Bibliographical review on the Poiseuille-Rayleigh-Bénard flows: The mixed convection flows in horizontal rectangular ducts heated from below

International audienceAn exhaustive bibliographical review on the Poiseuille-Rayleigh-Bénard (PRB) flows, the mixed convection flows in horizontal rectangular ducts uniformly heated from below, is presented. This review covers the period 1920-2001 and counts 154 references. The concerned parameter range is 0 < Pr ≤ 1000, 0 ≤ Re ≤ 1000 and 0 ≤ Ra ≤ 106. The interest of these flows in the industrial world is presented for the chemical vapor deposition studies (CVD) and for the cooling of the electronic equipments. After having done a synthesis of the temporal or spatial linear stability studies in the thermal entrance zone and in the fully-developed thermoconvective zone, we consider the linear or weakly non-linear spatio-temporal stability analyses, which take into account the concepts of convective and absolute instabilities and which are more appropriate to represent the dynamics of the PRB flows. All the stability results are systematically compared with the experimental and numerical results. The theoretical or experimental correlation formulae giving the variations of the Nusselt number, of the wave length, of the frequency and of the velocity of the transversal (R⊥) and/or longitudinal rolls (R//), as a function of Re, Ra, Pr and B = l/h, are collected. The influence of the inlet and of the outlet boundary conditions on the space and time development of the R⊥ in the experiments and in the numerical simulations is also analysed. A synthesis of the very recently discovered complex thermoconvective patterns (superposition of R⊥ and R//, periodic and aperiodic patterns, wavy or oblique rolls) is presented. To end, the badly known or badly understood aspects of the PRB flows are summed up and subjects for future investigations are proposed