On the Onset of Gravity Modulated Filtration Convection in Grade Fluids Via Mathieu Functions

Abstract

The effect of gravity modulation in controlling the onset of convection in a porous medium saturated with a second-grade fluid of Rivlin–Ericksen type is studied. The Brinkman equation of flow through porous media is considered with effective viscosity different from fluid viscosity. Necessary conditions for the occurrence of instability due to infinitesimal perturbations are found using the method of normal modes. Following Floquet analysis, the thresholds corresponding to synchronous and subharmonic solutions and the transition between them are predicted using the Mathieu functions.