caa a22 4500 605466599 CHVBK 20210128100307.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s00397-015-0863-x doi (NATIONALLICENCE)springer-10.1007/s00397-015-0863-x Sochi Taha Department of Physics & Astronomy, University College London, Gower Street, WC1E 6BT, London, UK aut Analytical solutions for the flow of Carreau and Cross fluids in circular pipes and thin slits [Elektronische Daten] [Taha Sochi] In this paper, analytical expressions correlating the volumetric flow rate to the pressure drop are derived for the flow of Carreau and Cross fluids through straight rigid circular uniform pipes and long thin uniform plane slits. The derivation is based on the application of Weissenberg-Rabinowitsch-Mooney-Schofield (WRMS) method to obtain flow solutions for generalized Newtonian fluids through pipes and our adaptation of this method to the flow through slits. The derived expressions are validated by comparing their solutions to the solutions obtained from direct numerical integration. They are also validated by comparison to the solutions obtained from the variational method which we proposed previously. In all the investigated cases, the three methods agree very well. The agreement with the variational method also lends more support to this method and to the variational principle which the method is based upon. We also compared the derived analytical solutions of Carreau and Cross fluids to the analytical solutions of power law fluids with comparable rheology and observed logical trends in the relation between the corresponding flow rates as a function of the applied pressure field. Springer-Verlag Berlin Heidelberg, 2015 Fluid mechanics nationallicence Rheology nationallicence Non-Newtonian fluids nationallicence Carreau nationallicence Cross nationallicence Power law nationallicence Pipe nationallicence Slit nationallicence Weissenberg-Rabinowitsch-Mooney-Schofield equation nationallicence Variational method nationallicence Rheologica Acta Springer Berlin Heidelberg 54/8(2015-08-01), 745-756 0035-4511 54:8<745 2015 54 397 https://doi.org/10.1007/s00397-015-0863-x 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/s00397-015-0863-x text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Sochi Taha Department of Physics & Astronomy, University College London, Gower Street, WC1E 6BT, London, UK aut NATIONALLICENCE 773 0- Rheologica Acta Springer Berlin Heidelberg 54/8(2015-08-01), 745-756 0035-4511 54:8<745 2015 54 397