This article addresses the effects of thermal radiation, stratification, and Joule heating for the flow of magnetohydrodynamics Sutterby nanofluid past over a stretching cylinder. The transport phenomenon of heat and mass are modeled under temperature-dependent thermal conductivity and diffusion coefficients, respectively. Moreover, traditional Fourier and Fick's laws have been implemented in thermal and mass transport expressions. The governing model that consists of a set of coupled partial

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... fferential equations is converted into system of nonlinear coupled ordinary differential equations via suitable similarity transformations. The resulting set of expressions is analytically treated through an optimal homotopy scheme. The effects of different dimensionless flow parameters on the velocity, temperature, and concentration fields are illustrated through graphs. The patterns of skin friction coefficient, local Nusselt, and Sherwood numbers are examined via bar charts. The major outcome of the proposed study is that variable thermal conductivity decays the temperature and radiation raises the temperature of the system. Stratification parameters show the reverse behavior for temperature and concentration boundary layers. Shear rate-dependent rheology in view of Sutterby liquid has the ability to reduce the flow of fluid. Therefore, the ability of flow in rheology of Sutterby liquid becomes reduced. Consequently, layer of momentum boundary has increased with respect to parameter of Sutterby liquid.