A general theorem concerning the stability of a particular non-Newtonian fluid
Author:
Samuel M. Genensky
Journal:
Quart. Appl. Math. 18 (1960), 245-250
MSC:
Primary 76.00
DOI:
https://doi.org/10.1090/qam/114478
MathSciNet review:
114478
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: It is the intention of the present paper to prove a theorem concerning the stability of a particular non-Newtonian fluid suggested to the author by Professor R. S. Rivlin of Brown University. The method used in proving this theorem is similar to that employed by H. Schlichting in his proof of a similar theorem for an inviscid fluid which was originally established by Lord Rayleigh. The acceleration gradients introduced by the non-Newtonian fluid model into the constitutive equations are found to alter the stability criterion set forth by Rayleigh for an inviscid fluid.
- Lord Rayleigh, On the Stability or Instability of certain Fluid Motions, II, Proc. Lond. Math. Soc. 19 (1887/88), 67–74. MR 1576885, DOI https://doi.org/10.1112/plms/s1-19.1.67
- Hermann Schlichting, Boundary layer theory, McGraw-Hill, New York; Pergamon Press, London; Verlag G. Braun, Karlsruhe, 1955. Translated by J. Kestin. MR 0076530
- R. S. Rivlin, Further remarks on the stress-deformation relations for isotropic materials, J. Rational Mech. Anal. 4 (1955), 681–702. MR 71980, DOI https://doi.org/10.1512/iumj.1955.4.54025
- R. S. Rivlin, Solution of some problems in the exact theory of visco-elasticity, J. Rational Mech. Anal. 5 (1956), 179–188. MR 75739, DOI https://doi.org/10.1512/iumj.1956.5.55004
Lord Rayleigh, On the stability or instability of certain fluid motions, I, Proc. Lond. Math. Soc. 9, 57–70 (1880); see also Scientific Papers 1, 474–487 (1899)
H. Schlichting, Boundary layer theory, translated by J. Kestin, McGraw-Hill, Inc., New York, 1955, pp. 314–323
R. S. Rivlin, Further remarks on the stress—deformation relations for isotropic materials, J. Ratl. Mech. and Anal. 4, 681–702 (1955)
R. S. Rivlin, Solutions of some problems in the exact theory of visco-elasticity, J. Ratl. Mech. and Anal. 5, 179–188 (1956)
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
76.00
Retrieve articles in all journals
with MSC:
76.00
Additional Information
Article copyright:
© Copyright 1960
American Mathematical Society