LINEAR AND NONLINEAR CONVECTIVE INSTABILITIES OF A MAXWELL-CATTANEO BIDISPERSIVE LAYER IN LOCAL THERMAL NON-EQUILIBRIUM

Abstract

The linear and nonlinear instabilities of a horizontal Nield-Kuznetsov bidispersive layer in local thermal non-equilibrium subject to the Maxwell-Cattaneo (MC) effect is studied. In the absence of the MC effect, we prove that only a steady mode can exist. The presence of the MC effect, which introduces a fundamental change to the heat equation, gives rise to oscillatory motions. The linear stability of the layer can then take the form of steady or oscillatory motion. The stability boundary shows that the oscillatory stability boundary bifurcates from that of the steady mode to develop a situation of lower energy for instability. The presence of microporosity tends to inhibit the instability of oscillatory motions and introduces a mean flux that is uniform across the layer. A formal nonlinear analysis leads to two coupled evolution equations of the Landau-Stuart form, for two linearly preferred oscillatory waves propagating in opposite directions. The equations reduce to one for the steady mode. It is shown that the linearly unstable modes can take one of four types of nonlinear growth: supercritical stability, nonlinear instability, subcritical instability, or stability, depending on the relative values of the medium parameters. Although the two amplitudes start to grow interactively, the supercritical solutions always occur in the form of one amplitude, while the other dies out. However, the solution is different from that obtained by considering each wave separately.