Thermovibrational Instability in a Fluid Saturated Anisotropic Porous Medium

A comprehensive investigation is made to understand the effect of harmonic vibration on the onset of convection in a horizontal anisotropic porous layer heated either from below or from above. The layer is subject to vertical mechanical vibrations of arbitrary amplitude and frequency. The porous medium is assumed to be both mechanically and thermally anisotropic, and Brinkman’s law is invoked to model the momentum balance. Both continued fraction and Hill’s infinite determinant methods are used to determine the convective instability threshold with the aid of Floquet theory. The synchronous and subharmonic resonant regions of dynamic instability are determined and their critical boundaries are found. The results show that anisotropy in permeability favors convection whereas that in thermal conductivity suppresses it with a wider cellular pattern at the instability threshold. The influence of vibration parameters and heating condition on the anisotropy effects and the competition between the synchronous and subharmonic modes are discussed. This study also reveals the existence of a closed disconnected instability region in certain areas of the parameter space for the first time in literature.