The central focus of this study is to explore the implications of magnetohydrodynamics on the heat transfer characteristics of Casson and Carreau fluids flowing through a porous medium along a stretching sheet. The influence of variable thermal conductivity and suction/injection parameters is also considered. Employing similarity transformations, the governing equations of magnetohydrodynamics for the Casson and Carreau fluid models are transformed into dimensionless nonlinear ordinary differential equations. The study examines velocity, concentration, and temperature profiles, as well as surface drag, Nusselt number, and Sherwood number, considering a range of flow parameters. The findings are presented through visual plots and tables. The fluid flow behavior is analyzed for various suction and injection scenarios. Analysis reveals that the velocity profile diminishes with an increase in the magnetic parameter, while the reverse trend is observed for rising Weissenberg numbers in both suction and injection cases.