Natural convection of viscoplastic fluids in side-heated open cavities

Abstract

This study considers the natural convection process of viscoplastic fluid in a side-open cavity filled with conductive solid blocks, which are uniformly distributed and form a square lattice. The cavity has adiabatic horizontal surfaces and a heated vertical surface parallel to a vast reservoir with quiescent fluid maintained at a temperature lower than the cavity wall temperature. The problem is modeled as a two-dimensional steady laminar flow, and the Bingham constitutive equation is used to represent the flow behavior of the material. A validated numerical approach and the finite volume method are used to solve the fluid and solid constituents within the cavity separately. The velocity and temperature fields are obtained following a parametric analysis conducted in terms of the total number of blocks (9 ≤ N ≤ 144), porosity (0.36 ≤ ϕ ≤ 0.84), solid-fluid thermal conductivity ratio (1 ≤ κ ≤ 100), Bingham number (0.1 ≤ Bn ≤ 1), and Brinkman number (0.1 ≤ Br ≤ 100). The Prandtl number (Pr = 500) and the Rayleigh number (Ra = 107) are fixed. The thermo-hydraulic effects are presented as streamlines, isotherms, unyielded regions, dimensionless velocity, dimensionless temperature, dimensionless mass flow rate at the cavity inlet, and average Nusselt number on the heated surface. We demonstrate that the interference effect of the blocks is analytically predictable. Other effects, such as channeling and fin-like diffusion, have also been observed. With decreasing porosity and increasing number of blocks, a pattern in the appearance of unyielded regions is detected. The increase in the magnitude of the material yield stress has a quantitative effect on reducing fluid circulation. Even for a higher range of practical values of the Brinkman number, the isotherms, streamlines, and unyielded regions change minimally perceptibly, so the viscous dissipation term can be neglected in the study. Finally, numerical correlations for the average Nusselt number and dimensionless mass flow rate are proposed as tools to assist engineers and researchers in similar projects.

Keywords

• Natural convection
• Porous medium
• Viscous dissipation
• Open cavity
• Brinkman number