Heat transfer enhancement in vertical convection under spatially harmonic temperature modulation

In this study, we investigate the impact of spatial temperature modulation on vertical convection (VC) and analyze how the efficiency of heat transfer varies with modulation parameters. Our analysis focuses on the behavior of VC under sinusoidal temperature variations imposed on the hot wall, while maintaining a fixed temperature at the cold wall. The simulations are carried out in both two dimensions (2D) and three dimensions (3D), spanning a range of Rayleigh numbers, 106≤Ra≤1010, and a dimensionless modulation wave number, 1≤k≤80, while keeping the Prandtl number fixed at Pr=4.38. We identify three distinct regimes that exhibit different heat transfer behaviors. The first regime corresponds to an unperturbed state where the modulation effect does not penetrate the thermal boundary layer (BL). In the second regime, known as the weakly modulated regime, temperature modulation influences the thermal BL edge and strengthens the bulk stratification, resulting in an enhanced Nusselt number. Transitioning to the strongly modulated regime, which shows a higher heat transfer enhancement rate compared to the weakly modulated regime, the emergence of reverse flow allows for horizontal emission of thermal plumes that penetrate into the bulk, which provides a new way to strengthen bulk stratification. This phenomenon further promotes the flow strength and thus the heat transfer efficiency. We find that in strongly modulated regime, modifying the phase shift can change the position of reverse flow, modulate heat transfer mainly by changing the bulk stratification effect. This study on spatial temperature modulation in vertical convection allows us to uncover the underlying physics and mechanisms that govern heat transfer enhancement. This knowledge can be leveraged to develop more efficient and effective heat transfer systems in various practical applications.