Lattice Boltzmann simulation of viscoplastic fluids on natural convection in an inclined enclosure with inner cold circular/elliptical cylinders (Part I: One cylinder)

In this paper, natural convection in an inclined heated cavity with an inner cold circular/elliptical cylinder 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 analyzed. Fluid flow, heat transfer, and yielded/unyielded parts have been conducted for certain pertinent parameters of Rayleigh number (Ra = 10⁴,10⁵ and 10⁶ ), 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 = 0.25, 0.5, 1, 2, and 4), 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 cylinder and the enclosure. The rise of the cylinder size in the enclosure enhances heat transfer and develops the unyielded parts. The enhancement of the ratio of the inner cylinder radii augments the heat transfer and declines the unyielded sections. The movement of the cylinder from the center to the left and right sides horizontally enhances heat transfer in different Bingham numbers, and moreover, alters the size and shape of the unyielded zones. As the cylinder moves from the bottom to the top side of the cavity vertically, the heat transfer increases gradually while the yielded/unyielded zones change. 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.