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Numerical study of natural convection in a square cavity containing a cylinder using the lattice Boltzmann method

Mohammed Jami (Département de Physique, Faculté des Sciences, Université Mohamed 1, Oujda, Morocco)
Ahmed Mezrhab (Département de Physique, Faculté des Sciences, Université Mohamed 1, Oujda, Morocco)
Hassan Naji (Ustl/Polytech'lille/Lml UMR 8107 CNRS, Département de Mécanique, Villeneuve d'Ascq, France)

Engineering Computations

ISSN: 0264-4401

Article publication date: 18 July 2008

Abstract

Purpose

This paper attempts to deal with the presentation of a numerical investigation of the laminar‐free convective heat transfer in a square enclosure containing a solid cylinder located at an arbitrary position. Effects of the cylinder position on the heat transfer and the flow structures inside the cavity are to be studied and highlighted.

Design/methodology/approach

The numerical code is based on the hybrid scheme with the lattice Boltzmann and the alternating‐directional implicit (ADI) splitting scheme. The energy equation is solved by ADI scheme and the flow field velocities have been computed using the lattice Boltzmann method (LBM). The bounce‐back condition combined with quadratic interpolation is used at solid boundaries.

Findings

The predicted results show that the cylinder location has a significant effect on the heat transfer. It is observed that: when the inner body does not generate heat, most of the heat transfer takes place if the body is located at the center of the enclosure. When the cylinder generates heat and is displaced from the left towards the right and from the lower part towards the upper part of the cavity, the heat transfer rate decreases on the hot wall and increases on the cold wall.

Research limitations/implications

The fluid flow (air) is assumed to be incompressible, laminar and 2D. The viscous heat dissipation is neglected in the energy equation and all physical proprieties are constant except for the density, whose variation with temperature is allowed for in the buoyancy term.

Practical implications

Natural convection in heated enclosures, housing inner bodies has received significant attention because of its interest and importance in industrial applications. Some applications are solar collectors, fire research, electronic cooling, aeronautics, chemical apparatus, building constructions, nuclear engineering, etc.

Originality/value

The paper contributes to the development of the LBM. In particular, it was found that the inherent numerical instabilities of this LBE are not modified by coupling with temperature. This is a good improvement compared to what is observed in the simulations of thermal systems using the full LBE formulation where the energy conservation is taken into account.

Keywords

Citation

Jami, M., Mezrhab, A. and Naji, H. (2008), "Numerical study of natural convection in a square cavity containing a cylinder using the lattice Boltzmann method", Engineering Computations, Vol. 25 No. 5, pp. 480-489. https://doi.org/10.1108/02644400810881400

Publisher

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Emerald Group Publishing Limited

Copyright © 2008, Emerald Group Publishing Limited