Numerical 3-D Study of Poiseuille Rayleigh Benard Soret Problem in a Finite Extent Paralellipipedic Duct

This article deals with mixed convection of a binary mixture within a rectangular duct heated from below and under Soret influence. Going forward, the problem is referred to as the Poiseuille Rayleigh Benard Soret (PRBS) problem. We study the pattern formation of a binary mixture heated from below in the presence of a horizontal flow. When the system exhibits a supercritical bifurcation, either 2-D or 3-D convective structures appear. In a layer of infinite extent the presence of through-flow breaks the rotational symmetry, and the system at the convective threshold has to decide between longitudinal and transverse rolls among several unstable modes; we focus attention on transverse rolls. These rolls are generally unsteady and form traveling waves along the duct, and the presence of through-flow reduces the size of the region of convective instability. We show that the spanwise A_y aspect ratio has a strong influence on the threshold of convection, and in binary mixtures with a negative separation ratio N, and in distinction to the case for positive values of N; traveling waves can move against the direction of the mean flow. In general, nonlinear front propagation dominates the dynamics. The phase velocities and wave numbers of these fronts are determined. For the case of very long cells, we install continuity conditions in order to simulate an infinite duct. Changes in the outlet boundary conditions, in order to save the physics, influence the stability and wavelengths in the upstream.