The boundary layer flow analysis of Williamson fluid moving on the stretched cylinder has applications in the polymer processing, drug delivery system, cooling systems, rheology of food products, dyeing, and finishing. The numerical solutions of governing Navier-Stokes equations at different scenarios of thermal and solutal aspects have lots of practical implications, including biomedical engineering, cooling and heating processes, chemical reactors, aerodynamics, environmental science, and thermal storage systems. From these practical applications, the authors were motivated to conduct a study in which the numerical behavior is examined by applying the Adams-Bashforth predictor and corrector approach of numerical analysis for the Williamson fluid model in the presence of varying viscosity, natural convection, and the inclined magnetic field. Furthermore, Joule heating, thermal radiation, and heat source/sink effects are included in the thermal aspects because these are the important concepts in thermal management and engineering and have applications in solar thermal energy systems, combustion engines, heat exchangers, nuclear reactors, thermal imaging, and safety. Apart from thermal aspects, the analysis of mass transfer focuses on the influence of chemical reactions and Soret-Dufour effects. The similarity transformations are adopted to convert partial differential equations into ordinary differential equations. Specifically, the well-known predictor and corrector numerical method named the Adams-Bashforth method in combination with the Runge-Kutta 4th order scheme is used to achieve the numerical solutions. The temperature, concentration, and velocity regions are displayed on the graphical and numerical conducts. A comparison is also made between the results obtained by the shooting method and the numerical findings of skin friction, Nusselt number, and Sherwood number determined by the Adams-Bashforth method. The determining results concluded that the restrictions in the flow of Williamson fluid are caused by variations in the inclination magnetic field, the surface curvature, and the Williamson parameter, whereas the motion of the fluid increases due to convection, which occurs due to thermal phenomena. The determined results indicate that the temperature distribution is enhanced due to the addition of thermal radiation, Eckert number, and magnetic field. The surface curvature, Soret number, and reaction coefficient marks the decrease impact on the concentration region. The temperature-dependent viscosity increases the drag force and friction coefficient. The Nusselt number is amplified by applying thermal radiation to the surface of the cylinder. The chemical reaction is the source of the increment in the Sherwood number.
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