Three-dimensional numerical simulations on Poiseuille-Rayleigh-Bénard convection of air in a horizontal rectangular channel

In order to reveal the combined influences of Rayleigh (Ra) number, Reynolds (Re) number and spanwise aspect ratio (B) on the flow pattern evolution and stability, and heat transfer of Poiseuille-Rayleigh-Bénard (PRB) convection, we presented a set of three-dimensional numerical simulations on PRB convection of air in the horizontal channels using commercial software Fluent in a range of 2 ≤ B ≤ 10, 0 ≤ Re ≤ 250 and 1.7 × 103 ≤ Ra ≤ 2.5 × 104. Various flow patterns are observed, including transversal rolls, longitudinal rolls, mixed rolls and wavy flow. The results show that the number of longitudinal rolls depends on B and Ra. The critical Rayleigh numbers for appearance and destabilization of the longitudinal rolls and the transversal rolls increase with increasing Re. With increasing B, the critical Rayleigh numbers for the primary and secondary instabilities will decrease and the critical Reynolds number also decreases. The heat transfer of PRB convection is enhanced with increasing Ra and B. A heat transfer correlation of the average Nusselt number with Ra and B is established.