Energy relaxation for transient convection in ferrofluids

The onset of transient instability driven by a coupling of thermal and magnetic effects in an initially quiescent ferrofluid layer is investigated using the energy method. Following the work of Kim et al. [Phys. Lett. A 372, 4709 (2008)], an energy stability criterion is derived for the underlying dynamical system by taking into account the different boundary conditions and the Prandtl number effects. The critical onset time of the instability is determined as a function of the Rayleigh number, the Prandtl number, and the thermomagnetic parameter. For larger times, our analysis predicts that the energy stability theory and the linear theory yield essentially the same results irrespective of whether the fluid under consideration is a magnetically polarizable or a nonmagnetic fluid and subcritical instabilities are not possible. For the global nonlinear stability boundary in the impulsively heated ferrofluid layer, the minimum critical onset time is found to occur when the values of the Rayleigh number and the thermomagnetic parameter are same.