Successive Linearization Method Solutions of Radiative Hydrodynamic Williamson‐Nanofluid Flow Through a Porous Slender Cylinder: Thermal Diffusion and Diffusion Thermo Effects

ABSTRACT The combined effects of diffusion thermo and thermal diffusion on the behavior of Williamson fluid are the primary focus of this research. Magnetohydrodynamic (MHD) flow through a porous medium is examined, considering the effects of thermal radiation, thermophoresis, and Brownian motion. These interactions are significant in practical applications such as cooling systems, heat exchangers, chemical processing, porous media flows, biomedical transport, filtration, and aerospace thermal management. A transformation from fundamental governing PDEs to ordinary differential equations can be achieved through the application of similarity modifications. Solving the coupled nonlinear ordinary differential equations is accomplished using the successive linearization method (SLM). Comparing SLM to other research in the same area allows us to observe its efficacy. A comparison with SLM confirms the accuracy of the results. The impacts of various engineering parameters on concentration, temperature, and velocity profiles are discussed physically through graphs. The skin‐friction coefficient, Sherwood number, and Nusselt number can be more easily calculated with the use of multi‐factor tables. The study reveals that curvature enhances velocity, temperature, and concentration profiles, while the Williamson parameter reduces fluid velocity due to increased non‐Newtonian resistance. Thermal radiation, thermophoresis, and Dufour effects significantly improve heat transfer, whereas higher Prandtl number reduces thermal diffusion. Moreover, Soret and thermophoresis effects enhance mass transfer, while Brownian motion and chemical reaction reduce concentration levels.