Hyper-chaotic convection in a two-phase Cattaneo LTNE porous medium with helical magnetic field and quasi-periodic sinusoidal modulation

This study examines of Cattaneo local thermal nonequilibrium (LTNE) driven hyper-chaotic convection in a two-phase porous media, considering the influence of a helical magnetic field and externally induced quasi-periodic gravitational modulation. A fluid-saturated porous layer, heated from below, has vertical gravity modulation characterized by two incommensurate frequencies, δ1 and δ2, resulting in intricate temporal forcing. The fluid phase is regulated by the Darcy–Brinkman model, whereas thermal transport in the solid phase adheres to a hyperbolic Cattaneo-type heat conduction equation, allowing for finite-speed thermal propagation. A double Fourier mode decomposition is utilized to simplify the governing system into high-dimensional nonlinear equations, enabling a thorough examination of dynamic transitions and bifurcations under varying modulation amplitudes. The LTNE framework demonstrates divergent thermal reactions between fluid and solid phases, resulting in hyper-chaotic attractors and coexisting coherent chaotic structures. Finally, results indicate that augmented inter-phase heat exchange exacerbates instability, while magnetic field strength, helical forcing, thermal relaxation time, and porous matrix resistance serve as stabilizing factors. These mechanisms, along with external influences, facilitate the efficient suppression or regulation of chaotic convection. This study offers novel insights into the regulation of non-equilibrium thermal systems, with prospective applications in advanced thermal management, energy systems, and smart material design.