This study aims to examine the magnetized flow of (MoS2-TiO2-MgO\documentclass[12pt]{minimal}
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\begin{document}$$(Mo{S}_{2}-Ti{O}_{2}-MgO$$\end{document}/engine oil) ternary hybrid nanofluid flow over a circular cylinder, which is submerged in a stationary fluid. The flow being examined is represented mathematically in order to incorporate the influences of viscous dissipation, thermal radiations, and magnetic field. The mathematical model incorporates boundary layer system of momentum and energy equations, exploring non-similar phenomena arising from buoyancy forces and viscous dissipation. Using appropriate non-similar transformations, the governing system is converted into nonlinear partial differential equations (PDEs). The numerical method bvp4c, a built-in MATLAB package, is employed to simulate local non-similarity (LNS) equations up to the second truncation level. Numerous graphs and numerical tables expound on the physical properties of nanofluid temperature and velocity profiles. It is concluded that the velocity profile increases as the buoyancy parameter increases. On the other hand, the temperature profile noticeably rises when the radiation and the heat source factors are increased. The heat transmission rate has a decline when the assessments of the magnetic and Eckert numbers increase. The skin friction coefficient experiences an increase as the estimates of magnetic properties and nanoparticle value rise. The drag coefficients and estimated local Nusselt correlations for pertinent parameters are shown in the form of tables. There are several practical applications of the present work including biomedical engineering for tissue modeling and polymer processing optimization, enhanced tissue integration, pollutant dispersion and in building ventilation systems, medical imaging, thermal management in electronics.