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DOI: 10.1615/ICHMT.2008.CHT.1780
page 9

Serge Blancher
Laboratoire des sciences de l'ingénieur Appliquées a la Mécanique et au génie Electrique (SIAME), Université de Pau et des Pays de l'Adour (UPPA), IFR, rue Jules Ferry, BP 7511, 64075 Pau Cedex, France

Carlos Perez Wilson
Departamento de Ingeneria Mathematica Universidad de Conception, Casilla 160 C, Conception, Chile


In mixed convection simulations, the Boussinesq approximation [1903] considers the variation of the density only in the buoyancy term as: ρrefref(T − Tref ) The question of the choice of the reference temperature Tref has been already studied by Wang et al. [2003] for the Poiseuille-Rayleigh-Benard problem: an horizontal channel flow heated from below. They compare the solution obtained by numerical simulation using different choices of Tref with the non Boussinesq solution. In their study they consider particulars Rayleigh and Reynolds numbers for which the flow consists of steady 3D longitudinal rolls. In the present study we consider the case where the Rayleigh and Reynolds numbers are such that the flow exhibits transverse unsteady 2D travelling wave. The numerical code "Aquilon" solves the coupled Navier Stokes and Energy equations by an unsteady, 2D finite volume method. We have considered different choices for Tref and we have compared the heat flux at the walls obtained with the Boussinesq and non Boussinesq cases. The local results are not satisfactory in the whole domain. Globally speaking, it seems better to chose Tref as the bottom wall temperature or the average temperature in view to compute the bottom heat flux. Otherwise better results are obtained using Tref = T0 for both top and bottom heat flux with a variable bottom wall temperature. So we propose a modified Boussinesq approximation in view to have a better simulation of the buoyancy force in the whole domain, writing the buoyancy force as: ρavav(T − Tav ), where Tav is the global average temperature in the whole domain. With this hypothesis, the Boussinesq simulations are better compared with the non Boussinesq case and would permit to have a better simulation of mixed convection problem particularly when then temperature boundary conditions are not uniform in space and time.

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