A comprehensive review of control strategies for Rayleigh–Bénard convection from classical feedback methods to artificial intelligence-driven optimization for enhanced energy transport and stability

Rayleigh–Bénard convection (RBC), the buoyancy-driven flow that arises when a fluid layer is heated from below and cooled from above, governs heat transport in engineering systems, geophysical and atmospheric circulation, stellar and planetary interiors, and numerous industrial processes. This review synthesizes theoretical, numerical, and experimental progress on controlling RBC, organizing methods into (i) passive strategies that modify geometry or boundary conditions and apply constant external fields, and (ii) active strategies that dynamically modulate parameters using feedback or machine learning-based controllers. Quantitatively, passive approaches can substantially delay the onset of convection: oscillatory boundary forcing increases the critical Rayleigh number Rac by up to ∼16×, and selected geometric or magnetic/rotational configurations shift stability by factors of order 1.5–3. Active approaches provide greater adaptability and depth of stabilization: Proportional feedback sustains the conductive state up to ∼4× the classical threshold, robust linear-quadratic-Gaussian designs up to ∼14.5×, while reinforcement learning reduces turbulent convective heat transport by 5.1% at Ra∼3×104, extending Rac by ∼30× over the uncontrolled case. We compare these methods on common performance metrics (extension of Rac, percentage change in Nusselt number, advantages and limitations) and discuss practical factors such as sensor placement, actuator bandwidth and saturation, and robustness to disturbances that govern deployability. The hybrid combining classical feedback with nonlinearity, augmented by multi-agent reinforcement learning, quantum-inspired optimization, and programable thermal metamaterials, provides scalable real-time solutions for precise thermal management in a wide range of scientific and industrial applications.