The nonclassical heat conduction equation based on the Maxwell-Cattaneo-Fox (MCF) model is used to study the Stokes’ first and second problems for the Rivlin-Ericksen fluids. The discontinuities in velocity gradients in fluid flows induced by impulsive or sudden heating of a plate and the influence of the thermal relaxation time and elastic parameter of the fluid on the velocity field are investigated. The structure of the waves in the temperature and velocity fields is presented. An anomalous behavior of the medium is characterized by infinite or negative values of the group velocity for the wave packets as the frequency attains or exceeds a critical value. The displacement thickness and the rate of heat transfer at the plate are determined.
Issue Section:
Conduction Heat Transfer
1.
Ackerman
C. C.
Bertman
B.
Fairbank
H. A.
Guyer
R. A.
1966
, “Second Sound in Solid Helium
,” Phys. Rev. Lett.
, Vol. 16
, pp. 789
–791
.2.
Boley
B. A.
1962
, “Discontinuities in Integral-Transform Solutions
,” Quart. Appl. Math.
, Vol. 19
, pp. 273
–284
.3.
Boley
B. A.
Tolins
I. S.
1962
, “Transient Coupled Thermoelastic Boundary Value Problems in the Half-Space
,” ASME J. Appl. Mech.
, Vol. 29
, pp. 637
–646
.4.
Brillouin, L., 1960, Wave Propagation and Group Velocity, Academic Press, New York.
5.
Cattaneo
C.
1948
, “Sullacondizione del calore
,” Atti del Semin. Matem. e Fis. della Univ. Modena
, Vol. 3
, pp. 83
–101
.6.
Chester
M.
1963
, “Second Sound in Solids
,” Phys. Rev.
, Vol. 131
, pp. 2013
–2015
.7.
Green
A. E.
Lindsay
K. A.
1972
, “Thermoelasticity
,” J. Elast.
, Vol. 2
, pp. 1
–7
.8.
Joseph
D. D.
Preziosi
L.
1989
, “Heat Waves
,” Rev. Modern Phys.
, Vol. 61
, pp. 41
–73
.9.
Joseph
D. D.
Preziosi
L.
1990
, addendum to the paper “Heat Waves
,” Rev. Modern Phys.
, Vol. 62
, pp. 375
–391
.10.
Kaliski
S.
1965
, “Wave Equations in Thermoelasticity
,” Bull. Acad. Polon. Sci.
, Ser. Sci. Tech., Vol. 13
, pp. 253
–260
.11.
Lindsay
K. A.
Straughan
B.
1978
, “Acceleration Waves and Second Sound in a Perfect Fluid
,” Arch. Rational Mech. Anal
, Vol. 68
, pp. 53
–87
.12.
Lord
H. W.
Shulman
Y.
1967
, “A Generalized Dynamical Theory of Thermoelasticity
,” J. Mech. Phys. Solids
, Vol. 15
, pp. 299
–309
.13.
Maxwell
J. C.
1867
, “On the Dynamical Theory of Gases
,” Phil. Trans. Royal Soc.
, Vol. 157
, pp. 49
–88
.14.
McTaggart
C. L.
Lindsay
K. A.
1985
, “Nonclassical Effects in the Be´nard Problem
,” SIAM J. Appl. Math.
, Vol. 45
, pp. 70
–92
.15.
Nerest, W., 1917, Die theoretischen Grundlagen des n Wa¨rmestatzes, Knapp, Halle.
16.
Norwood
F. R.
Warren
W. E.
1969
, “Wave Propagation in the Generalized Dynamical Theory of Thermoelasticity
,” Quart. J. Mech. and Applied Math.
, Vol. 22
, pp. 283
–290
.17.
Onsanger
L.
1931
, “Reciprocal Relations in Irreversible Processes
,” Phys. Rev.
, Vol. 37
, pp. 405
–426
.18.
Peshkov
V.
1944
, “Second Sound in Helium II
,” J. Phys. (Moscow)
, Vol. 8
, pp. 381
381
.19.
Puri
P.
1973
, “Plane Waves in Generalized Thermoelasticity
,” Int. J. Engng. Sci.
, Vol. 11
, pp. 735
–744
.20.
Puri
P.
1975
, errata to “Plane Waves in Generalized Thermoelasticity
,” Int. J. Engng. Sci.
, Vol. 13
, pp. 339
–340
.21.
Puri
P.
1984
, “Impulsive Motion of a Flat Plate in a Rivlin-Ericksen Fluid
,” Rheol. Acta
, Vol. 23
, pp. 451
–453
.22.
Puri
P.
Kythe
P. K.
1995
, “Nonclassical Thermal Effects in Stokes’ Second Problem
,” Acta Mechanica
, Vol. 112
, pp. 1
–9
.23.
Puri
P.
Kythe
P. K.
1997
, “Discontinuities in Velocity Gradients and Temperature in the Stokes’ First Problem With Nonclassical Heat Conduction
,” Quart. Appl. Math.
, Vol. 55
, pp. 167
–176
.24.
Rivlin
R. S.
Ericksen
J. L.
1955
, J. Rational Mechanics and Analysis
, Vol. 4
, p. 323
323
.25.
Schlichting, H., 1960, Boundary Layer Theory, 4th Ed., McGraw-Hill Book Company, Inc., p. 72.
26.
Smith
R. L.
1970
, “The Velocities of Light
,” Am. J. Phys.
, Vol. 38
, pp. 978
–984
.27.
Truesdell, C., and Toupin, R. A., 1960, The Classical Field Theories in Encyclopedia of Physics, III/1, Springer-Verlag, Berlin.
28.
Tzou, D. Y., 1997, Macro-to Microscale Heat Transfer, Taylor & Francis, 1997, p. 20.
This content is only available via PDF.
Copyright © 1998
by The American Society of Mechanical Engineers
You do not currently have access to this content.
