The thermal aspects of Cu - A1203/water hybrid nanofluid in a porous medium across a vertically stretched cylinder with the incorporation of heat sink/source impact are investigated in this numerical study. A magnetic field along the transverse direction of the stretching cylinder and the thermal buoyancy effect is considered in the flow problem. A pertinent similarity variable has been employed to simplify the boundary layer equations which govern the flow and convert the coupled nonlinear partial differential equations into a set of non-linear ordinary differential equations. The numerical results are computed using the 3-stage Lobatto IIIa technique, Bvp4c. The impacts of non-dimensional parameters, including Prandtl number, heat source/sink parameter, magnetic parameter, porosity parameter, curvature parameter, thermal stratification parameter, and thermal buoyancy parameter on the velocity curve, thermal curve, skin-friction coefficient, and Nusselt number, are illustrated graphically and numerically portrayed in tables. The important results demonstrate that hybrid nanofluids are more thermally conductive than nanofluids. Therefore, the hybrid nanofluid has a considerable impact on improving thermal developments. It has been found that the absolute skin friction of the hybrid nanofluid is up to 31% higher compared to the nanofluid. The heat transport rate of the hybrid nanofluid is 7.5% enhanced in comparison to the nanofluid. The influence of heat stratification of the hybrid nanofluid flow is appreciably significant.