Thermal Analysis and Dynamics Behavior of Cattaneo-Christov Heat-Flux-Based (Fe3O4-Cu)/Water, EG-Water and Palm Oil Hybrid Nanofluid Flows through Porous Media

Abstract The present investigation addresses the heat transfer in a thermal convection flow governed by the Darcy--Brinkman framework within a porous layer saturated by a hybrid nanofluid composed of iron oxide-copper nanofragments dispersed across three distinct base fluids, namely water, an ethylene glycol-water mixture, and palm oil, under the Cattaneo--Christov heat flux model. A normal mode linear stability analysis is carried out. A Galerkin truncation procedure is applied to the Darcy-Brinkman-Boussinesq governing equations, coupled with a two-temperature energy model, producing a five-dimensional autonomous dynamical system that constitutes a generalization of the classical Lorenz equations. Numerical integration is performed using a fourth-order Runge--Kutta scheme, and the dynamical behavior of the system is thoroughly characterized through four complementary diagnostic tools: bifurcation diagrams of local extrema of the convective variable, the maximal Lyapunov exponent computed via the renormalization method, and phase portrait reconstructions. A comprehensive discussion of the physical outcomes is subsequently presented, examining the respective influences of the nanoparticle volume fraction, the Darcy number, the thermal time-lag parameter, and the Hartmann number on the critical stationary Darcy-Rayleigh number, the critical wave number, and the physical onset temperature, assessed comparatively across the three base fluids. The magnetic field is shown to delay the onset of convection and shift the transitional peak of the mean Nusselt number toward higher Rayleigh--Darcy numbers, while all configurations gradually approach a common asymptotic heat-transfer level in the fully developed regime. Beyond its theoretical contribution, this study offers practical guidance for optimizing thermal enhancement strategies and improving the thermodynamic performance of energy systems in thermal engineering, with particular relevance to porous heat exchangers.