Discontinuities in velocity gradients and temperature in the Stokes’ first problem with nonclassical heat conduction

Puri, P.; Kythe, P. K.

doi:10.1090/qam/1433760

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

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 (1978), no. 1, 53–87. MR 489302, DOI https://doi.org/10.1007/BF00276179
Carol L. McTaggart and K. A. Lindsay, Nonclassical effects in the Bénard problem, SIAM J. Appl. Math. 45 (1985), no. 1, 70–92. MR 775483, DOI https://doi.org/10.1137/0145003

P. Puri and P. K. Kythe, Nonclassical thermal effects in Stokes’ second problem, Acta Mechanica 112, 1–9 (1995)

D. D. Joseph and Luigi Preziosi, Heat waves, Rev. Modern Phys. 61 (1989), no. 1, 41–73. MR 977943, DOI https://doi.org/10.1103/RevModPhys.61.41

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)

Hermann Schlichting, Boundary layer theory, McGraw-Hill, New York; Pergamon Press, London; Verlag G. Braun, Karlsruhe, 1955. Translated by J. Kestin. MR 0076530

A. Erdélyi (Ed.), Tables of Laplace Transforms, Vol. 1, Bateman Manuscript Project, McGrawHill, New York, 1954

Bruno A. Boley, Discontinuities in integral-transform solutions, Quart. Appl. Math. 19 (1962), 273–284. MR 131729, DOI https://doi.org/10.1090/S0033-569X-1962-0131729-2
B. A. Boley and I. S. Tolins, Transient coupled thermoelastic boundary value problems in the half-space, Trans. ASME Ser. E. J. Appl. Mech. 29 (1962), 637–646. MR 147052