The nanoparticles migration from the conventional buongirnio model is useful in several industrial applications as well as engineering and biomedical. Even if the blood flows through artery, the drug delivery process, etc. are more recent phenomena that are beneficial for the use of nanoparticles in the conventional liquid. Based upon the characteristics, the present study reveals the flow of conducting Jeffery-Hamel nanofluid for the inclusion of KKL (Koo- Kleinstreuer-Li) model conductivity within a stretching/shrinking channel surface as well as channel angle. Additionally, influence of dissipative for the interaction of both Joule and viscous and the radiative heat enrich the profiles significantly. The water-based nanoliquid is immersed with the CuO nanoparticle enhances the flow properties like thermal conductivity, viscosity, etc. Numerical treatment is adopted with the help of shooting based Runge-Kutta to carry forward the solutions for the flow profiles. The heat transfer rate as well as shear rate is deployed for the various parameters and analyzed their behaviors briefly.