Advancing heat transport in radiated Carreau–Yasuda non-Newtonian fluids under nonlinear stretching conditions and variable heat flux: A similarity solution approach

This paper investigates the steady two-dimensional flow and heat transfer characteristics of a non-Newtonian Carreau–Yasuda fluid induced by a nonlinearly stretching impermeable sheet under the combined impacts of thermal radiation, magnetic field, variable heat flux, viscous dissipation, and internal heat generation. The study introduces a nonlinear similarity transformation that converts the governing partial differential equations into a coupled system of ordinary differential equations. These equations are solved numerically using the shooting method, while the Homotopy Perturbation Method (HPM) is employed for validation. The comparison between both approaches confirms excellent consistency and reliability of the numerical results. The impact of key dimensionless parameters such as the magnetic field parameter, Eckert number, and heat generation factor are systematically examined. The results show that increasing the magnetic field parameter from 0.0 to 1.0 enhances the surface temperature by approximately 33.3%. Likewise, raising the Eckert number from 0.0 to 1.0 increases the thermal profile by 42.4%, while the internal heat generation parameter causes a significant rise of 48.5% in temperature over the same range. These trends highlight the pronounced thermal thickening effects of Lorentz forces, viscous dissipation, and volumetric heating. The Nusselt number and skin friction coefficient are presented in tabular form to illustrate the sensitivity of heat transfer and flow resistance to varying physical parameters. Overall, the agreement between numerical and semi-analytical results confirms the reliability of the model, which can be applied to practical systems such as polymer sheet extrusion and thermal management devices.