Electroosmotic–Peristaltic Propulsion of Ionic Jeffrey Fluid in Hall‐Current‐Modulated Magnetised Ciliated Porous Microchannel With Joule Heating and Soret–Dufour Cross‐Diffusion

This study develops an analytical model for peristaltic-electroosmotic transport of an ionic Jeffrey fluid in a magnetised ciliated microchannel. Employing the Poisson-Boltzmann description with Debye-Hückel linearisation for electric potential distribution and adopting the long-wavelength, low Reynolds number approximations, the governing momentum, thermal energy and species concentration equations are reduced to analytically tractable forms. Closed-form expressions are obtained for velocity, temperature, concentration, pressure rise and wall shear stress. Parametric investigations reveal that elevated Hartmann number suppress fluid motion through enhanced Lorentz force resistance, whereas increasing Hall current and electroosmotic parameters accelerate ionic liquid transport by counteracting electromagnetic damping. The Darcy number exhibits a regime-dependent influence on pressure development across retrograde, augmented and free-pumping zones. Thermal analysis reveals that Joule heating and elevated Prandtl numbers amplify temperature fields, whereas thermal radiation and increased Biot numbers facilitate effective cooling by improving boundary heat dissipation. Ciliary geometric parameters, such as length and eccentricity, demonstrate non-linear interactions with electrokinetic forces, which significantly influence momentum, heat and mass transport characteristics. The results provide theoretical insight that may be useful for future studies of biomedical microfluidic transport and related design-oriented applications.