In this study, the dual solutions of two-dimensional hybrid nanofluid flow and heat transfer past a porous medium permeable shrinking sheet with influence of heat generation/absorption and convective boundary condition were examined using the bvp4c solver with the MATLAB computational framework. The utilization of two-dimensional hybrid nanofluid flow and heat transfer in the presence of a porous medium permeable shrinking sheet, considering the effects of heat generation/absorption and convective boundary conditions, has wide-ranging applications in industries such as cooling systems, aerospace, chemical engineering, biomedical applications, energy systems, microfluidics, automotive thermal management, industrial drying, and nuclear reactor cooling, etc. These applications employ the improved thermal characteristics of hybrid nanofluids and the efficient heat control offered by porous media and convective boundary conditions. The governing partial differential equations (PDEs) are transformed into a collection of higher-order ordinary differential equations (ODEs) together with their corresponding boundary conditions. These equations are subsequently shown both numerically and graphically. The main objective of this inquiry is to examine the relationship between the solid volume fraction of copper and the permeability parameter of the porous medium, specifically focusing on the values of f''(0) and - (0) according to the suction effect. The current research has also integrated the temperature and velocity profile of a hybrid nanofluid flow, which corresponds to the influence of porous medium permeability, heat generation/absorption, and convective boundary condition. Dual solutions are acquired by certain combinations of parameters. Non unique solutions are obtained when the critical point reaches , for suction effects. Increasing the intensity of heat generation absorption and convective boundary condition leads to a more pronounced temperature profile and thicker boundary layer.
