Application of the Lambert W function to steady shearing flows of the Papanastasiou model

You, Z; Huilgol, RR; Mitsoulis, E

dc.contributor.author	You, Z	en
dc.contributor.author	Huilgol, RR	en
dc.contributor.author	Mitsoulis, E	en
dc.date.accessioned	2014-03-01T01:27:56Z
dc.date.available	2014-03-01T01:27:56Z
dc.date.issued	2008	en
dc.identifier.issn	0020-7225	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/18645
dc.subject	Analytical solution	en
dc.subject	Lambert W function	en
dc.subject	Papanastasiou model	en
dc.subject	Steady shearing flow	en
dc.subject.classification	Engineering, Multidisciplinary	en
dc.subject.other	Channel flow	en
dc.subject.other	Mathematical models	en
dc.subject.other	Numerical methods	en
dc.subject.other	Steady flow	en
dc.subject.other	Stress analysis	en
dc.subject.other	Tensors	en
dc.subject.other	Lambert W functions	en
dc.subject.other	Papanastasiou models	en
dc.subject.other	Steady shearing flow	en
dc.subject.other	Stress tensors	en
dc.subject.other	Shear flow	en
dc.title	Application of the Lambert W function to steady shearing flows of the Papanastasiou model	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.ijengsci.2008.02.002	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.ijengsci.2008.02.002	en
heal.language	English	en
heal.publicationDate	2008	en
heal.abstract	Using the Lambert W function, the constitutive relation of the Papanastasiou model is inverted so that the second invariant of the first Rivlin-Ericksen tensor can be expressed as a function of the second invariant of the extra stress tensor. In steady shearing flows, this results in the magnitude of the shear rate becoming a function of the magnitude of the shear stress. Since the distribution of the latter is known explicitly in channel, Poiseuille and Couette flows, one can investigate the nature of analytical solutions in these flows. It is shown that explicit answers are found for channel and Poiseuille flows only, with the Couette flow requiring a numerical solution in general. From the channel flow results, it is obvious that there is a great amount of congruence between the predictions of the Papanastasiou model and the Bingham fluid. In turn, this lends further confidence to the application of the Papanastasiou model to study the flows of Bingham fluids. (C) 2008 Elsevier Ltd. All rights reserved.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	International Journal of Engineering Science	en
dc.identifier.doi	10.1016/j.ijengsci.2008.02.002	en
dc.identifier.isi	ISI:000257612200005	en
dc.identifier.volume	46	en
dc.identifier.issue	8	en
dc.identifier.spage	799	en
dc.identifier.epage	808	en