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AbstractIn the present work, the author used a multistep numerical approach, namely the Milne (Predictor and Corrector) method with the Runge-Kutta method, to discuss the synergistic impacts of magnetohydrodynamic (MHD) and stagnation point flow involving a tangent hyperbolic fluid on the surface of a stretched cylinder. The flow field study is constructed with the impact of heat source/sink, chemically reactive species, and the joule heating effect. The phenomenon of concentration and temperature stratification is also taken into account. The Soret and Dufour effects are used to determine the solutal and thermal performance. To create a mathematical model of a physical occurrence, momentum, energy, and concentration laws are employed. The appropriate transformations can be used to convert nonlinear partial differential equations into ordinary differential equations. The Milne (Predictor-Corrector) method along with the Runge-Kutta 4th order scheme is used to determine the numerical findings. The graphical and numerical findings are depicted to show how several parameters influence the respective fields. The finding indicates that the velocity of fluid reduces by making variation in the Hartmann number whereas the temperature region enhances due to Hartmann number. The movement of fluid increases when the stretching ratio parameter is higher but decreases when the Weissenberg number and curvature parameter are higher. The Soret number reduces the concentration region and Dufour number enhances the temperature profile. The temperature distribution rises with higher inputs of the heat source but declines for the heat sink constrain and thermal stratification coefficient. Similarly, the concentration region upsurges for the stretching ratio parameter, while it decreases for the chemical reaction rate and solutal stratification. [ABSTRACT FROM AUTHOR]