Heat transport model for the transition between scaling regimes in quasistatic and full magnetoconvection

In magnetoconvection, the flow is governed by the interplay between gravitational buoyancy and the Lorentz force, with one of these forces dominating in different regimes. In this paper, we develop a model with a single adjustable parameter that accurately captures the smooth transition from a buoyancy-dominated regime to one dominated by the Lorentz force. A perturbative extension of the model accounts for distinct transition features that occur at high Prandtl numbers. We validate the model for magnetoconvection in both the quasistatic regime and at finite magnetic Reynolds numbers using data from direct numerical simulations and existing experimental data sets. The model contains a natural extension to rotating convection and offers a potential generalisation to rotating magnetoconvection. • Heat transport in magnetoconvection is studied from a buoyancy-dominated regime to one dominated by the Lorentz force. • A model with a single adjustable parameter is proposed that captures the smooth transition between these regimes. • The model is validated using direct numerical simulations and existing experimental data. • The model may be applied under the quasistatic approximation and at finite magnetic Reynolds numbers. • The model contains a natural extension to rotating convection.