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Abstract : In this paper, we study the two-layered blood flow model within the framework of Lie symmetry analysis to investigate a range of closed-form solutions. Our investigation involves optimal classification, revealing the existence of six optimal subalgebras within the model. Further, we streamline the model by reducing it into a system of ordinary differential equations (ODEs), thereby deriving several exact solutions. Our analysis establishes the presence of the nonlinear self-adjointness property in the governing equation, leading to the