Regular Article

Study of heat transfer in an enclosure with a square cylinder using Lattice Boltzmann method^*

¹ Laboratoire de Mécanique & Energétique, Faculté des Sciences, Université Mohammed Premier, 60000 Oujda, Morocco
² National School of Applied Sciences of Al Hoceima, Morocco
³ Université Blaise Pascal, Institut Pascal-GEPEB Axis, UMR 6602, B.P. 10488, 63000 Clermont Ferrand, France
⁴ Université Blaise Pascal, Institut Pascal-MMS Axis, UMR 6602, IUT d’Allier, B.P. 2235, avenue Aristide Briand, 03101, Montlucon, France

^a e-mail: amezrhab@yahoo.fr

Received: 1 March 2017
Revised: 21 March 2017
Accepted: 30 March 2017
Published online: 14 June 2017

Abstract

The purpose of this paper is to numerically examine the conjugate surface radiation-natural convection heat transfer in a 2D differentially heated enclosure with an inner square body, which generates heat. The numerical model is based on the coupling of the MRT-lattice Boltzmann model with finite difference method (FDM). The first one is used to compute the velocity field, while the second is adopted to obtain the temperature field. Various key parameters are studied, such as Rayleigh number (10³ ≤ Ra ≤ 10⁶), temperature-difference ratio ΔT*(0 ≤ ΔT* ≤ 50), body’s thermal conductivity (0 < K_s < ∞) and locations. In this study, the air is considered as perfectly transparent to radiation. Among the salient findings, we can state that (i) the inner body location has a meaningful effect on isotherms, streamlines and total heat transfer through the enclosure, (ii) the heat transfer is affected considerably by increasing the body size and radiation exchange, specially at high Ra.