Study of Thermovibrational Convection in a Fluid Saturated Porous Medium

Abstract

The investigation delves into the intriguing realm of fluid dynamics, specifically exploring the influence of gravity modulation on the onset of convection in a horizontal fluid saturated porous layer subject to bottom heating. In this scenario, the flow through the porous layer is governed by an extended form of Darcy’s law incorporating Brinkman’s boundary layer correction. Through a comprehensive stability analysis utilizing the method of small perturbations and employing normal mode analysis, the study endeavors to unravel the intricate interplay between gravity modulation and convection onset. To tackle this complex problem the study harnesses the power of Mathieu’s functions, renowned for their utility in describing periodic phenomena in various scientific disciplines. Central to the investigation is the concept of instability and its manifestation through synchronous and subharmonic modes. Instability represents a critical threshold in system’s behaviour, marking the point at which small perturbations can lead to
significant deviations from initial state. By elucidating the mechanisms governing instability and transition phenomena, the study lays ground work for future research aimed at harnessing these phenomena for practical applications.