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.
Similar content being viewed by others
References
Chien Weizang, Variational principles and generalized variational principles in hydrodynamics of viscous fluid.Applied Mathematics and Mechanics (English Ed.),5, 3 (1984), 1281.
C. C. Lin and L. Rubinov, On the flow behind curved shocks,J. Math. Physics,27 (1945), 105.
V. I. Skobelkin, Variational principle in hydrodynamics,Soviet Physics-JEPT,4, 1 (1957), 68.
K. G. Guderly, An extremum principle for three dimensional compressible inviscid flows,SIAN. J. Appl. Math.,23, 27 (1972), 259.
A. R. Manwell, A variational principle of steady homogenetic compressible flow with finite shocks,Wave Motion,2 (1980) 83.
M. Hafez and D. Lowell Numerical solution of transonic stream function equation,AIAA Journal,21, 3 (1983).
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.
M. J. Grochet, A. R. Davis and K. Walters,Numerical Simulation of Non-Newtonian Flow, Elsevier (1984).
Author information
Authors and Affiliations
Additional information
Communicated by Liu Yulu
Rights and permissions
About this article
Cite this article
Min, S. Variational principles in hydrodynamics of a non-Newtonian fluid. Appl Math Mech 19, 963–969 (1998). https://doi.org/10.1007/BF02457956
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02457956