Fractional-Order Williamson Fluid Flow with Slip and Cross-Diffusion Over a Variable-Thickness Sheet
Keywords:
Fractional calculus, Williamson fluid, heat and mass transfer, Crank-Nicolson method, slip conditions, Soret and Dufour effectsAbstract
This study investigates heat and mass transfer in non-Newtonian Williamson fluid flow over a variable-thickness stretching sheet, incorporating Caputo fractional derivatives, velocity slip conditions, and Soret and Dufour effects. A fractional-order model captures memory effects, enhancing the representation of shear-thinning behavior and cross-diffusion phenomena. Governing equations are solved numerically using a hybrid Crank-Nicolson and spectral method, with stability and convergence rigorously analyzed . Results reveal that increasing the fractional order (α) from 0.1 to 0.9 yields a 300% increase in heat transfer rate (from 250 W/m² to 1000 W/m²) and a 53% reduction in thermal boundary layer thickness (from 0.015 m to 0.007 m). Slip conditions further reduce boundary layer thickness by 16%, while magnetic field and cross-diffusion effects amplify transfer rates by 43%. The model offers 20-30% improved accuracy over traditional approaches, with applications in polymer extrusion and biomedical microfluidics. Future work will explore variable material properties and multi-phase flows.
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