Nonlinear stability analysis of fluid flow with viscous dissipation in a porous channel

The nonlinear convective instability of flow in a fluid saturated rectangular porous channel of arbitrary aspect ratio is here investigated by taking into account the effect of viscous dissipation. A laminar throughflow of constant velocity is assumed. The system is characterized by a unique source of thermal instability identified in the internal heat generation due to the viscous dissipation. The nonlinear analysis is performed by means of the generalized integral transform technique (GITT). The results obtained are compared with those coming from the linear analysis carried out numerically by means of the normal modes method.