| Summary: | This study focuses on analyzing the behavior of a time-varying magnetohydrodynamic (MHD) Williamson nanofluid (WNF) flowing over a stretched plate. The main objective is to understand the heat and mass transport properties of the nanofluid in this scenario. The mathematical model involves a system of partial differential equations (PDEs) that are transformed into a set of ordinary differential equations (ODEs) using a similarity transformation. These ODEs are then solved using the well-established MATLAB BVP4C technique; a part of the finite difference method. To ensure the reliability and accuracy of the approach, the obtained results are compared with previously published literature, serving as a validation step. The numerical findings are presented graphically and in tabular form. The study focuses on examining the impact of various external factors on the friction factor, Nusselt number, and Sherwood number, providing a comprehensive evaluation of heat transfer and mass transport characteristics. Specifically, the study investigates the flow and heat transfer properties near a stretched plate with a permeable layer. Also, takes into account the transverse dispersion, and heat generation effects in MHD WNF moreover with magnetic field and slip boundary conditions. The results of the study indicate that increasing the Brownian motion parameter (Nb) and Thermophoresis parameter (Nt) leads to higher local Nusselt numbers, reflecting the increased rates of transferring the heat. Similarly, an increase in the Nt is associated with higher local Sherwood numbers, indicating enhanced mass transport. Conversely, higher values of the Brownian motion parameter (Nb) result in lower local Sherwood numbers. By analyzing the influence of various external factors, such as nanofluid properties and magnetic fields, a better understanding of heat transfer and mass transport characteristics can be obtained.
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