Stabilization of adiabatic Couette-Poiseuille flow by temperature dependent viscosity
Authors:
Moses A. Boudourides and Nicolas Ch. Charalambakis
Journal:
Quart. Appl. Math. 47 (1989), 747-751
MSC:
Primary 76E05
DOI:
https://doi.org/10.1090/qam/1031689
MathSciNet review:
MR1031689
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: We consider the adiabatic plane Couette-Poiseuille flow of a viscous incompressible fluid between two parallel planes driven by the shearing of the upper plane and a pressure gradient. The viscosity is assumed to depend on the temperature in an appropriate way to insure that every classical solution of the governing equations is asymptotically attracted by the steady Couette-Poiseuille flow profile with the temperature increasing unlimitedly. The proof is based on a priori estimates, obtained by the help of certain identities for solutions of the governing equations.
- G. K. Batchelor, An introduction to fluid dynamics, Second paperback edition, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1999. MR 1744638
- C. M. Dafermos, Stabilizing effects of dissipation, Equadiff 82 (Würzburg, 1982) Lecture Notes in Math., vol. 1017, Springer, Berlin, 1983, pp. 140–147. MR 726578, DOI https://doi.org/10.1007/BFb0103245
- C. M. Dafermos and L. Hsiao, Adiabatic shearing of incompressible fluids with temperature-dependent viscosity, Quart. Appl. Math. 41 (1983/84), no. 1, 45–58. MR 700660, DOI https://doi.org/10.1090/S0033-569X-1983-0700660-8
- A. E. Tzavaras, Effect of thermal softening in shearing of strain-rate dependent materials, Arch. Rational Mech. Anal. 99 (1987), no. 4, 349–374. MR 898715, DOI https://doi.org/10.1007/BF00282051
G. K. Batchelor, An Introduction to Fluid Dynamics, Cambridge University Press, London, 1970
C. M. Dafermos, Stabilizing effects of dissipation, Equadiff 82, Lecture Notes in Mathematics, vol. 1017, H. W. Knobloch and K. Schmitt (eds.), Springer-Verlag, Berlin, 1983, pp. 140–147
C. M. Dafermos and L. Hsiao, Adiabatic shearing of incompressible fluids with temperature dependent viscosity, Quart. Appl. Math. 41, 45–58 (1983)
A. E. Tzavaras, Effect of thermal softening in shearing of strain-rate dependent materials, Arch. Rational Mech. Anal. 99, 349–374 (1987)
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
76E05
Retrieve articles in all journals
with MSC:
76E05
Additional Information
Article copyright:
© Copyright 1989
American Mathematical Society
