This article investigates the effects of radiation and heat transfer in the context of Magnetohydrodynamic (MHD) flow of a Carreau liquid over a non-linearly shrinking sheet, using a numerical approach. To tackle the problem, the governing partial differential equations (PDEs) are appropriately transformed into a set of ordinary differential equations (ODEs). These resulting non-linear ODEs are then solved numerically using the fourth-order Runge-Kutta (R-K) method, accompanied by the shooting technique to ensure accuracy and convergence. The study reveals various significant physical characteristics such as the Prandtl number, Weissenberg number, radiation parameter, heat source, and magnetic parameter, all of which play critical roles in influencing the flow and heat transfer behavior. These characteristics are analyzed and presented graphically, providing a clear understanding of how different physical parameters affect the MHD Carreau liquid flow. The findings offer valuable insights into the dynamics of such systems under varying physical conditions, contributing to the broader understanding of heat and mass transfer in complex fluids.
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