Hybrid nanofluid flow deliberation with double diffusion convection for complex cilia wave in non‐uniform ciliated microchannel

Abstract The convective double‐diffusion phenomenon plays a vital role in maintaining efficient and regulated transport of fluids, nutrients, and waste within the body. It significantly influences numerous physiological processes, and its understanding is crucial for the developing of medical treatments, enhancing of drug delivery systems, and designing artificial organs. This study investigates the complex cilia‐driven motion of magnetohydrodynamic (MHD) Oldroyd four‐constant nanofluids by incorporating double‐diffusive convection and cross‐diffusion effects, validated through artificial neural networks (ANN)‐based intelligent computing a novel approach not previously reported in the literature. The Soret and Dufour effects are analyzed for complex cilia waves in Oldroyd four‐constant nanofluids within a non‐uniform channel. A novel mathematical formulation for cilia‐induced motion is developed and simplified using lubrication approximation theory. Computational solutions are obtained using the well‐established numerical method bvp4c, and further validated through ANN. Detailed numerical results are presented for velocity distribution, temperature profile, nanoparticle solutal concentration and volume fraction, pressure gradient, magnetic force function, heat transfer coefficient, and wall shear stress. The findings reveal that nanofluid transport is influenced by channel non‐uniformity, enhanced by relaxation time and the nanoparticle Grashof number, while temperature rises with Brownian motion and thermophoresis effects. The diffusion of nanoparticles is suppressed by the Soret and Dufour parameters but is strengthened by Brownian motion and thermophoresis. Pumping characteristics are found to increase with relaxation time but decline with channel non‐uniformity.