Linear stability of mixed convection flows in horizontal rectangular channels of finite transversal extension heated from below

Xavier Nicolas (1, 2) , J.-M. Luijkx , J. K. Platten

1 LETEM - Laboratoire d'Etudes des Transferts d'Energie et de Matière
2 IMFT - Institut de mécanique des fluides de Toulouse

We present a study of the linear hydrodynamic stability of purely conductive Poiseuille flow in three-dimensional horizontal rectangular channels uniformly heated from below. Its originality is to modelize the flow using realistic conditions on all the boundaries of the channel, in particular, no-slip conditions on the vertical lateral boundaries. The aim of this paper is to provide quantitative results for the values of the critical dimensionless parameters. When the Rayleigh number Ra is higher than the critical value Ra*, the instabilities are shown to be three-dimensional horseshoe-shaped transversal rolls for Reynolds numbers Re smaller than the critical value Re*, and longitudinal rolls for Re > Re*. The results are given for a wide range of the Prandtl number (10-6 ≤ Pr ≤ 105) and of the transversal aspect ratio B of the duct (0.1 ≤ B ≤ 5.4 and B → ∞). We present a study of the linear hydrodynamic stability of purely conductive Poiseuille flow in three-dimensional horizontal rectangular channels uniformly heated from below. Its originality is to modellize the flow using realistic conditions on all the boundaries of the channel, in particular, no-slip conditions on the vertical lateral boundaries. The aim of this paper is to provide quantitative results for the values of the critical dimensionless parameters. When the Rayleigh number Ra is higher than the critical value Ra*, the instabilities are shown to be three-dimensional horseshoe-shaped transversal rolls for Reynolds numbers Re smaller than the critical value Re*, and longitudinal rolls for Re > Re*. The results are given for a wide range of the Prandtl number (10-6 ≤ Pr ≤ 105) and of the transversal aspect ratio B of the duct (0.1 ≤ B ≤ 5.4 and B → ∞).

Mots clés: Aspect ratio; Boundary conditions; Channel flow; Flow patterns; Hydrodynamics; Mathematical models; Prandtl number; Reynolds number; Linear hydrodynamic stability; Poiseuille flow; Rayleigh number; Mixed convection; channel; convection; mathematical analysis; stability

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Thermique [physics.class-ph]; Thermique [physics.class-ph]

Xavier Nicolas, J.-M. Luijkx, J. K. Platten. Linear stability of mixed convection flows in horizontal rectangular channels of finite transversal extension heated from below. International Journal of Heat and Mass Transfer, 2000, 43 (4), pp.589-610. ⟨10.1016/S0017-9310(99)00099-X⟩. ⟨hal-00695287⟩