Due to their widespread use in engineering, hybrid nanofluids have been the primary focus of mathematical and physical research. Only the improvement of hybrid nanofluids’ variable heat conductivity and viscosity has been considered so far. Hybrid nanofluid flow across an inclined cylinder has many potential uses, including heat transfer and cooling in electrical devices, energy storage, refrigerants, and the automobile industry. Examining the effects of buoyant force, variable viscosity, variable thermal conductivity, mass suction, convective thermal conditions, and a magnetic field on the stagnation point flow of a Al2O3–Cu/H2O hybrid nanofluid in an inclined cylinder is our objective in this work. In order to find solutions to boundary-condition flow-describing partial differential equations, we turn them into ordinary differential equations using similarity transformations. We achieve this by employing a numerical strategy known as the fourth-order Runge–Kutta technique, which incorporates shooting techniques. A graphical representation of the findings emphasizes the influence of many physical parameters on flow dynamics. In addition, we address the influence of drag force and rate of heat transfer on various elements, such as the Biot parameter, magnetic variable, viscosity variable, and thermal conductivity variable. The mixed convection and magnetic parameters cause the velocity profile to rise while the temperature profile falls. The research’s results elucidate the cause behind the rise in thermal contour of hybrid nanofluids, which is seen when there is an increment in thermal conductivity, radiation parameter, and Biot number. The heat transfer rate exhibits a significant increase of 36.87% in the aiding flow scenario when a 2.0 mass suction is applied in conjunction with a 0.01 hybrid nanofluid, as compared to the conventional fluid. In the scenario of opposing flow, the heat transfer rate exhibits a significant increase of 36.96% when compared to that of ordinary fluid. Heat transfer increases 43.00% when Rd increases from 0.1 to 0.5 for both assisting and opposing flow.