Analytical Study of Nonlinear Behavior and Convection Patterns in Darcy-Brinkman Porous Medium with Maxwell-Cattaneo Ferroconvection

Abstract

This study investigates the onset of ferroconvection in a porous medium, considering the combined effects of second sound and couple stress using classical stability analysis. We assume local thermal equilibrium between the fluid and solid matrix. Employing normal mode analysis with appropriate boundary conditions, we determine critical values for both stationary and oscillatory instabilities. Results indicate that oscillatory instability supersedes the stationary mode. This oscillatory porous media ferroconvection arises from the interplay of magnetization nonlinearity, second sound, and magnetic forces. The analysis further explores the influence of various parameters on the oscillation frequency and convective cell size. This research significantly advances our understanding of ferrofluid applications in coupled stress environments. The findings contribute substantially to technological advancements leveraging the unique rheological properties of ferrofluids under applied stress. A comprehensive understanding of the interplay between magnetic fields and stress-induced behavior in ferrofluids is crucial for optimizing their performance in engineering applications. This study, therefore, provides valuable insights for developing and refining technologies reliant on the controlled manipulation of magnetic fluids under coupled stress fields. The implications are far-reaching, impacting diverse fields such as advanced damping systems, microfluidic devices, and targeted drug delivery. Major Findings: The research enhances understanding of ferrofluid applications in coupled stress environments, contributing to technological advancements in engineering applications. It provides insights for developing and refining technologies involving controlled magnetic fluid manipulation under coupled stress fields.

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