Study of heat transfer in a rotating weakly electrically conducting Newtonian fluid: Primary and Küppers-Lortz regimes

In this paper, we study the primary and secondary (Küppers-Lortz) instabilities of rotating Rayleigh–Bénard convection for a weakly electrically conducting Newtonian fluid with idealistic boundaries. The critical Rayleigh number is obtained for each instability. Fourth-order and ninth-order Lorenz model are derived using the truncated Fourier-Galerkin expansion and the onset of primary and secondary instabilities is studied. Using a non-linear analysis, we derive the expression for the Nusselt number for both primary and secondary instabilities. The analysis reveals that the heat transfer in the case of primary instability is an over-prediction when compared with that of the secondary instability. An increase in the strength of the magnetic field is to delay the onset of primary and secondary instabilities and decrease the heat transfer. These insights advance the understanding of magnetohydrodynamic stability in rotating convective systems and have implications for geophysical and astrophysical fluid dynamics.