In this article, the behavior of Maxwell nanofluid flow over a stretchable cylinder is investigated. The nanofluid under study is synthesized by integrating single-walled carbon nanotubes and multi-walled carbon nanotubes into sodium alginate as the base fluid. The effects of thermal radiation, external magnetic field, and viscous dissipation on the fluid flow are considered to enhance the heat transfer efficiency. The governing set of partial differential equations is modeled and subsequently transformed into a set of ordinary differential equations using appropriate similarity transformations. The resulting equations are solved numerically using the Runge-Kutta-Fehlberg method in conjunction with the shooting procedure. Graphical simulations are utilized to illustrate the influence of various key parameters on the relevant physical quantities. The temperature profiles amplify with a rise in the Eckert number, curvature, and radiation parameters but decline with increasing nanoparticle concentration, while engineering metrics, including the skin friction coefficient and local Nusselt number, are analyzed and tabulated to evaluate the performance characteristics of the nanofluid system. The skin friction coefficient increases with higher curvature, magnetic field strength, Maxwell fluid parameters, and nanoparticle concentration, while the Nusselt number decreases with rising Eckert number, nanoparticle concentration, and Maxwell fluid parameters.