<p>This study presents a novel mathematical model for Sutterby nanofluid flow over a stretched sheet, uniquely integrating the combined effects of variable thermal conductivity, viscous dissipation, and nonlinear thermal radiation. The novelty of this work lies in the simultaneous consideration of these complex phenomena within the framework of a Sutterby nanofluid, a specific combination that has not been extensively studied previously. The model is motivated by applications in engineering and industrial processes where enhanced heat transfer is critical. We formulate the governing equations as partial differential equations incorporating the nanofluid properties and boundary conditions. Applying appropriate similarity variables reduces the governing partial differential equations to a coupled system of nonlinear ordinary differential equations, which are solved numerically using the Chebyshev spectral collocation method due to its high accuracy for strongly nonlinear systems. A detailed convergence analysis is carried out to ensure the stability and reliability of the spectral solution, confirming the exponential rate of convergence characteristic of Chebyshev-based schemes. The impacts of key physical parameters that govern the mathematical model are presented in both tabular and graphical formats. Notable findings indicate that the velocity profile increases with the power-law index and the Deborah number, whereas the temperature and concentration profiles decrease. The applied magnetic field enhances the thermal and concentration fields while attenuating the velocity profile. The temperature of Sutterby nanofluid grows with a higher fluid conductivity parameter. The findings of this study were assessed against existing literature, showing strong consistency that substantiates the reliability of the present solutions. Consequently, the current model offers initial guidance for various biotechnological and industrial uses.</p>