Investigation of asymmetric heating in Poiseuille-Rayleigh-Bénard water flow: A numerical study

Abstract

In this paper, a numerical investigation of the impact of asymmetric heating on laminar mixed convection in Poiseuille-Rayleigh-Bénard water flow within parallel horizontal channels is presented. The study has been carried out in a rectangular channel with a transverse aspect ratio of 10, and considered both low (Ra = 1.28 × 10⁴) and high (Ra = 1.4 × 10⁵) Rayleigh numbers, with Reynolds numbers of 50 and 100. A uniform heat flux was applied to the top and bottom walls of the heated region to assess its effect on the system's thermoconvective behavior and heat transfer efficiency. Two flux ratio scenarios were considered: q_t/q_b = 1 and q_t/q_b = 2.

The results indicate that increasing the flux ratio intensifies the destabilizing temperature gradient and significantly enhances buoyancy-induced flow, thereby influencing the patterns of thermoconvective structures. Specifically, flux ratios lead to an increased number of plumes originating from the bottom of the channel, while reducing their height and confining them between the bottom wall and the upper thermal boundary layer. It is also observed that flux ratios do not affect the mechanisms involved in the formation of longitudinal rolls. Furthermore, at low Rayleigh numbers, asymmetric heating has a pronounced impact on the establishment length. In contrast, this effect diminishes and becomes negligible at higher Rayleigh numbers. Numerical computations further reveal that near the bottom wall, the Nusselt number exhibits singular behavior, approaching infinity. Regardless of Reynolds and Rayleigh numbers, flux ratios significantly enhance heat transfer within the system. Additionally, near the top wall, the buoyancy effects from the bottom wall have negligible impact on heat transfer, except in the case where q_t/q_b = 2, Re = 50 and Ra = 1.4 × 10⁵, where instability in the upper thermal layer was observed.