This study investigates the heat transport mechanisms and irreversibility in Power-Law fluid dynamics through converging/diverging channels with heat source/sink and radiative effects. Entropy generation (EG) analysis is employed to identify the mechanisms responsible for inefficiencies and irreversibility in the system, which conventional energy analysis cannot capture. The governing flow equations are formulated using the principles of conservation for the Carreau liquid model, while the EG equation is derived based on the second law of thermodynamics. To enhance the originality of the model, a new approach is introduced that incorporates the Jaffrey-Hamel flow alongside the Buongiorno model and viscous heat effects. This model is designed to investigate the flow of thermal radiation within a wedge-shaped channel. This theoretical investigation has practical implications for various industrial processes, including combustion and biofuel production, where minimizing the generation of entropy can enhance efficiency and productivity. The simulation is addressed using the spectral collocation method, facilitated via Mathematica 11.3 software. The results indicate that an increase in the power-law index leads to a reduction in both the Nusselt and Sherwood numbers, signifying diminished heat and mass transfer rates. Additionally, higher Weissenberg numbers contribute to a significant decrease in velocity distribution within a divergent channel, highlighting the role of viscoelastic effects in flow resistance. The study provides valuable insights into optimizing heat transport in industrial applications such as combustion chambers, biofuel processing, and polymer extrusion, where minimizing entropy generation can enhance system efficiency and energy conservation.