Numerical simulation of fractional electro-osmotic Walter-B flow in a magnetized porous medium with Soret–Dufour and chemical reaction effects

Abstract

The thermal management of microfluidic devices and renewable energy systems relies heavily on the efficient transport of non-Newtonian fluids. Specifically, these electro-kinetic and transport mechanisms are directly applied in the real-world design of electro-kinetic micropumps and biomedical lab-on-a-chip devices. Fractional calculus extends classical differentiation to non-integer orders, enabling realistic modeling of systems with memory and spatial nonlocality. This study examines the unsteady electro-osmotic flow of a Walter-B viscoelastic fluid past a semi-infinite vertical plate embedded in a Darcy porous medium under a transverse magnetic field. The model incorporates thermal radiation, internal heat generation, Soret-Dufour cross-diffusion, and a first-order chemical reaction, while Caputo fractional derivatives are used to represent memory-dependent heat and mass diffusion mechanism. The governing equations are non-dimensionalized and solved numerically using a fully implicit finite-difference scheme based on the second-order fractional backward-difference formula (FBDF2), ensuring stability and accuracy. To the best of the authors’ knowledge, this is the first study that combines fractional electro-osmotic Walter-B flow with simultaneous Soret–Dufour effects and chemical reaction within an FBDF2-based fully implicit finite-difference framework. The results reveal that smaller fractional orders intensify memory effects and delay thermal and solutal relaxation, reflecting the inherent nonlocality of fractional transport. Quantitatively, the Soret number enhances the heat transfer rate by approximately 5.38% while reducing the mass transfer rate by about 11.02%. The radiation parameter markedly improves thermal transport, producing nearly 33.36% enhancement in the Nusselt number. In contrast, the thermal Grashof number slightly reduces the skin-friction coefficient by 3.20%, whereas the electro-osmotic parameter decreases it by 7.95%. Moreover, the Dufour number yields a modest 2.10% increase in the Sherwood number.