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Variational principles in hydrodynamics of a non-Newtonian fluid

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Abstract

In this paper, the principle of maximum power losses for the incompressible viscous fluid proposed by professor Chien Weizang in reference [1] is further extended to the hydrodynamic problem of the non-Newtonian fluid with constitutive law expressed% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXgatC% vAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wDYLwzYbItLDharyavP1wz% ZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbb% L8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpe% pae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabeqaam% aaeaqbaaGcbaGaeqyTdu2aaSbaaSqaaeHbhv2BYDwAHbacgiGaa83-% aaqabaGccqGH9aqpcqGHciITcqaHepaDcqGGVaWlcqGHciITcuaHdp% WCgaqbamaaBaaaleaacaWF-daabeaaaaa!4B05!\[\varepsilon _\"y = \partial \tau /\partial \sigma '_\"y \]. The constraint conditions of variation are eliminated by the method of identified Lagrangian multiplier and a generalized variational principle is established.

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References

  1. Chien Weizang, Variational principles and generalized variational principles in hydrodynamics of viscous fluid.Applied Mathematics and Mechanics (English Ed.),5, 3 (1984), 1281.

    Article  MathSciNet  Google Scholar 

  2. C. C. Lin and L. Rubinov, On the flow behind curved shocks,J. Math. Physics,27 (1945), 105.

    MathSciNet  Google Scholar 

  3. V. I. Skobelkin, Variational principle in hydrodynamics,Soviet Physics-JEPT,4, 1 (1957), 68.

    MathSciNet  Google Scholar 

  4. K. G. Guderly, An extremum principle for three dimensional compressible inviscid flows,SIAN. J. Appl. Math.,23, 27 (1972), 259.

    Article  Google Scholar 

  5. A. R. Manwell, A variational principle of steady homogenetic compressible flow with finite shocks,Wave Motion,2 (1980) 83.

    Article  MATH  MathSciNet  Google Scholar 

  6. M. Hafez and D. Lowell Numerical solution of transonic stream function equation,AIAA Journal,21, 3 (1983).

  7. M. Shen and Q. R. Sun, Variational principle and generalized variational principle in hydrodynamics of a class of non-Newtonian fluid,Applied Mathematics and Mechanics (English Ed.),16, 4 (1995), 369.

    Article  MATH  MathSciNet  Google Scholar 

  8. M. J. Grochet, A. R. Davis and K. Walters,Numerical Simulation of Non-Newtonian Flow, Elsevier (1984).

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Communicated by Liu Yulu

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Min, S. Variational principles in hydrodynamics of a non-Newtonian fluid. Appl Math Mech 19, 963–969 (1998). https://doi.org/10.1007/BF02457956

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