate that convective forces are more intense in the side-opened cavity than in a closed cavity. In all simulated cases, heat transfer in the downward-opened geometry is predominantly driven by pure conduction. For low Ra or high Bn values, fluid flow occurs outside the cavity, entering only near the opening, where critical deformations are exceeded. Conversely, a flow channeling effect within the cavity is observed for high Ra or low Bn values. Focusing individually on the side-opened geometry, the third paper investigates parameters that have not yet been explored, such as porosity, thermal conductivity ratio, and Brinkman number. The results demonstrate that reducing porosity and increasing the number of blocks significantly impact the flow and temperature fields, promoting the formation of unyielded regions and the transition of heat transport from convection to conduction. Overall, increasing the thermal conductivity (κ) enhances the average Nusselt number in cases where the geometry becomes more restrictive, with increased fluid viscoplasticity and a shorter distance between the solid blocks and the heated surface. Finally, the flow diagrams and correlations proposed throughout this collection of articles serve as fundamental tools for engineering designs involving viscoplastic fluids and complex geometric configurations in thermal systems.