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Heat waves. (English) Zbl 1129.80300
Rev. Mod. Phys. 61, No. 1, 41-73 (1989); Addendum 62, 375 (1990).
Summary: The concept of transmission of heat by waves is reviewed and interpreted. We introduce the notion of an effective thermal conductivity, an effective heat capacity, and relaxation functions for heat and energy, along lines used recently to describe the elastic response of viscous liquids. An annotated bibliography of the literature on heat waves, from the beginning until now, gives a complete or nearly complete survey of the history of this subject.

MSC:
80-02 Research exposition (monographs, survey articles) pertaining to classical thermodynamics
01A60 History of mathematics in the 20th century
80A20 Heat and mass transfer, heat flow (MSC2010)
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References:
[1] Achenbach, J. D., J. Mech. Phys. Solids 16 pp 273– (1968)
[2] Ackerman, C. C., Phys. Rev. Lett. 16 pp 789– (1966)
[3] Ackerman, C. C., Ann. Phys. (N.Y.) 50 pp 128– (1968)
[4] Ackerman, C. C., Phys. Rev. Lett. 22 pp 764– (1969)
[5] Agarwal, V. K., J. Elasticity 8 pp 171– (1978) · Zbl 0372.73017
[6] Agarwal, V. K., Acta Mech. 31 pp 39– (1979) · Zbl 0393.73121
[7] Agarwal, V. K., Am. J. Phys. 49 pp 503– (1981)
[8] Amos, D. E., ASME J. Appl. Mech. 37 pp 1145– (1970)
[9] Atkin, R. J., J. Elasticity 5 pp 237– (1975)
[10] Atkins, K. R., Philos. Mag. 41 pp 1078– (1950)
[11] Band, W., Phys. Rev. 73 pp 226– (1948)
[12] Banerjee, D. K., J. Acoust. Soc. Am. 56 pp 1444– (1974) · Zbl 0297.73011
[13] Barday, D. W., Int. J. Eng. Sci. 21 pp 663– (1983) · Zbl 0512.73011
[14] Barnabes, C., Nuovo Cimento B 28 pp 377– (1975)
[15] Baumeister, K. J., J. Heat Transfer 91 pp 543– (1969)
[16] Beck, H., in: Dynamical Properties of Solids (1975)
[17] Beevers, C. E., Int. J. Heat Mass Transfer 15 pp 369– (1973)
[18] Bertman, B., Sci. Am. 222 pp 92– (1970)
[19] Bogy, D. B., J. Math. Phys. 11 pp 917– (1970) · Zbl 0189.10402
[20] Boley, B., in: High Temperature Structures and Materials (1964)
[21] Brazel, J. P., in: Non-Fourier effects in the transmission of heat (1967)
[22] Brown, J. B., Phys. Lett. 21 pp 241– (1966)
[23] Bubnov, B. A., Int. J. Heat Mass Transfer 19 pp 175– (1974) · Zbl 0316.35045
[24] Caffarelli, G. V., Boll. Un. Mat. Ital., Ser. 6 5A pp 33– (1986)
[25] Cattaneo, C., Atti del Semin. Mat. e Fis. Univ. Modena 3 pp 3– (1948)
[26] Cattaneo, C., C. R. Acad. Sci. 247 pp 431– (1958)
[27] Chan, S. H., Am. Inst. Chem. Eng. J. 17 pp 1498– (1971)
[28] Chang, R., Philos. Mag. 16 pp 1021– (1968)
[29] Chen, P., Z. Angew. Math. Phys. 20 pp 448– (1969) · Zbl 0175.52101
[30] Chen, P. J., Z. Angew. Math. Phys. 21 pp 232– (1970) · Zbl 0218.73007
[31] Chen, P., Z. Angew. Math. Phys. 25 pp 791– (1974)
[32] Chester, M., Phys. Rev. 131 pp 2013– (1963)
[33] Coleman, B. D., Arch. Ration. Mech. Anal. 80 pp 135– (1982) · Zbl 0501.73008
[34] Coleman, B. D., in: New Perspectives in Thermodynamics (1986)
[35] Coleman, B. D., Arch. Ration. Mech. Anal. 94 pp 267– (1986) · Zbl 0621.73132
[36] Coleman, B. D., Phys. Rev. B 37 pp 1492– (1988)
[37] Coleman, B. D., Arch. Ration. Mech. Anal. 6 pp 355– (1960) · Zbl 0097.16403
[38] Coleman, B. D., Comput. Math. Appl. 9 pp 527– (1983) · Zbl 0569.35047
[39] DeFacio, B., J. Math. Phys. 16 pp 971– (1974)
[40] deSocio, L. M., Q. Appl. Math. 41 pp 253– (1982) · Zbl 0518.73100
[41] Dingle, R. B., Proc. Phys. Soc. London Sect. A 60 pp 374– (1952) · Zbl 0046.23206
[42] Einstein, A., Sitzungsber. Dtsch. Akad. Wiss. Berlin 8 pp 380– (1920)
[43] Enz, C. P., Ann. Phys. 46 pp 114– (1968)
[44] Eringen, A. C., Phys. Rev. 117 pp 1174– (1960) · Zbl 0095.43702
[45] Finn, J. M., Z. Angew. Math. Phys. 23 pp 922– (1972)
[46] Fox, N., Int. J. Eng. Sci. 7 pp 437– (1969) · Zbl 0167.54404
[47] Fox, N., J. Inst. Math. Its Appl. 5 pp 373– (1969) · Zbl 0198.58802
[48] Goldstein, S., Q. J. Mech. Appl. Math. IV pp 129– (1951) · Zbl 0045.08102
[49] Grad, H., in: Handbuch der Physik 12: Thermodynamics of Gases (1958)
[50] Green, A. E., J. Elasticity 2 pp 1– (1972) · Zbl 0775.73063
[51] Greenberg, J. M., IMA J. Appl. Math. 38 pp 1– (1987) · Zbl 0656.35079
[52] Gurtin, M. E., Arch. Ration. Mech. Anal. 31 pp 113– (1968) · Zbl 0164.12901
[53] Gurzi, R. N., Zh. Eksp. Teor. Fiz. 46 pp 719– (1964)
[54] Guyer, R. A., Phys. Rev. 133 pp 1411A– (1964)
[55] Guyer, R. A., Phys. Rev. 148 pp 766– (1966)
[56] Guyer, R. A., Phys. Rev. 148 pp 778– (1966)
[57] Hardy, R. J., Phys. Rev. B 2 pp 1193– (1970)
[58] Jackson, H. E., Phys. Rev. Lett. 25 pp 26– (1970)
[59] Joseph, D. D., J. Non-Newtonian Fluid Mech. 19 pp 237– (1986)
[60] Joseph, D. D., J. Fluid Mech. 171 pp 289– (1986) · Zbl 0609.76033
[61] Kaliski, S., Bull. Acad. Pol. Sci. XIII pp 211– (1965)
[62] Kao, T. T., AIAA J. 14 pp 818– (1976)
[63] Kazimi, M. S., J. Heat Transfer. 97 pp 615– (1975)
[64] Kranys, M., Nuovo Cimento B 50 pp 48– (1967)
[65] Kranys, M., J. Phys. A 10 pp 1847– (1977) · Zbl 0368.73010
[66] Kwok, P., Physics 3 pp 221– (1967)
[67] Landau, L., J. Phys. 5 pp 71– (1941)
[68] Lebon, G., J. Mec. 15 pp 579– (1976)
[69] Lianis, G., Arch. Ration. Mech. Anal. 55 pp 300– (1974) · Zbl 0295.73008
[70] Lifshitz, E., J. Phys. 8 pp 110– (1944)
[71] Lord, H. W., Acta Mech. 10 pp 85– (1970) · Zbl 0209.56804
[72] Lord, H. W., J. Mech. Phys. Solids 15 pp 299– (1967) · Zbl 0156.22702
[73] Luikov, A. V., Inghenerno-fizicheskifi Zh. 9 pp 287– (1965)
[74] Luikov, A. V., Int. J. Heat Mass Transfer 19 pp 245– (1976)
[75] MacDonald, R. A., Therm. Conduct. 14 pp 145– (1976)
[76] MacDonald, R. A., Phys. Rep. 46 pp 1– (1978)
[77] Maugin, G. A., J. Phys. A 7 pp 465– (1974)
[78] Maurer, M. J., J. Appl. Phys. 40 pp 5123– (1969)
[79] Maurer, M. J., J. Heat Transfer 95 pp 284– (1973)
[80] Maxwell, J. C., Philos. Trans. Soc. London 157 pp 49– (1867)
[81] McCarthy, M., Int. J. Eng. Sci. 8 pp 467– (1970) · Zbl 0212.58303
[82] McCarthy, M., Pol. Acad. Sci. Inst. Fundam. Tech Res. 11 pp 123– (1970)
[83] McNelly, T. F., Phys. Rev. Lett. 24 pp 100– (1970)
[84] Meixner, J., Arch. Ration. Mech. Anal. 39 pp 108– (1970) · Zbl 0218.35043
[85] Mezhov-Deglin, L. P., Zh. Eksp. Teor. Fiz. 46 pp 1926L– (1964)
[86] Mikhail, I. F. I., J. Phys. C 8 pp 3087– (1975)
[87] Miller, R. K., J. Math. Anal. 66 pp 313– (1978) · Zbl 0391.45012
[88] Moodie, T. B., Acta Mech. 50 pp 97– (1983) · Zbl 0526.73129
[89] Morro, A., Rend. Semin. Mat. Univ. Padova 63 pp 169– (1980)
[90] Morro, A., Arch. Mech. Warszawa 32 pp 145– (1980)
[91] Morse, P. M., in: Methods of Theoretical Physics I (1953) · Zbl 0051.40603
[92] Müller, I., Arch. Ration. Mech. Anal. 34 pp 259– (1969) · Zbl 0182.59801
[93] Müller, I., Arch. Ration. Mech. Anal. 41 pp 319– (1971) · Zbl 0225.73003
[94] Nachlinger, R., Q. Appl. Math. 31 pp 267– (1973)
[95] Narain, A., Rheol. Acta 21 pp 228– (1982) · Zbl 0498.76006
[96] Narain, A., Rheol. Acta 22 pp 528– (1983) · Zbl 0541.76007
[97] Narayanamurti, V., Phys. Rev. Lett. 28 pp 1461– (1972)
[98] Nayfeh, A., AIAA J. 15 pp 957– (1977) · Zbl 0402.73030
[99] Nayfeh, A., Z. Angew. Math. Phys. 23 pp 50– (1972) · Zbl 0237.73016
[100] Nernst, W., in: Die Theoretischen Grundlagen des n Warmestatzes (1917)
[101] Nettleton, R. E., Phys. Fluids 3 pp 216– (1960)
[102] Norwood, F. R., Q. J. Mech. Appl. Math. 22 pp 283– (1968) · Zbl 0187.23705
[103] Nunziato, J. W., Q. Appl. Math. 29 pp 187– (1971) · Zbl 0227.73011
[104] Nunziato, J. W., SIAM J. Appl. Math. 25 pp 1– (1973) · Zbl 0237.35037
[105] Oldroyd, J. G., Proc. R. Soc. London Ser. A 200 pp 523– (1950) · Zbl 1157.76305
[106] Onsager, L., Phys. Rev. 37 pp 405– (1931) · Zbl 0001.09501
[107] Osborne, D. V., Low Temp. Phys. NBS (US) pp 139– (1950)
[108] Pao, Y. H., Lett. Appl. Eng. Sci. 1 pp 35– (1973)
[109] Peierls, R. E., in: Quantum Theory of Solids (1955)
[110] Peshkov, V., J. Phys. 8 pp 381– (1944)
[111] Peshkov, V., in: International Conference on Fundamental Particles and Low Temperatures, Cavendish Laboratory, Cambridge, July 22-27, 1946: Report (1946)
[112] Popov, E. B., J. Appl. Math. Mech. (USSR) 31 pp 349– (1967)
[113] Preziosi, L, J. Non-Newtonian Fluid Mech. 25 pp 239– (1987) · Zbl 0683.76006
[114] Prohofsky, E. W., Phys. Rev. 133 pp 1402A– (1964)
[115] Renardy, M., Rheol. Acta 21 pp 251– (1982) · Zbl 0488.76002
[116] Roetman, E. L., Int. J. Eng. Sci. 13 pp 699– (1975) · Zbl 0306.35061
[117] Rogers, S. J., Phys. Rev. B 3 pp 1440– (1971)
[118] Sadd, M. H., J. Heat Transfer 99 pp 25– (1977)
[119] Saut, J. C., Arch. Ration. Mech. Anal. 81 pp 53– (1983) · Zbl 0543.73005
[120] Sawatzky, R. P., Acta Mech. 56 pp 165– (1985) · Zbl 0568.73003
[121] Seifert, G., Q. Appl. Math. 38 pp 246– (1980) · Zbl 0448.45009
[122] Simons, S., Phys. Lett. A 66 pp 453– (1978)
[123] Solomon, A., Q. Appl. Math. 43 pp 295– (1985) · Zbl 0591.35083
[124] Sussman, J. A., Proc. Phys. Soc. London 81 pp 1122– (1963) · Zbl 0113.22601
[125] Swenson, R., Am. J. Phys. 46 pp 76– (1978)
[126] Swenson, R., J. Non-Equil. Thermodyn. 3 pp 39– (1978) · Zbl 0369.35038
[127] Taitel, Y., Int. J. Heat Mass Transfer 15 pp 369– (1972)
[128] Tavernier, J., C. R. Acad. Sci. 254 pp 69– (1962) · Zbl 0106.21202
[129] Tisza, L., C. R. Acad. Sci. 207 pp 1035– (1938)
[130] Tsai, D. H., in: NBS (U.S.) Spec. Publ. (1971)
[131] Tsai, D. H., J. Phys. C 6 pp L171– (1973)
[132] Tsai, D. H., Phys. Rev. B 14 pp 4714– (1976)
[133] Vernotte, P., C. R. Acad. Sci. 247 pp 2103– (1958)
[134] Vernotte, P., C. R. Acad. Sci. 246 pp 3154– (1958)
[135] Vernotte, P., C. R. Acad. Sci. 252 pp 2190– (1961)
[136] Vick, B., J. Heat Transfer 105 pp 902– (1983)
[137] von Gutfeld, R. J., in: Physical Acoustics: Principles and Methods (1968)
[138] Ward, J. C., Philos. Mag. 42 pp 314– (1951)
[139] Ward, J. C., Philos. Mag. 43 pp 48– (1952)
[140] Weyman, H. D., Am. J. Phys. 35 pp 488– (1965)
[141] Whitham, G. B., Commun. Pure Appl. Math 12 pp 113– (1959) · Zbl 0084.42701
[142] Wiggert, D. C., J. Heat Transfer 99 pp 35– (1977)
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