The current study investigates heat transfer enhancement due to the radiative magnetohydrodynamics (MHD) flow of a hybrid nanofluid (Formula presented.) past a porous stretching cylinder under the influence of variable viscosity as well as suction. The nonlinear partial differential equations governing the proposed physical model are transformed into nonlinear ordinary differential equations by applying suitable similarity transformation. The scaled-down system is solved numerically by the fourth-order Runge–Kutta method along with shooting technique for the achievement of asymptotic boundary condition. The velocity and temperature profiles are obtained for various physical factors of the problem, namely, magnetic interaction factor (Formula presented.), Reynolds number (Formula presented.), volume fraction factor of copper (Formula presented.), variable viscosity (Formula presented.), and radiation factor (Formula presented.), together with suction (Formula presented.), by fixing the Prandtl number of the core fluid (ethylene glycol) constant at 25.825. The numerical values of skin friction and the rate of heat transfer are obtained and tabulated. To validate the proposed physical model, numerical simulations are provided with comparison. The paper highlights the effects of physical factors, namely, radiation, variable viscosity, and suction parameters, on the flow of a hybrid nanoflluid for heat transfer enhancement. © 2021 Wiley Periodicals LLC