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The discovery of hybrid carbon nanotubes shows the tendency toward the improvement of heat transfer performance in comparison to various classical fluids. This paper expands the novelty in utilizing the hybrid carbon nanotubes over vertical stretching/shrinking cylinder in presence of hydromagnetic and thermal radiation. It is essential to analyze the hydromagnetic due to its high potential capability especially in drug and gene release, hyperthermia effects as well as cell separation and manipulation in bio-medical field. The investigation on thermal radiation effect is added in this current study as it enhances the rate of heat transfer. To initiate this problem, partial differential equations (PDE) for the hybrid nanofluid flow with relevant boundary conditions (BCs) is set up and transformed into an ordinary differential equation (ODE). Adopting the similarity solutions and numerically solved using bvp4c (MATLAB). Findings on the variation of local Nusselt number, skin friction coefficient, shear stress and local heat flux having the effects of magnetic, M ,   curvature, ϒ, thermal radiation, Nr, mixed convection parameter, λ as well as volume fraction of nanoparticles, φ are demonstrated and elaborated in detail. Moreover, the research reveals that duality of solutions occurs when the buoyance force is in opposing flow with respect to the fluid motion, λ < 0 , as well as shrinking area, ε < 0 . The occurrence of magnetic reduces the heat transfer as well as skin friction coefficient. In addition, the skin friction coefficient and local Nusselt number tend to improve as volume fraction of nanoparticles and curvature are increased. In contrast, the low of thermal radiation enhance the heat transfer. Indeed, the consequences of using hybrid carbon nanotubes help intensify the skin friction coefficient and Nusselt number compared to SWCNT nanofluid and MWCNT nanofluid. These crucial findings may benefit the scientists and academicians hence giving an add-on value to their expertise. A stability analysis must be performed since there exists a non-unique solution throughout the computation. [ABSTRACT FROM AUTHOR]