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Hybrid nanofluids have been proposed as a new class of nanofluids, whose thermal properties and potential utility have been identified to serve the purpose of enhancing heat transfer rates. The main objective of the present analysis is to study the emerging unsteady hybrid nanofluid flows through porous medium with the impacts of melting temperature and slip velocity on the surface. Additionally, the heat transportation is analyzed with the presence of, thermal radiation, Joule heating and heat source/sink over a stretched/shrunk surface. Here two distinct nanoparticles (Cu- Al2O3) considered to examine the flow field over the shrinking/stretching surface. The Navier-Stokes equations are used in the process of developing the mathematical model under the mentioned assumptions. By utilizing the suitable transformations, the modeled equations are converted into non-linear ordinary differential equations. The formulated mathematical differential system is solved numerically by bvp4c technique in MATLAB. Dual nature study is focused in which solid lines show the first solution and dash lines for the second solutions. The behavior of hybrid nanofluids in terms of velocity and temperature distribution have been visualized graphically. For better understanding of the flow features and heat transfer rate, variation in skin friction coefficients and the Nusselt number of hybrid nanofluids are closely examined. We find from the present study that the rate of heat transfer is enhanced in the hybrid nanofluids by the impact of melting temperature. Moreover, in the first solution, skin friction coefficient rises with the enlargement of magnetic field parameter while heat transfer rate reduces in this situation. Additionally, the velocity profile reduces by the influence of unsteadiness parameter in the first solution while rises in the second solution. The heat transfer process at the surface is improved when a stronger Melting temperature is taken into account.