Study of MHD Williamson fluid flow over a stretched cylinder with Hall, thermal dynamics, and chemical reactions effects

A comprehensive analysis is conducted on the magnetohydrodynamic (MHD) flow of a non-Newtonian Williamson fluid around a stretching cylinder, incorporating Hall current, heat generation, variable thermal conductivity, and convective boundary conditions in the presence of radial magnetic field. This study additionally examines the thermophoretic and Brownian motion characteristics with the selected non-Newtonian model. By employing appropriate physical assumptions, the problem is mathematically formulated as a system of nonlinear partial differential equations. To facilitate the analysis, these equations are further simplified by using the similarity transformations. The resulting equations are subsequently solved numerically utilizing the MATLAB bvp4c solver. The outcomes related to thermal, momentum, and mass transport are presented graphically, highlighting the influence of varying flow parameters. Additionally, key engineering quantities, such as the local skin friction coefficient, local Nusselt number, and Sherwood number, are summarized in a tabular format. The main findings of this study indicate that an increase in the Hall parameter enhances the momentum profiles, whereas the presence of a magnetic field parameter leads to a reduction in these profiles. Further, the thermophoretic parameter significantly enhances the distribution of heat and mass, whereas the Brownian motion parameter exhibits a counteractive effect, resulting in a reduction of mass distribution alongside an elevation in temperature. The skin friction coefficient is surged by \(0.43\% \) $0.43\%$ and dropped by \(11\%\) $11\%$ by increasing Hall parameter from 0.1 to 0.5 and the magnetic field parameter raised by 0.3 – 0.7, respectively. Also, comparative analysis is conducted between the MATLAB-derived results and previously published data. Moreover, this study has significant implications for heat and mass transfer in Williamson nanofluids, with potential applications in chemical reactors, pollution control, fuel cells, and solar stills.