Transition between buoyancy- and Coulomb-dominated regimes in Rayleigh–Bénard convection with an additional side-heated wall and bottom-wall unipolar charge injection

A unified lattice Boltzmann method is employed to investigate Rayleigh–Bénard convection (RBC) subjected to sidewall heating and unipolar charge injection from the bottom wall. The study focuses on how the complex and nonlinear coupling between the buoyancy and Coulomb effects modify the heat transfer, flow structure and the transition between buoyancy- and Coulomb-dominated regimes. The results show that a side-heated wall, in the absence of charge injection, enhances the heat transfer rate and changes the scaling law between the Nusselt number $\textit{Nu}$ and Rayleigh number $Ra$ from $\textit{Nu} = 0.22Ra^{0.29}$ (classical RBC) to $\textit{Nu} = 0.56 Ra^{0.22}$ due to an additional buoyancy effect from the sidewall. When the electric charge is injected from the bottom wall, it is shown that the thermal boundary layer thickness decreases, leading to a further enhancement of heat transfer. Furthermore, systematic simulations over a broad range of $Ra$ and electric Rayleigh numbers $T$ reveal that, at given $T$ , $\textit{Nu}$ remains constant when $Ra$ is low, indicating a Coulomb-dominated regime. Beyond a critical value of $Ra$ , a power-law relationship between $\textit{Nu}$ and $Ra$ emerges, signifying a transition to the buoyancy-dominated regime. This transition can be well predicted by a dimensionless parameter, which is developed considering buoyancy to Coulomb forces. In addition, by analysing the flow structure using the Fourier mode decomposition, a phase diagram describing the dominant flow modes is proposed. The results demonstrate that the proposed dimensionless parameter not only delineates the transition between the two heat transfer regimes but also accurately captures the flow mode shift. Our findings offer new insights into the complex interaction between buoyancy and Coulomb effects and their influence on heat transfer and flow structure, with potential implications for the design of heat exchangers aimed at actively and efficiently controlling heat transfer.