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Rayleigh–Bénard convection in a Boussinesq–Stokes ferromagnetic fluid under sinusoidal and non‐sinusoidal internal heat modulation

Internal heat modulation has several applications in nuclear reactor design and safety, as well as meteorology. In this paper, the influence of internal heat modulation on Rayleigh–Bénard convection in a Boussinesq–Stokes ferromagnetic fluid is explored using linear and nonlinear analyses. The impact of the square, sine, triangular, and sawtooth wave type of internal heat modulation on the onset of convection and heat transport is considered. Using a Venezian method, linear stability analysis is performed to derive the correction Rayleigh number and the critical Rayleigh number for all four waveforms. A nonautonomous Lorenz model is derived and solved for the amplitude to obtain the Nusselt number, which quantifies the heat transport. The impact of the nondimensional parameter on the convective onset and heat transfer under heat source/sink modulation is analyzed. The study shows that all four types of internal heat modulation destabilize the system. It is also found that the presence of a heat source/sink modulation affects the impact of all four types of internal heat modulation on heat transport.