In this study, we will look at the analytical characterization of water and motor oil‐based nanofluid flow and the effects of viscous dissipation and variable viscosity on stretching surfaces. The primary goal of this research is to improve heat transfer efficiency in a range of systems, including cooling applications, refrigeration systems, and heat exchangers. The addition of nanoparticles to the base fluid increases its thermal conductivity, which boosts heat transfer rates. The flow system considers the impact of viscous dissipation. In addition, this methodology accounts for temperature and velocity slips during stretching. We utilized the proper transformations to convert a set of PDEs to NLODEs. To solve this system of equations, we use hybrid nanofluid. The impact of different parameters obtained from temperature and velocity equations involving the porosity parameter, power law number, ratio velocity, dynamic viscosity, Forchheimer parameter, and Eckert number input factors are shown in the form of graphs.