MHD hybrid nanofluids and power law heat flux past a permeable surface with Joule heating impact

Heat transfer is frequently employed in various industrial processes such as paper production, electronic device cooling, and the synthesis of new materials. Hence, this study aims to investigate the effect of Joule heating and magnetohydrodynamics (MHD) on the flow of a hybrid nanofluid with a power law heat flux past a shrinking sheet. The transformed governing equations are solved numerically using MATLAB's bvp4c solver, and the results are validated against previously published data, showing excellent agreement (error < 0.01%), confirming the model's accuracy. The analysis reveals that an increase in the magnetic parameter from 0.0 to 0.2 results in an increase of approximately 10.4% in the skin friction coefficient, while the local Nusselt number increases by about 18.8%, indicating that the magnetic field strengthens shear stress and enhances heat transfer. Meanwhile, the Joule heating parameter elevates the temperature gradient within the boundary layer, reducing the heat transfer rate, whereas the suction parameter enhances both the momentum and thermal gradients near the surface, improving surface heat transfer efficiency. Stability analysis confirms that only the first solution is physically stable. These findings demonstrate that coupling MHD and Joule heating effects in hybrid nanofluids enhances thermal regulation and provides significant potential for advanced cooling and manufacturing applications.