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Correct Expression of the Material Derivative in Continuum Physics
Version 1
: Received: 1 March 2020 / Approved: 2 March 2020 / Online: 2 March 2020 (15:39:55 CET)
Version 2 : Received: 19 April 2020 / Approved: 22 April 2020 / Online: 22 April 2020 (09:51:56 CEST)
Version 3 : Received: 27 April 2020 / Approved: 28 April 2020 / Online: 28 April 2020 (09:40:46 CEST)
Version 4 : Received: 14 June 2020 / Approved: 15 June 2020 / Online: 15 June 2020 (09:55:06 CEST)
Version 2 : Received: 19 April 2020 / Approved: 22 April 2020 / Online: 22 April 2020 (09:51:56 CEST)
Version 3 : Received: 27 April 2020 / Approved: 28 April 2020 / Online: 28 April 2020 (09:40:46 CEST)
Version 4 : Received: 14 June 2020 / Approved: 15 June 2020 / Online: 15 June 2020 (09:55:06 CEST)
How to cite: Sun, B. Correct Expression of the Material Derivative in Continuum Physics. Preprints 2020, 2020030030. https://doi.org/10.20944/preprints202003.0030.v2 Sun, B. Correct Expression of the Material Derivative in Continuum Physics. Preprints 2020, 2020030030. https://doi.org/10.20944/preprints202003.0030.v2
Abstract
The material derivative is important in continuum physics. This Letter shows that the expression $\frac{d }{dt}=\frac{\partial }{\partial t}$+ (v • ∇), used in most literature and textbooks, is incorrect. The correct expression $ \frac{d (:)}{dt} = \frac{\partial }{\partial t}$(:) + v · [∇(:)] is formulated.
Keywords
material derivative; continuum physics
Subject
Physical Sciences, Fluids and Plasmas Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Commenter: Bohua Sun
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