AbstractThe complex heat transfer processes occurring in a magnetized water‐based hybrid nanofluid flowing past a stretching or shrinking wedge are investigated in this work. The research highlights the significant influence of the wedge angle on fluid flow patterns and temperature gradients, emphasizing how larger angles cause changes in pressure, flow separation, and temperature profiles. Additionally, the study emphasizes the importance of radiation effects near surfaces, where increased radiation often leads to cooling due to thermal energy emission. The findings have implications in industries such as aerospace, electronics, thermal management, and groundwater resources management where precise temperature control is critical for safe and efficient operations. The numerical method applied to solve the governing equations in the study is the fourth‐order Runge–Kutta technique with shooting technique. This method efficiently solves the boundary value problem by converting it into a system of first‐order initial value problems. Then shooting technique is used to solve the system, starting with an adequate initial guess. The study's results are presented in tabular and graphical forms, providing valuable insights into the complex fluid dynamics and thermal behavior in the given setting, enabling more informed decision‐making and optimization in relevant engineering applications. Increased radiation frequently results in a cooling effect owing to thermal energy output. Heat sinks/heat sources are crucial in temperature regulation and are effective in lowering temperatures via processes. We also emphasize the importance of radiation impacts near surfaces, where increased radiation frequently leads to cooling owing to thermal energy emission. The numerical values of skin friction and Nusselt number for various parameters in the cases of shrinking and stretching provide crucial insights into the heat transmission and frictional properties of the system under examination. These quantitative results contribute to a better understanding of the complex fluid dynamics and thermal behavior in the given setting, emphasizing the significance of the research findings.