Theory of Minimum Dissipation Rate in Fluid Dynamics

DOI

10.2991/978-94-6463-316-0_24How to use a DOI?

Keywords

Theory of Minimum Rate of Energy Dissipation; Necessary and Sufficient Condition; Viscous Items; Inertia Items; Motion Equations

Abstract

The incompressible, viscous and steady fluid is studied basing the energy dissipation equation, motion equations, continuity equation and boundary conditions. It is proved that the necessary and sufficient condition of the energy rate obtaining the extreme value is the vorticity field meeting the harmonic equations. The vorticity field meeting the harmonic equations is equivalent to the viscous items with potential. The relationship between the energy rate and the motion equations has also been studied. For the real motion, the necessary and sufficient condition of the energy rate obtaining the extreme value is equivalent to the inertia items with potential. Finally, an example about the theory is given.

Copyright

© 2023 The Author(s)

Open Access

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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TY  - CONF
AU  - Hao Wu
AU  - Zhipei Zhang
PY  - 2023
DA  - 2023/12/14
TI  - Theory of Minimum Dissipation Rate in Fluid Dynamics
BT  - Proceedings of the 2023 5th International Conference on Civil Engineering, Environment Resources and Energy Materials (CCESEM 2023)
PB  - Atlantis Press
SP  - 219
EP  - 235
SN  - 2352-5401
UR  - https://doi.org/10.2991/978-94-6463-316-0_24
DO  - 10.2991/978-94-6463-316-0_24
ID  - Wu2023
ER  -