Early onset of convection induced by spatially periodic heating in melting Rayleigh–Bénard systems

In this paper, the onset of convection in melting Rayleigh–Bénard convection (RBC) under spatially periodic heating is numerically investigated using a custom-made code implementing interpolation-supplemented Lattice Boltzmann Method (LBM). We firstly focus on the criterion to identify the convection onset, and the results indicate that the first local minimum of the bottom Nusselt number serves as a robust indicator for identifying the convection onset, in the presence of the modulated heating boundary conditions at the bottom plate. Building on this criterion, it is found that introducing a sinusoidal temperature variation at the bottom wall significantly advances the onset of convection: both the critical Fourier number and the critical melted liquid fraction decrease, with the most pronounced advancement (up to approximately 75%) occurring at a moderate wavenumber around k=2. The mechanism is attributed to the additional horizontal temperature difference that generates buoyancy variations as in the configuration of vertical convection, enhancing convection instability and coupling horizontal and vertical convective motions. This effect remains robust across a wide range of Rayleigh numbers (10⁵≤Ra≤10⁸) and Stefan numbers (0.05≤Ste≤10), though its strength diminishes at large k due to enhanced horizontal heat conduction that spreads the temperature distribution. A regime map in the (k,Ste) parameter space reveals three distinct behaviours governed by the competition between the extra effect of vertical convection and that of the latent-heat-induced delay. The findings deepen the understanding of phase-change convection instabilities and suggest new strategies for accelerating melting and improving heat transfer in phase-change thermal management systems.