Effect of time-periodic boundary temperatures/body force on Rayleigh–Benard convection in a ferromagnetic fluid

Abstract

We discuss the thermal instability in a layer of a ferromagnetic fluid when the boundaries of the layer are subjected to synchronous/asynchronous imposed time-periodic boundary temperatures (ITBT)/time–periodic body force (TBF). Only infinitesimal disturbances are considered. The Venezian approach is adopted in arriving at the critical Rayleigh and wave numbers for small amplitudes of ITBT. A perturbation solution in powers of the amplitude of the applied temperature field is obtained. When the ITBT at the two walls are synchronized then, for moderate frequency values, the role of magnetization in inducing sub-critical instabilities is delineated. A similar role is shown to be played by the Prandtl number. The magnetization parameters and Prandtl number have the opposite effect at large frequencies. The system is most stable when the ITBT is asynchronous. The effect of TBF on the onset of convection is found to be qualitatively similar to the effect of an asynchronous ITBT. Low Prandtl number fluids are shown to be more easily vulnerable to destabilization by TBF compared to very large Prandtl number fluids. The problem has relevance in many ferromagnetic fluid applications wherein regulation of thermal convection is called for.