Using a one-dimensional hierarchical model based on the Cosserat theory approach to fluid dynamics we can reduce the full 3D system of equations for the axisymmetric unsteady motion of a non-Newtonian incompressible second-grade viscous fluid to a system of equations depending on time and on a single spatial variable. From this new system we obtain the steady relationship between average pressure gradient and volume flow rate over a finite section of a straight constricted tube, and the corresponding equation for the wall shear stress.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-6,
author = {Fernando Carapau and Ad\'elia Sequeira},
title = {1D dynamics of a second-grade viscous fluid in a constricted tube},
journal = {Banach Center Publications},
volume = {83},
year = {2008},
pages = {95-103},
zbl = {1148.76002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-6}
}
Fernando Carapau; Adélia Sequeira. 1D dynamics of a second-grade viscous fluid in a constricted tube. Banach Center Publications, Tome 83 (2008) pp. 95-103. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-6/