A dynamical model for studying the stability of thermo-solutal convection under the effect of vertical vibration

摘要

This paper concerns the thermal stability analysis of porous layer saturated by a binary fluid under the influence of mechanical vibration. The linear stability analysis of this thermal system leads us to study the following damped coupled Mathieu equations. where Ra_T is thermal Rayleigh number, R is acceleration ratio (bω~2/g), Le is the Lewis number, k is the dimensionless wave-number, ε~* is normalized porosity and N is the buoyancy ratio (H and F are perturbations of temperature and concentration fields). In the follow up, the non-linear behavior of the problem is studied via a generalization of the Lorenz model (five coupled non-linear differential equations with periodic coefficients). In the presence or absence of gravity, the stability limit for the onset of stationary as well as Hopf bifurcations is determined.