Discontinuities in velocity gradients and temperature in the Stokes’ first problem with nonclassical heat conduction
Authors:
P. Puri and P. K. Kythe
Journal:
Quart. Appl. Math. 55 (1997), 167-176
MSC:
Primary 80A20; Secondary 76D99
DOI:
https://doi.org/10.1090/qam/1433760
MathSciNet review:
MR1433760
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Abstract: The nonclassical heat conduction equation based on the MCF model is used to study the discontinuities in velocity gradients and temperature in fluid flows induced by impulsive or sudden heating of a plate. The influence of the thermal relaxation time in the temperature and velocity fields is investigated.
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C. C. Ackerman, B. Bertman, H. A. Fairbank, and R. A. Guyer, Second sound in solid helium, Phys. Rev. Lett. 16, 789–791 (1966)
M. Chester, Second sound in solids, Phys. Rev. 131, 2013–2015 (1963)
S. Kaliski, Wave equations in thermoelasticity, Bull. Acad. Polon. Sci., Ser. Sci. Tech. 13, 253–260 (1965)
H. W. Lord and Y. Shulman, A generalized dynamical theory of thermoelasticity, J. Mech. Phys. Solids 15, 299–309 (1967)
A. E. Green and K. A. Lindsay, Thermoelasticity, J. Elast. 2, 1–7 (1972)
K. A. Lindsay and B. Straughan, Acceleration waves and second sound in a perfect fluid, Arch. Rational Mech. Anal. 68, 53–87 (1978)
C. L. McTaggart and K. A. Lindsay, Nonclassical effects in the Bénard problem, SIAM J. Appl. Math. 45, 70–92 (1985)
P. Puri and P. K. Kythe, Nonclassical thermal effects in Stokes’ second problem, Acta Mechanica 112, 1–9 (1995)
D. D. Joseph and L. Preziosi, Heat waves, Rev. Modern Phys. 61, 41–73 (1989)
F. R. Norwood and W. E. Warren, Wave propagation in the generalized dynamical theory of thermoelasticity, Quart. J. Mech. Appl. Math. 22, 283–290 (1969)
P. Puri, Plane waves in generalized thermoelasticity, Internat. J. Engrg. Sci. 11, 735–744 (1973); 13, 339–340 (1975)
H. Schlichting, Boundary Layer Theory, 4th Ed., McGraw-Hill, New York, 1960, p. 72
A. Erdélyi (Ed.), Tables of Laplace Transforms, Vol. 1, Bateman Manuscript Project, McGrawHill, New York, 1954
B. A. Boley, Discontinuities in integral-transform solutions, Quart. Appl. Math. 19, 273–284 (1962)
B. A. Boley and I. S. Tolins, Transient coupled thermoelastic boundary value problems in the half-space, J. Appl. Mech. 29, Trans. ASME 84, 637–646 (1962)
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Article copyright:
© Copyright 1997
American Mathematical Society