Journal Article10.1108/HFF-09-2015-0368
A short remark on Chien’s variational principle of maximum power losses for viscous fluids
Hongyan Liu,Na Si,Ji-Huan He +2 more
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TL;DR: In this article, an approximate variational principle of minimum power loses is established, which agrees with the Helmholtz's principle, and the paradox is solved, which can be directly used for numerical methods and analytical analysis.
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Abstract: Purpose – The purpose of this paper is to point out a paradox in variational theory for viscous flows. Chien (1984) claimed that a variational principle of maximum power loses for viscous fluids was established, however, it violated the well-known Helmholtz’s principle. Design/methodology/approach – Restricted variables are introduced in the derivation, the first order and the second order of variation of the restricted variables are zero. Findings – An approximate variational principle of minimum power loses is established, which agrees with the Helmholtz’s principle, and the paradox is solved. Research limitations/implications – This paper focusses on incompressible viscose flows, and the theory can be extended to compressible one and other viscose flows. It is still difficult to obtain a variational formulation for Navier-Stokes equations. Practical implications – The variational principle of minimum power loses can be directly used for numerical methods and analytical analysis. Originality/value – It ...
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On the semi-inverse method and variational principle
Xue-Wei Li,Ya Li,He Ji-Huan +2 more
TL;DR: In this article, Liu et al. proved the equivalence between He-Lee 2009 and the generalized variational principle and that by Tao and Chen (Tao, Z. L., Chen, G. H., 2013) for one dimensional heat conduction.
A constrained variational principle for heat conduction
Ji-Huan He,Eric Wai Ming Lee +1 more
TL;DR: In this article, a variational principle for the heat conduction was obtained by the semi-inverse method, which was first appeared in the literature in the early nineties.
22
Variational principles and generalized variational principles in hydrodynamics of viscous fluids
钱伟长,Chien Wei-zang +1 more
TL;DR: In this paper, the variational principles of hydrodynamic problems for the incompressible and compressible viscous fluids are established, which are principles of maximum power losses, and they are also discussed on the basis of Lagrangian multiplier methods.
16
Remark on a constrained variational principle for heat conduction
Zhao-Ling Tao,Guo-Hua Chen +1 more
TL;DR: In this paper, the heat conduction equation was re-studied by the semi-inverse method combined with separation of variables; a new variational principle for the Heat Conduction equation is obtained.