Symmetry-based investigation of transport enhanced blood flow model

To study the blood flow circulation dynamics, the present work thoroughly investigates the one-dimensional blood flow and transport in arteries and veins. We construct the one-dimensional optimum subalgebra and provide exact solutions of the governing equations using Lie symmetry analysis. A systematic framework is developed to generate a network of nonlocally related partial differential equation systems. These systems, constructed from local conservation laws and symmetry-based approaches, yield nonlocal symmetries that are classified and applied to obtain further exact solutions. One such solution is used to study the evolution of weak discontinuity waves. The findings shed light on blood circulation dynamics and suggest potential uses in hemodynamic modeling and analysis.