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1D dynamics of a second-grade viscous fluid in a constricted tube

Carapau, F.; Sequeira, Adélia

Banach Center Publ., Inst. Math, Polish Acad. Sc., 81 (2008), 95-103

Using a one-dimensional hierarchical model based on the Cosserat theory approach to fluid dynamics we can reduce the full 3D system of equations for the axisymmetric unsteady motion of a non-Newtonian incompressible second-grade viscous fluid, to a system of equations depending on time and on a single spatial variable. From this new system we obtain the steady relationship between average pressure gradient and volume flow rate over a finite section of a straight constricted tube, and the corresponding equation for the wall shear stress.