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Rheologica Acta
Published in: Rheologica Acta 7/2015

01-07-2015 | Letter to the Editor

Reply to “Comment on Sochi’s variational method for generalised Newtonian flow” by Pritchard and Corson

Author: Taha Sochi

Published in: Rheologica Acta | Issue 7/2015

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Excerpt

In a recent communication by Dr David Pritchard and Dr Lindsey T. Corson (henceforth PC) to be published in this Issue of Rheologica Acta, they criticized the use of the variational principle and the derived variational formulation to obtain flow relations for generalized Newtonian fluids (GNF) in circular pipes which was proposed by the author in a recent publication in Rheologica Acta (Sochi 2014a) (hereafter, we abbreviate this reference with RA). The criticism is mainly based on the variational formulation given by Eq. 9 of RA, i.e.
$$ \frac{\partial}{\partial r}\left( \upmu \frac{d\gamma}{dr} \right) = 0 $$
(1)
where r is the tube radius, μ is the generalized Newtonian viscosity and γ is the rate of strain. …
previous article Comment on Sochi’s variational method for generalised Newtonian flow

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Footnotes
1
We use G slightly differently from the one used by PC where our G, although still represents the magnitude of the pressure gradient, contains a dimensionless geometric factor. The purpose of this is to simplify the notation and to be more general by accommodating different geometries.
 
Literature
Arfken GB, Weber HJ (2005) Mathematical methods for physicists, 6th edn. Elsevier Academic Press
Sochi T (2014a) Using the Euler-Lagrange variational principle to obtain flow relations for generalized Newtonian fluids. Rheol Acta 53(1):15–22CrossRef
Sochi T (2014b) Further validation to the variational method to obtain flow relations for generalized Newtonian fluids. arXiv:1407.​1534
Sochi T (2014c) Variational approach for the flow of Ree-Eyring and Casson fluids in pipes. arXiv:1412.​6209
Sochi T (2015a) Variational approach for resolving the flow of generalized Newtonian fluids in circular pipes and plane slits. arXiv:1503.​01262
Sochi T (2015b) Analytical solutions for the flow of Carreau and Cross fluids in circular pipes and thin slits. arXiv:1502.​03314
Metadata
Title
Reply to “Comment on Sochi’s variational method for generalised Newtonian flow” by Pritchard and Corson
Author
Taha Sochi
Publication date
01-07-2015
Publisher
Springer Berlin Heidelberg
Published in
Rheologica Acta / Issue 7/2015
Print ISSN: 0035-4511
Electronic ISSN: 1435-1528
DOI
https://doi.org/10.1007/s00397-015-0859-6

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Letter to the Editor

Comment on Sochi’s variational method for generalised Newtonian flow

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