This dissertation presents a theoretical investigation of magnetohydrodynamic (MHD) flow of non-Newtonian nanofluids over stretching surfaces, with particular focus on the combined effects of Hall currents and ion slip under strong magnetic fields. The study employs the Buongiorno nanofluid model to analyze four distinct non-Newtonian fluid types—Williamson, Casson, tangent hyperbolic, and Jeffrey fluids—incorporating key physical phenomena such as nonlinear thermal radiation, viscous dissipation, Joule heating, chemical reaction, and heat generation/absorption subject to porous medium. Using appropriate similarity transformations, the governing partial differential equations are converted into a system of nonlinear ordinary differential equations. These equations are solved numerically using a fifth-order and sixth-order Runge–Kutta method combined with the shooting technique, implemented in the Python programming language. To ensure the reliability of numerical solutions, the results are validated by comparing them with standard previously published studies under specific limiting conditions. The excellent agreement confirms the accuracy and robustness of the computational methods employed. The results are presented through detailed graphs and tables that illustrate the influence of various physical parameters on the velocity, temperature, and concentration profiles. In addition, important engineering quantities such as the skin friction coefficient, the Nusselt number, and the Sherwood number are evaluated and interpreted. The impact of each parameter is analyzed to provide a clear physical insight into how it affects the behavior of the fluid within the boundary layer. Among the various outcomes, the findings reveal that for all the considered fluid models, the Hall and ion slip parameters consistently enhance the principal (streamwise) velocity profiles within the boundary layer, indicating a reduction in the Lorentz-force resistance due to the modified current density. In contrast, these parameters exert a suppressive effect on both the temperature and the nanoparticle concentration distributions, leading to thinner thermal and concentration boundary layers. Furthermore, the nonlinear thermal radiation parameter demonstrates a positive influence by significantly increasing the fluid temperature and nanoparticle concentration, thereby intensifying the thermal transport and diffusion processes. Overall, the dissertation provides valuable contributions to the theoretical understanding of MHD non-Newtonian nanofluid flows and provides practical insight for engineering applications