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On the flow of a simple fluid in an orthogonal rheometer. (English) Zbl 0513.76002
MSC:
76A05Non-Newtonian fluids
References:
[1]Maxwell, B., &R. P. Chartoff, Studies of a polymer melt in an orthogonal rheometer.Trans. Soc. Rheol. 9, 41–52 (1965). · doi:10.1122/1.548979
[2]Blyler, L. L., & S. J. Kurtz, Analysis of the Maxwell orthogonal rheometer.J. Appl. Poly. Sci.,11, 127–131.
[3]Bird, R. B., &E. K. Harris, Analysis of steady state shearing and stress relaxation in the Maxwell orthogonal rheometer.A.I. Ch. E. Journ. 14, 758–761 (1968).
[4]Huilgol, R. R., On the properties of the motion with constant stretch history occurring in the Maxwell rheometer.Trans. Soc. Rheol. 13 513–526 (1969). · doi:10.1122/1.549140
[5]Kearsley, E. A., On the flow induced by a Maxwell-Chartoff rheometer.Jour. of Research of the Natl. Bureau of Standards 74c, 19–20 (1970).
[6]Abbot, T. N., &K. Walters, Rheometrical flow systems, Part 2. Theory for the orthogonal rheometer, including an exact solution of the Navier-Stokes equations.J. Fluid. Mech.,40, 205–213 (1970). · Zbl 0184.52102 · doi:10.1017/S0022112070000125
[7]Rajagopal, K. R., &A. S. Gupta, Flow and stability of a second grade fluid between two parallel plates rotating about non-coincident axes.Intl. J. Eng. Science,19, 1401–1409 (1981). · Zbl 0469.76003 · doi:10.1016/0020-7225(81)90037-9
[8]Rajagopal, K. R., The flow of a second order fluid between rotating parallel plates.J. of Non-Newtonian Fluid Mech.,9, 185–190 (1981). · Zbl 0476.76008 · doi:10.1016/0377-0257(87)87015-5
[9]Wang, C.-C., A representation theorem for the constitutive equation of a simple material in motions with constant stretch history.Arch. Rational Mech. Anal.,20, 329–340 (1965).
[10]Noll, W., Motions with constant stretch history.Arch. Rational Mech. Anal.,11, 97–105 (1962). · Zbl 0112.18301 · doi:10.1007/BF00253931
[11]Coleman, B. D., Substantially stagnant motions.Trans. Soc. Rheol.,6, 293–300 (1962). · doi:10.1122/1.548928
[12]Coleman, B. D., Kinematical concepts with applications in the mechanics and thermodynamics of incompressible viscoelastic fluids.Arch. Rational Mech. Anal.,9, 273–300 (1962).
[13]Huilgol, R. R., A class of motions with constant stretch history.Quart. of Appl. Mathematics,29, 1–15 (1971).
[14]Rivlin, R. S., &J. L. Ericksen, Stress-deformation relations for isotropic materials.J. Rational Mech. Anal.,4, 323–425 (1955).
[15]Truesdell, C., &W. Noll, The non-linear field theories of mechanics,Flügge’s Handbuch der Physik, III/3. Berlin-Heidelberg-New York, Springer (1965).
[16]Berker, R., A new solution of the Navier-Stokes equation for the motion of a fluid contained between two parallel planes rotating about the same axis.Archiwum Mechaniki Stosowanej,31, 265–280 (1979).
[17]Rajagopal, K. R., & A. S. Gupta, Flow and stability of second grade fluids between two parallel rotating plates.Archiwum Mechaniki Stosowanej, In Press.
[18]Berker, R., Intégration des équations du mouvement d’un fluide visqueux, incompressible,Handbuch der Physik, VIII/2, Berlin-Göttingen-Heidelberg (1963).
[19]Drouot, R., Sur un cas d’intégration des équations du mouvement d’un fluide incompressible du deuxième ordre,C. R. Acad. Sc. Paris, 265A, 300–304 (1967).
[20]Berker, R., An exact solution of the Navier-Stokes equation, the vortex with curvilinear axis,Intl. J. Eng. Science,20, 217–230 (1982). · Zbl 0487.76039 · doi:10.1016/0020-7225(82)90017-9