The focus of this study revolves around the dynamics of MHD hybrid nanofluid flow and heat transfer on a contracting plate embedded in porous media, accounting for Darcy slip and thermal radiation effects. The investigation employs a blend of copper (Cu) and aluminum oxide (Al2 O3) nanoparticles suspended in water (H2O) as the fundamental working fluid. By employing mathematical transformations, the complex partial differential equations are transformed into a set of ordinary differential equations (ODEs). These ODEs are subsequently solved numerically using the function-bvp4c within the MATLAB software tool, exploring multiple scenarios across various key parameters. This analysis carries significant importance as it sheds light on the thermal behaviour of the Cu- Al2 O3/ H2O nanofluid mixture under the influence of crucial physical parameters with magnetic field M, heat generation parameter β, velocity slip parameter A, thermal radiation parameter R, thermal slip parameter B, porosity parameter P, and suction parameter S. The research outcomes are both contemporary and pioneering, offering a wealth of practical applications within modern industries.