<p>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<b>-</b> Kleinstreuer<b>-</b>Li) model conductivity within a stretching/shrinking channel surface as well as channel angle. Additionally, the influence of dissipative heat for the interaction of both Joule and viscous dissipation along with the radiative heat enrich the flow profiles significantly. The water-based nanoliquid is immersed with the CuO nanoparticles enhances the flow properties like thermal conductivity, viscosity, etc. Numerical treatment is adopted with the help of shooting based Runge-Kutta fourth-order to carry forward the solutions for various flow profiles. The heat transfer rate as well as rate of shear stress are deployed for the various parameters and analyzed their behaviors briefly. Further, the important outcomes are; the enhanced concentration of the proposed nanoparticles retards the rate of shear stress whereas the impact augments the heat transfer arte. Moreover, the dissipative heat conducted by the inclusion of the Eckert number augments the heat transport properties significantly.</p>