Lattice Boltzmann simulation of viscoplastic fluids on natural convection in inclined enclosure with inner cold circular/elliptical cylinders (Part III: Four cylinders)

In this paper, natural convection in a heated cavity with four inner cold circular/elliptical cylinders in a diamond shape filled with viscoplastic fluids has been simulated by Lattice Boltzmann Method (LBM). In this study, the Bingham model without any regularization has been studied and moreover viscous dissipation effect has been analysed. Fluid flow, heat transfer, and yielded/unyielded parts have been conducted for certain pertinent parameters of Rayleigh number (Ra = 10⁴, 10⁵ and 10⁶), Eckert number, the size of the inner cylinder, various inclined angles of the cavity (Θ = 0°, 40°, 80°, 120°), the ratio of the inner cylinder radii (A = 0.5, 1, and 2), and different positions of the inner cylinder. Moreover, the Bingham number (Bn) is studied in a wide range of different studied parameters. Results indicate that the enhancement of the Rayleigh number augments the heat transfer, with a decrease in the size of the unyielded zones. For specific Rayleigh number and the position of the cylinder, the increase in the Bingham number declines the heat transfer and expands the unyielded sections between the inner cylinders and the enclosure. The enhancement of the ratio of the inner cylinder radii augments the heat transfer and declines the unyielded sections. The increase in the equal vertical and horizontal distances between cylinders (δ= Ω) enhances heat transfer, and moreover, enlarges the unyielded zones. The rise of the distance between horizontal cylinders in fixed distance of the vertical cylinders (Ω = 0.2) augments heat transfer while expands the unyielded zones. The enhancement of the distance between vertical cylinders in fixed distance of the horizontal cylinders (δ=0.2) augments heat transfer while alters the unyielded zones. The increase in the inclined angle of the enclosure alters the heat transfer and the yielded/unyielded zones noticeably. The rise of Eckert number even for higher range of practical values (Ec = 0.01, 0.1, and 1) alters the heat transfer and unyielded parts marginally, so the viscous dissipation term can be negligible in this study.