caa a22 4500 60616717X CHVBK 20210128100701.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s10665-014-9714-5 doi (NATIONALLICENCE)springer-10.1007/s10665-014-9714-5 Weidman Patrick Department of Mechanical Engineering, University of Colorado, 80309-0427, Boulder, CO, USA aut Motion induced between parallel plates with offset centers of radial stretching and shrinking [Elektronische Daten] [Patrick Weidman] The flow between parallel plates separated by distance $$h$$ h is investigated where the upper plate radially stretches at a rate $$a$$ a , the lower plate radially shrinks at the same rate, and the centers of stretching and shrinking are horizontally separated by a distance $${2\,l}$$ 2 l . A reduction of the Navier-Stokes equation yields two ordinary differential equations dependent on a Reynolds number $$R = ah^2/\nu $$ R = a h 2 / ν . In addition, a free parameter $$\gamma $$ γ appears that corresponds to a uniform pressure gradient acting along the line connecting the stretching/shrinking centers. We consider three cases: $$\gamma = 0$$ γ = 0 , $$\gamma = O(1)$$ γ = O ( 1 ) , and $$\gamma = O(R)$$ γ = O ( R ) . The flow is described by two functions of the plate-normal coordinate $$\eta = z/h$$ η = z / h : the first $$f(\eta )$$ f ( η ) has an analytical solution, whereas the second $$g(\eta )$$ g ( η ) must be solved numerically. Small- $$R$$ R solutions are found, and large- $$R$$ R asymptotic behaviors of the wall shear stresses and the centerline velocities are obtained by matching the viscous boundary-layer flows to the interior inviscid motion. Springer Science+Business Media Dordrecht, 2014 Boundary-layer flow nationallicence Matched asymptotic expansions nationallicence Stretching/shrinking nationallicence Journal of Engineering Mathematics Springer Netherlands 90/1(2015-02-01), 195-209 0022-0833 90:1<195 2015 90 10665 https://doi.org/10.1007/s10665-014-9714-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10665-014-9714-5 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Weidman Patrick Department of Mechanical Engineering, University of Colorado, 80309-0427, Boulder, CO, USA aut NATIONALLICENCE 773 0- Journal of Engineering Mathematics Springer Netherlands 90/1(2015-02-01), 195-209 0022-0833 90:1<195 2015 90 10665