Title: Poiseuille Rayleigh-Benard problem in a horizontal duct of finite length in streamwise direction: stability analysis

Authors: H.B. Hamed, R. Bennacer, H. Sammouda

Addresses: LEEVAM, 5, mail Gay Lussac, Neuville sur Oise, 95031, Cergy-Pontoise, France. ' LEEVAM, 5, mail Gay Lussac, Neuville sur Oise, 95031, Cergy-Pontoise, France. ' LETTM, Faculty of Sciences Monastir, Department of Physics, 5019-Tunisia

Abstract: This paper deals with mixed convection within a rectangular duct heated from below, which is named Poiseuille-Rayleigh-Benard (PRB) problem. In particular, we study the transition towards transverse 2D-rolls appearing at low Reynolds. The effect of longitudinal confinement on the PRB stability problem and to numerically highlight the effect of the existing of thermal input area before the settling of the transverse 2D-rolls. The supercritical Rayleigh for the onset of convection is predicted numerically, based on the linear stability analysis. Since the flow is confined, the aspect ratio effect is taken into account and analysed. It is demonstrated that, the critical Rayleigh number depends on the Peclet number and the length of the domain and tends toward the classical natural convection critical Rayleigh value ad infinitum.

Keywords: mixed convection; horizontal duct; instability; critical Rayleigh number; linear stability; finite element method; FEM; stability analysis; incompressible Newtonian fluid flow.

DOI: 10.1504/PCFD.2008.019962

Progress in Computational Fluid Dynamics, An International Journal, 2008 Vol.8 No.6, pp.342 - 350

Published online: 18 Aug 2008 *

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