Modulation of melting Rayleigh–Bénard convection by temporally periodic heating

In this paper, the effects of temporally periodic bottom-plate heating on melting Rayleigh–Bénard (RB) convection are numerically investigated using an improved lattice Boltzmann method. The criterion for identifying convection onset under oscillatory heating is first examined. These results show that conventional indicators based on the liquid fraction and local Nusselt numbers lose robustness, whereas the global Nusselt number remains reliable for detecting convection onset. Temporally periodic heating significantly modifies both convection onset and melting dynamics. Specifically, the onset of convection exhibits a non-monotonic dependence on the modulation frequency f. In the low-frequency regime, convection onset is markedly advanced, with the maximum advancement occurring under a timescale-matching condition of Fo_c ≈ T ∗ / 2. In the high-frequency regime, thermal disturbances become confined within a thin thermal Stokes layer, and the system gradually recovers behavior close to the unmodulated case. A similar non-monotonic dependence is observed for the total melting time, which can be reduced by more than 50% under appropriate modulation. The optimal frequency for the shortest melting time differs from that for the earliest convection onset, indicating that global melting efficiency is consistent with an approximate timescale matching condition, Fo_m ≈ T * / 2. These modulation effects remain robust over a broad Rayleigh number range (10⁵ ≤ R a ≤ 10⁸). Moreover, the present findings reveal a unified role of temporal and spatial periodic modulation in melting RB convection, suggesting an effective strategy for enhancing melting and heat transfer in latent-heat thermal-management systems.