Managing heat transfer effectiveness in a Darcy medium with a vertically non-linear stretching surface through the flow of an electrically conductive non-Newtonian nanofluid

This study encapsulated the research methodology utilized in the flow behaviors of Williamson nanofluid and analyzed the associated mass heat transfer. The study concentrated on examining the magnetohydrodynamic behavior of nanofluids in the presence of heat generation effects and the inclusion of dissipative energy on a vertical nonlinear stretching surface submerged within a Darcy porous medium. The rationale for including variable viscosity and variable conductivity in this research was to precisely evaluate the mechanisms of heat and mass transfer, particularly with regard to the fluctuations in fluid properties. The objective was to enhance the understanding of how these varying properties impact the overall heat and mass transfer processes. The initial formulation of the phenomenon, initially presented as partial differential equations, was transformed into ordinary differential equations by employing appropriate dimensionless variables. The ultimate streamlined version of the model was then numerically solved utilizing the shooting method. By employing the numerical shooting method, we portrayed nanofluid patterns in velocity, temperature, and concentration fields, alongside essential parameters such as skin friction coefficient, Sherwood number, and Nusselt number. The significant key findings highlighted that both the porous parameter and the magnetic number increasingly affected temperature and concentration distributions. Additionally, increasing the thermophoresis parameter resulted in higher concentration and corresponding temperature levels. Graphical presentation and physical explanations were used for analysis, and the study's outcomes were compared to existing literature, affirming a strong agreement that validated the solutions.