Optimization and sensitivity analysis of heat transport enhancement in Rayleigh–Bénard convection using machine learning control

Rayleigh–Bénard convection with non-uniform bottom heating, widely applied in systems such as solar collectors and electronic cooling, has been proven to be an effective and valuable approach for enhancing heat transfer. Nevertheless, the optimal control strategy and its mechanisms associated with convective structure alterations remain unclear. A machine learning method using the artificial bee colony algorithm was proposed for optimizing bottom temperature distribution and conducting sensitivity analysis. Non-uniform temperature was modeled via sinusoidal modulation parameterized by amplitude A, mode number n, and phase shift θ. At a Rayleigh number of Ra = 10⁴, simulations were performed for aspect ratios Г = 2, 6, and 10, yielding respective Nusselt number Nu increases of 9.8 %, 7.8 % and 8.3 % compared to the uniform-temperature case. The results reveal that, for all models, the optimal A reaches its maximum, n matches the number of convection cells, and θ is ∼1.5π. Flow and temperature fields analysis indicates that the optimal case maintains a high temperature difference between the near-wall fluid and bottom surface when the fluid transition in a descending to ascending order, sustaining higher local Nu compared to the case with a uniform bottom temperature. A sensitivity analysis showed that deviating from the optimal n significantly reduced heat transfer, while A had a noticeable impact, and θ deviations became less influential as Г increased. This work proposed a general, automated optimization framework for enhancing Rayleigh–Bénard convection, and the results offer valuable guidance for future research and engineering applications.