Purposeand Methodology: The heat transport investigation in non-Newtonian fluids suspended by distinct sort of nanoparticles is a rich motive in the present time. Therefore, inspired by the physical characteristics of base fluid and ternary nanoparticles (Al2O3-CuO-Cu), a comprehensive analysis conducted over a cylinder with wavy radius with special emphasis in Saddle and Nodal points. The key effects of dissipation, the first order thermal slip, surface convection and stretching/shrinking added in the model. The acquired model is then examined via RK-scheme and portrayed the results against the physical ranges of the parameters. Key findingsA comprehensive discussion of the results provided that the nanofluid velocity increased for higher Casson number (α=0.5,1.0,1.5,2.0) and is examined optimum for stretched cylinder surface. The higher viscous dissipation which results the effects of Eckert number (Ec=0.01,0.02,0.03,0.04), surface convection due to Biot number (B1=0.1,0.2,0.3,0.4) and the first order thermal slip (α1=0.1,0.3,0.5,0.7) are the key physical factors to acquire the favorable heat transfer amount for the practical interest. Further, the particles concentration in the range of 1%–6% is observed good to increase the heat transmission in ternary nanoliquid and the values of effective characteristics (dynamics viscosity and thermal conductivity) upsurges against the concentration factor up to 6%.