Fluid dynamics of expanding and contracting tube: a case study of methods of series summation
نویسنده
چکیده
The fluid dynamics of expanding and contracting tube is investigated mathematically using both the Navier-Stokes and continuity equations for an incompressible viscous fluid. The problem admits similarity solution, thereby reducing the unsteady Navier-Stokes equations to a parameter dependent fourth order nonlinear ordinary differential equation. Analytical solutions are constructed for the problem using perturbation technique together with a new special type of Hermite-Padé approximants and important properties of the overall structure of the flow are discussed. The model is appropriate to simulate wind tunnel tests on rheological phenomenon in physiological systems.
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