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Summer Program Seminars 2006


Thursday, May 25, 2006 @ 10:00AM
Cullimore Hall, Room 611
New Jersey Institute of Technology

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Flow in Pulsating Channels in the Presence of a Horizontal Pressure Gradient



Leo Espin

Department of Mathematical Sciences

New Jersey Institute of Technology

Newark, New Jersey


 

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ABSTRACT

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We study the two-dimensional flow between parallel plane walls that is produced by oscillatory displacement of one of the walls when a pressure gradient tangent to the stationary wall provides a net flow.  We consider solutions of the Navier-Stokes equations for this configuration which are exact in the sense that they can be described by solutions of one-dimensional partial differential equations.  The limit of small Reynolds number is solved analytically while the problem for order one Reynolds numbers is solved numerically.  Numerical results are presented for a range of Reynolds numbers.  The exact solution is a consequence of a stagnation-type flow and a decoupling between the vertical and horizontal components of velocity.  It has been shown in previous work that the oscillatory flow can become chaotic, for example, and in such situations the through flow due to the pressure gradient is forced by aperiodic coefficients.  In the special case of time-periodic solutions, the horizontal velocity is governed by a partial differential equation with periodic coefficients.