This article focuses on the two-dimensional unsteady flow of an incompressible Casson nanofluid over a shrinking horizontal sheet under the influence of inclined magnetic field and in an advance dissipative heat due to Joule heating. The proposed Buongiorno model for the inclusion of Brownian and thermophoresis enriches the flow profiles. Casson model constituents a plastic fluid model that exhibits shear thinning characteristics and high shear viscosity. The proposed fluid model also approximates the rheological behavior of other liquids like physiological suspensions, cosmetics, syrups, etc. The governing partial differential equations (PDEs) that account for effect of Buongiorno model are converted in to nonlinear ordinary differential equations (ODEs) through suitable similarity variables. Further, approximate analytical technique such as Adomian Decomposition Method is beneficial to carry out the solution of the transformed governing equations and the significant nature of the contributing parameter for both the steady and unsteady case is presented via graphs. Moreover, the major contribution is; the Casson parameter along with suction/injection favors in the smooth enhancement in the velocity profiles and the fluid temperature also encouraged by the augmentation in Brownian and thermophoresis parameter.
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