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Computational intellectual analytical theory of computational analytical approach to rotating flow of non-Newtonian fluid

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Abstract

A combination of the computational symbolic calculation, mathematical approach and physico-mechanical model leads to a computational intellectual analytical approach developed by the author. There is a principal difference between the computer proof and the computer derivation completed by the computer, also difference between the numerical and symbolic calculations. In this investigation the computational analytical approach is extended, and an unsteady flow of non-Newtonian fluid in the gap between two rotating coaxial cylinders is studied. The Oldroyd fluid B model is used by which the Weissenberg effects are explained in a good comparison with the experiments. The governing equations are reduced to a partial differential equation of 3 rd order for the dimensionless velocity. Using the computer software Macsyma and an improved variational approach the problem with the intial and boundary conditions is then reduced to a problem of an ordinary differential equation for different approximations. The analytical solutions are given for the 1 st, 2 nd and 3 rd approximations. The present investigation shows the ability of the computational symbolic manipulation in solving the problems of non-Newtonian fluid flows. There is a possibility of that to solve the problems in mathematics and mechanics. An important conclusion can be drawn from the results that the transition from a steady state to another steady state is non-unique.

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References

  1. Han Shifang. A variational method for research on an unsteady flow of upper-convected Maxwell fluid[J].Acta Mathematica Scietia, 1992,12(2):519–525.

    Google Scholar 

  2. Han Shifang, Roesner K G. Time dependent flow of upper-convected Jeffrey fluid between two rotating cylinders[A]. In:Proc of XI Intern Congress on Rheology [C]. Brussels, 1992, 216–218.

  3. Han Shifang, Roesner K G. The time dependent flow of upper-convected Jeffrey fluid between coaxial cylinders[J].Computational Fluid Dynamics J, Japan, 1993,2(1):91–104.

    Google Scholar 

  4. Han Shifang, Roesner K G. Unsteady flow of polymer fluid between coaxial cylinders [J].J of Hydrodynamics, 1993, Ser B2(1):52–62.

    Google Scholar 

  5. Han Shifang. Computational simulation of non-Newtonian fluid flow[A]. In:Proc of First CFD Conference[C]. Hong Kong, 1995, 91–100.

  6. Han Shifang, About an application of computational analytical approach in mechanics of viscoelastic fluids [A].Proc of 3 rd National Conference on Rheology [C]. Invited Lecture. Shanghai: Press of Chemical University of East China, 1990. (in Chinese)

    Google Scholar 

  7. Han Shifang. Unsteady flow of non-Newtonian fluids-computational analytical intellectual theory [A].Proc of 4 th National Conference on Rheology [C]. Invited Lecture. Guangzhou: Press of South China University of Science and Technology, 1990. (in Chinese)

    Google Scholar 

  8. Han Shifang. Unsteady flows of Maxwell-Oldroyd fluid in tube[A]. In:Proc 4-th Asian Congress on Fluid Mech[C]. Hong Kong, 1989. 73–76.

  9. Han Shifang.Continuum Mechanics of Non-Newtonian Fluids [M]. Chengdu: Sichuan Press of Science and Technology, 1988. (in Chinese)

    Google Scholar 

  10. Han Shifang, et al. Non-steady flow of upper-convected Maxwell fluid in circular tube [J].Acta Mechanica Sinica, 1990,6(3):221–226.

    Google Scholar 

  11. Han Shifang, Ramkisson H. A variational analytical approach to time dependent flow of Oldroyd B fluid in circular tube [J].Applied Mathematics and Mechanics (English Ed), 1995,16(2):169–178.

    Article  Google Scholar 

  12. Han Shifang. Computational analytical approach in non-Newtonian fluid mechanics [J].Computer Application, 1993,13(4):19–21. (in Chinese)

    Google Scholar 

  13. Ramkissoon H, Han Shifang. Unsteady motion of a spehere in elastic-viscous fluid[J].Intern J Engng Sci, 1993,31(1):19–26.

    Article  MATH  Google Scholar 

  14. Roesner K G. The impact of computer algebra on fluid dynamics[A]. In:Proc 2 nd European Fluid Mechanics Conference General Review Lecture[C]. Warsaw: 1994, 10–14.

  15. Kantorovich L W, Krylov W I.Approximate Methods of Higher Analysis[M]. Interscience, New York: Elsevier, 1958, 256–258.

    Google Scholar 

  16. Gorla R S R, Modden P E. A variational approach to non-steady non-Newtonian flow in circular tube[J].J Non-Newtonian Fluid Mech, 1984,16(1):251–265.

    Article  MATH  Google Scholar 

  17. Ch Bodart, Crochet M J. Numerical study of the stability of viscoelastic flows[A]. In:Theoretical and Applied Rheology, Proc[C]. XI th Intern Congress on Rheology, 1992, 256–258.

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Authors and Affiliations

  1. Chengdu Branch, Academia Sinica, 610041, Chengdu, P R China

    Han Shifang

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  1. Han Shifang
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Communicated by Kang Zhenhuang

Foundation item: the National Natural Science Foundation of China (19672063); the Alexander von Humboldt Foundation in Germany

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Shifang, H. Computational intellectual analytical theory of computational analytical approach to rotating flow of non-Newtonian fluid. Appl Math Mech 20, 1237–1250 (1999). https://doi.org/10.1007/BF02463792

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  • DOI: https://doi.org/10.1007/BF02463792

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