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Simple oscillatory flows of fluids with general boundary conditions
 Košárková, Lenka ; Hron, Jaroslav (advisor) ; Průša, Vít (referee)
In mathematical models of a blood flow it is often a key role to choose appropriate boundary conditions imposed on the system of partial differential equations. Our aim is to investigate the oscillatory Hagen-Poiseuille flow in infinite pipe with Navier's slip condition on the boundary. Obtained velocity profiles can be then used as an inflow condition for numerical solutions of oscillatory flow in a finite pipe, where slip at the boundary is allowed. At first we recall the analytical solution for steady Hagen-Poiseuille flow in an infinite pipe with Navier's slip boundary condition. By replacing the constant pressure gradient with time periodic pressure gradient we get oscillatory Hagen-Poiseuille flow, where we derive in detail known analytical solution with respect to the no-slip boundary condition. Our contribution is in deriving analytical solution when considering the Navier's slip boundary condition, for which we show the velocity profiles and phase lag between the pressure gradient and the fluid's response. 1
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2 Košárková, Lucie
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