STUDY ON THE HEAT TRANSFER ENHANCEMENT MECHANISM OF RAYLEIGH-BÉNARD CONVECTION WITH WAVENUMBER MATCHING BETWEEN WAVY WALLS AND SPATIAL TEMPERATURE MODULATION

Thermal convection is ubiquitous in natural phenomena and engineering applications, with Rayleigh–Bénard (RB) convection serving as a canonical model for investigating the underlying mechanisms of fluid flow and heat transfer. While current research on RB convection under individual complex geometric boundaries or only non-uniform heating conditions is relatively mature, our understanding of flow and heat transfer problems involving the coupling of wavy walls with spatial temperature modulation remains insufficient. In this study, direct numerical simulations (DNS) are performed using the finite difference method, coupled with an immersed boundary method to accurately resolve the bottom wavy wall. We investigate the heat transfer characteristics and flow field evolution mechanisms of RB convection under the synergistic influence of a sinusoidal wavy wall and periodic non-uniform heating. The results indicate that spatial temperature modulation dictates heat transfer by regulating the initiation sites and distribution of thermal plumes. When the modulation wavenumber k_\theta matches the roughness wavenumber k_ob , such that the imposed temperature peaks coincide with the wave crests, thermal plumes are efficiently integrated into the large-scale circulation. This resonance maximizes the system's heat transfer efficiency, with the Nusselt number (Nu) reaching up to 130% ~ 145% of that in standard RB convection; furthermore, this enhancement effect becomes more pronounced as the matched wavenumber increases. Conversely, when the wavenumbers are mismatched, the heat transfer efficiency approaches that of standard RB convection. Notably, under the condition of k_\theta = 2k_ob , where temperature peaks are located at the troughs of the roughness elements, thermal plumes are severely obstructed by the geometric structures, leading to a significant suppression of heat transfer that intensifies with higher wavenumbers. This work reveals that wavenumber matching is a critical mechanism for modulating thermal transport efficiency in convective systems, providing significant insights for the understanding and design of high-performance thermal control systems.