Oscillating Pressure Gradient-driven Unidirectional Viscous Flow in a 2D Channel
Journal Title: International Journal of Innovation in Science and Mathematics - Year 2018, Vol 6, Issue 2
Abstract
A unidirectional viscous flow in a two-dimensional channel is driven by an oscillating pressure gradient. The channel walls are at y = 0, 2h and the pressure gradient is –rho with respect to x = G*cos(sigma*t). We determine the velocity profile u(y,t) for the streamwise flow and comment on how this changes in character as the frequency varies. We show that the viscous shear stress on the lower wall, in the high frequency limit, is out of phase by pi over 4 compared to the pressure gradient. As the problem is linear, the flow has the same frequency as the pressure gradient; so, u can be written as Re{q(y) exp (i*sigma*t)} for some function q(y), which can be separated into real and imaginary parts.
Authors and Affiliations
Steve Anglin
Keywords
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