### Abstract

The flow between parallel plates separated by distance h is investigated where the upper and lower plates respectively stretch and shrink at the same rate a and the centers of stretching/shrinking are horizontally offset by distance 2l. A reduction of the Navier-Stokes equation yields two ordinary differential equations dependent on a Reynolds number R=ah2/ν and a free parameter γ measuring the strength of a uniform pressure gradient acting along the line connecting the stretching/shrinking centers. The flow is described by two functions of the plate-normal coordinate η=z/h: the first f(η) has an analytical solution while the second g(η) must be resolved numerically. Three cases are considered: γ=0, γ=O(1) and γ=O(R). The small-R solutions and the large-R asymptotic behaviors of the wall shear stresses are found. Analytical results presented in graphical form are compared with corresponding asymptotic behaviors.

Date

Oct 28, 2014 3:30 PM — 4:30 PM

Location

Bechtel Collaboratory, Discovery Learning Center

Engineering Center, University of Colorado at Boulder, Boulder, CO 80309

University of Colorado Boulder