Overlapping Multi-Domain Paired Quasilinearization Method for the Solution of the MHD Williamson-Nanofluid Flow Over an Exponentially Stretching Surface

This study examines a non-Newtonian fluid model representing shear-thinning behaviour with applications in both biological and industrial fields. While prior research has investigated the fluid's dynamics in various contexts, the combined effects of the Williamson fluid model and additional parameters remain underexplored. This work focuses on the analysis of magnetohydrodynamic Williamson-nanofluid flow over an exponentially stretched surface. To solve the transformed model equations, an advanced numerical approach, the overlapping multi-domain paired quasilinearization method (OMD-PQLM), is employed. This method enhances the traditional paired quasilinearization method (PQLM) by subdividing the integration interval with overlapping techniques, enabling efficient and accurate solutions to the nonlinear ODEs. Key parameters studied include the Hall parameter, chemical reaction parameter, thermophoresis particle parameter, Brownian motion parameter, and magnetic parameter. Notably, the Williamson parameter significantly affects velocity profiles, temperature distribution, and concentration, with its shear-thinning properties altering flow characteristics and leading to higher temperature and concentration distributions. The OMD-PQLM demonstrated superior accuracy compared to the standard PQLM. This comprehensive analysis provides valuable insights into the OMD-PQLM’s effectiveness and the behaviour of Williamson-nanofluid systems under various conditions, contributing to advancements in nanofluid applications, air conditioning, cooling processes, and thermal energy storage.