메뉴 건너뛰기




Volumn 62, Issue 5, 2011, Pages 937-952

Fractional order heat conduction law in magneto-thermoelasticity involving two temperatures

Author keywords

Fourier's law; Fractional calculus; Laplace transforms; Magneto thermoelasticity; Modified Riemann Liouville fractional derivative; New fractional Taylor's series; State space approach; Two temperature theory

Indexed keywords

FOURIER'S LAW; FRACTIONAL CALCULUS; FRACTIONAL TAYLOR'S SERIES; MAGNETO-THERMOELASTICITY; RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVES; STATE SPACE APPROACH; TWO-TEMPERATURE;

EID: 80053121733     PISSN: 00442275     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00033-011-0126-3     Document Type: Article
Times cited : (98)

References (62)
  • 1
    • 0000949743 scopus 로고
    • On a theory of heat conduction involving two temperatures
    • Chen P. J., Gurtin M. E.: On a theory of heat conduction involving two temperatures. ZAMP 19, 614-627 (1968).
    • (1968) Zamp , vol.19 , pp. 614-627
    • Chen, P.J.1    Gurtin, M.E.2
  • 2
    • 2142708425 scopus 로고
    • A note on non-simple heat conduction
    • Chen P. J., Gurtin M. E., Williams W. O.: A note on non-simple heat conduction. ZAMP 19, 969-970 (1968).
    • (1968) Zamp , vol.19 , pp. 969-970
    • Chen, P.J.1    Gurtin, M.E.2    Williams, W.O.3
  • 3
    • 2142717102 scopus 로고
    • On the thermodynamics of non-simple elastic materials with two temperatures
    • Chen P. J., Gurtin M. E., Williams W. O.: On the thermodynamics of non-simple elastic materials with two temperatures. ZAMP 20, 107-112 (1969).
    • (1969) Zamp , vol.20 , pp. 107-112
    • Chen, P.J.1    Gurtin, M.E.2    Williams, W.O.3
  • 4
    • 0015554096 scopus 로고
    • Wave propagation in the two-temperature theory of thermoelasticity
    • Warren W. E., Chen P. J.: Wave propagation in the two-temperature theory of thermoelasticity. Acta Mech. 16, 21-33 (1973).
    • (1973) Acta Mech. , vol.16 , pp. 21-33
    • Warren, W.E.1    Chen, P.J.2
  • 5
    • 5844296531 scopus 로고
    • On the linear coupled thermoelasticity with two temperatures
    • Ieşan D.: On the linear coupled thermoelasticity with two temperatures. ZAMP 21, 583-591 (1970).
    • (1970) Zamp , vol.21 , pp. 583-591
    • Ieşan, D.1
  • 6
    • 33748070515 scopus 로고    scopus 로고
    • Theory of two-temperature generalized thermoelasticity
    • Youssef H.: Theory of two-temperature generalized thermoelasticity. IMA J. Appl. Math. 71, 383-390 (2006).
    • (2006) IMA J. Appl. Math. , vol.71 , pp. 383-390
    • Youssef, H.1
  • 7
    • 33750205429 scopus 로고    scopus 로고
    • On the propagation of harmonic plane waves under the two-temperature theory
    • Puri P., Jordan P. M.: On the propagation of harmonic plane waves under the two-temperature theory. Int. J. Eng. Sci. 44, 1113-1126 (2006).
    • (2006) Int. J. Eng. Sci. , vol.44 , pp. 1113-1126
    • Puri, P.1    Jordan, P.M.2
  • 8
    • 33750202795 scopus 로고
    • Thermoelastic waves in non-simple media
    • Chakrabarti S.: Thermoelastic waves in non-simple media. Pure Appl. Geophys. 109, 1682-1692 (1973).
    • (1973) Pure Appl. Geophys. , vol.109 , pp. 1682-1692
    • Chakrabarti, S.1
  • 9
    • 60449085028 scopus 로고    scopus 로고
    • State space approach of two-temperature magneto-thermoelasticity theory with thermal relaxation in a medium of perfect conductivity
    • Ezzat M. A., El-Bary A. A.: State space approach of two-temperature magneto-thermoelasticity theory with thermal relaxation in a medium of perfect conductivity. Int. J. Eng. Sci. 47, 618-630 (2009).
    • (2009) Int. J. Eng. Sci. , vol.47 , pp. 618-630
    • Ezzat, M.A.1    El-Bary, A.A.2
  • 10
    • 57349137504 scopus 로고    scopus 로고
    • State space approach to solids and fluids
    • Ezzat M. A.: State space approach to solids and fluids. Can. J. Phys. Rev. 86, 1241-1250 (2008).
    • (2008) Can. J. Phys. Rev. , vol.86 , pp. 1241-1250
    • Ezzat, M.A.1
  • 11
    • 2142827202 scopus 로고    scopus 로고
    • On existence, structural stability, convergence and spatial behavior in thermoelasticity with two temperatures
    • Quintanilla R.: On existence, structural stability, convergence and spatial behavior in thermoelasticity with two temperatures. Acta Mech. 168, 61-73 (2004).
    • (2004) Acta Mech. , vol.168 , pp. 61-73
    • Quintanilla, R.1
  • 12
    • 0001753108 scopus 로고
    • Generalized thermoelasticity and its applications
    • In: Hetnarski, R. B. (ed.) Elsevier, New York
    • Ignaczak, J.: Generalized thermoelasticity and its applications. In: Hetnarski, R. B. (ed.) Thermal Stress, vol. III, pp. 279-354. Elsevier, New York (1989).
    • (1989) Thermal Stress , vol.III , pp. 279-354
    • Ignaczak, J.1
  • 13
    • 0001194946 scopus 로고    scopus 로고
    • Hyperbolic thermoelasticity. A review of recent literature
    • Chandrasekharaiah D. S.: Hyperbolic thermoelasticity. A review of recent literature. Appl. Mech. Rev. 51, 705-729 (1998).
    • (1998) Appl. Mech. Rev. , vol.51 , pp. 705-729
    • Chandrasekharaiah, D.S.1
  • 16
    • 49949149766 scopus 로고
    • A generalized dynamical theory of thermoelasticity
    • Lord H., Shulman Y.: A generalized dynamical theory of thermoelasticity. Mech. Phys. Solids 15, 299-309 (1967).
    • (1967) Mech. Phys. Solids , vol.15 , pp. 299-309
    • Lord, H.1    Shulman, Y.2
  • 19
    • 0004135196 scopus 로고
    • Addendum to the paper: heat waves
    • Joseph D. D., Preziosi L.: Addendum to the paper: heat waves. Rev. Mod. Phys. 62, 375-391 (1990).
    • (1990) Rev. Mod. Phys. , vol.62 , pp. 375-391
    • Joseph, D.D.1    Preziosi, L.2
  • 20
    • 0000366367 scopus 로고
    • Sur une forme de l'e'quation de la Chaleur e'liminant le paradoxe d'une propagation instantane'e
    • Cattaneo C.: Sur une forme de l'e'quation de la Chaleur e'liminant le paradoxe d'une propagation instantane'e. C. R. Acad. Sci. 247, 431-433 (1958).
    • (1958) C. R. Acad. Sci. , vol.247 , pp. 431-433
    • Cattaneo, C.1
  • 21
    • 0018458936 scopus 로고
    • Uniqueness in generalized thermoelasticity
    • Ignaczak J.: Uniqueness in generalized thermoelasticity. J. Therm. Stress. 2, 171-175 (1979).
    • (1979) J. Therm. Stress. , vol.2 , pp. 171-175
    • Ignaczak, J.1
  • 22
    • 0021696401 scopus 로고
    • A temperature-rate dependent thermo-piezoelectricity
    • Chandrasekharaiah D. S.: A temperature-rate dependent thermo-piezoelectricity. J. Therm. Stress. 7, 293-306 (1984).
    • (1984) J. Therm. Stress. , vol.7 , pp. 293-306
    • Chandrasekharaiah, D.S.1
  • 23
    • 0023089999 scopus 로고
    • On uniqueness and stability in generalized thermoelasticity
    • Sherief H.: On uniqueness and stability in generalized thermoelasticity. Quart. J. Appl. Math. 45, 773-778 (1987).
    • (1987) Quart. J. Appl. Math. , vol.45 , pp. 773-778
    • Sherief, H.1
  • 24
    • 0036606307 scopus 로고    scopus 로고
    • The uniqueness and reciprocity theorems for generalized thermoviscoelasticity for anisotropic media
    • Ezzat M. A., El-Karamany A. S.: The uniqueness and reciprocity theorems for generalized thermoviscoelasticity for anisotropic media. J. Therm. Stress. 25, 507-522 (2002).
    • (2002) J. Therm. Stress. , vol.25 , pp. 507-522
    • Ezzat, M.A.1    El-Karamany, A.S.2
  • 25
    • 0142258800 scopus 로고    scopus 로고
    • On uniqueness and reciprocity theorems for generalized thermo-viscoelasticity with thermal relaxation
    • Ezzat M. A., El-Karamany A. S.: On uniqueness and reciprocity theorems for generalized thermo-viscoelasticity with thermal relaxation. Can. J. Phys. 81, 823-833 (2003).
    • (2003) Can. J. Phys. , vol.81 , pp. 823-833
    • Ezzat, M.A.1    El-Karamany, A.S.2
  • 26
    • 0022583112 scopus 로고
    • Fundamental solution of generalized thermoelastic problem for short times
    • Sherief H.: Fundamental solution of generalized thermoelastic problem for short times. J. Therm. Stress. 9, 151-164 (1986).
    • (1986) J. Therm. Stress. , vol.9 , pp. 151-164
    • Sherief, H.1
  • 27
    • 3242694129 scopus 로고    scopus 로고
    • Fundamental solution in generalized magneto-thermoelasticity with two relaxation times for perfect conductor cylindrical region
    • Ezzat M. A.: Fundamental solution in generalized magneto-thermoelasticity with two relaxation times for perfect conductor cylindrical region. Int. J. Eng. Sci. 4, 1503-1519 (2004).
    • (2004) Int. J. Eng. Sci. , vol.4 , pp. 1503-1519
    • Ezzat, M.A.1
  • 28
    • 33644672654 scopus 로고    scopus 로고
    • Propagation of discontinuities in magneto-thermoelastic half-space
    • Ezzat M. A., El-Karamany A. S.: Propagation of discontinuities in magneto-thermoelastic half-space. J. Therm. Stress. 29, 331-358 (2006).
    • (2006) J. Therm. Stress. , vol.29 , pp. 331-358
    • Ezzat, M.A.1    El-Karamany, A.S.2
  • 29
    • 9944261982 scopus 로고    scopus 로고
    • Discontinuities in generalized thermo-viscoelasticity under four theories
    • El-Karamany A. S., Ezzat M. A.: Discontinuities in generalized thermo-viscoelasticity under four theories. J. Therm. Stress. 27, 1187-1212 (2004).
    • (2004) J. Therm. Stress. , vol.27 , pp. 1187-1212
    • El-Karamany, A.S.1    Ezzat, M.A.2
  • 30
    • 84977255207 scopus 로고
    • Linear models of dissipation whose Q is almost frequency independent II
    • Caputo M.: Linear models of dissipation whose Q is almost frequency independent II. Geophys. J. R. Astron. Soc. 13, 529-539 (1967).
    • (1967) Geophys. J. R. Astron. Soc. , vol.13 , pp. 529-539
    • Caputo, M.1
  • 31
    • 0001983732 scopus 로고    scopus 로고
    • Fractional calculus: some basic problems in continuum and statistical mechanics
    • A. Carpinteri and F. Mainardi (Eds.), New York: Springer
    • Mainardi F.: Fractional calculus: some basic problems in continuum and statistical mechanics'. In: Carpinteri, A., Mainardi, F. (eds) Fractals and Fractional Calculus in Continuum Mechanics, pp. 291-348. Springer, New York (1997).
    • (1997) Fractals and Fractional Calculus in Continuum Mechanics , pp. 291-348
    • Mainardi, F.1
  • 33
    • 0003223705 scopus 로고
    • Generalized fractional calculus and applications
    • Longman-Wiley, New York
    • Kiryakova, V.: Generalized fractional calculus and applications. In: Pitman Research Notes in Mathematics Series, vol. 301. Longman-Wiley, New York (1994).
    • (1994) Pitman Research Notes in Mathematics Series , vol.301
    • Kiryakova, V.1
  • 39
    • 51649182765 scopus 로고
    • Linear model of dissipation in anelastic solids
    • Caputo M., Mainardi F.: Linear model of dissipation in anelastic solids. Rivis ta el Nuovo cimento 1, 161-198 (1971).
    • (1971) Rivis Ta El Nuovo Cimento , vol.1 , pp. 161-198
    • Caputo, M.1    Mainardi, F.2
  • 40
    • 0016103247 scopus 로고
    • Vibrations on an infinite viscoelastic layer with a dissipative Memory
    • Caputo M.: Vibrations on an infinite viscoelastic layer with a dissipative Memory. J. Acous. Soc. Am. 56, 897-904 (1974).
    • (1974) J. Acous. Soc. Am. , vol.56 , pp. 897-904
    • Caputo, M.1
  • 41
    • 0020765202 scopus 로고
    • A theoretical basis for the application of fractional Calculus to viscoelasticity
    • Bagley R. L., Torvik P. J.: A theoretical basis for the application of fractional Calculus to viscoelasticity. J. Rheol. 27, 201-210 (1983).
    • (1983) J. Rheol. , vol.27 , pp. 201-210
    • Bagley, R.L.1    Torvik, P.J.2
  • 42
    • 0021440218 scopus 로고
    • Applications of fractional calculus to the theory of viscoelasticity
    • Koeller R. C.: Applications of fractional calculus to the theory of viscoelasticity. Trans. ASME-J. Appl. Mech. 51, 299-307 (1984).
    • (1984) Trans. ASME-J. Appl. Mech. , vol.51 , pp. 299-307
    • Koeller, R.C.1
  • 43
    • 0030867045 scopus 로고    scopus 로고
    • Applications of fractional calculus to dynamic problems of linear and nonlinear heredity mechanics of solids
    • Rossikhin Yu. A., Shitikova M. V.: Applications of fractional calculus to dynamic problems of linear and nonlinear heredity mechanics of solids. Appl. Mech. Rev. 50, 15-67 (1997).
    • (1997) Appl. Mech. Rev. , vol.50 , pp. 15-67
    • Rossikhin, Y.A.1    Shitikova, M.V.2
  • 44
    • 0036829341 scopus 로고    scopus 로고
    • Strange kinetics, porous media, and NMR
    • Kimmich R.: Strange kinetics, porous media, and NMR. J. Chem. Phys. 284, 243-285 (2002).
    • (2002) J. Chem. Phys. , vol.284 , pp. 243-285
    • Kimmich, R.1
  • 45
    • 0000145521 scopus 로고    scopus 로고
    • On Mittag-Lettler-type function in fractional evolution processes
    • Mainardi F., Gorenflo R.: On Mittag-Lettler-type function in fractional evolution processes. J. Comput. Appl. Math. 118, 283-299 (2000).
    • (2000) J. Comput. Appl. Math. , vol.118 , pp. 283-299
    • Mainardi, F.1    Gorenflo, R.2
  • 46
    • 84972547716 scopus 로고
    • Integrodifferential equation which interpolates the heat equation and wave Equation (I)
    • Fujita Y.: Integrodifferential equation which interpolates the heat equation and wave Equation (I). Osaka J. Math. 27, 309-321 (1990).
    • (1990) Osaka J. Math. , vol.27 , pp. 309-321
    • Fujita, Y.1
  • 47
    • 84972571026 scopus 로고
    • Integrodifferential equation which interpolates the heat equation and wave equation (II)
    • Fujita Y.: Integrodifferential equation which interpolates the heat equation and wave equation (II). Osaka J. Math. 27, 797-804 (1990).
    • (1990) Osaka J. Math. , vol.27 , pp. 797-804
    • Fujita, Y.1
  • 48
    • 13844253772 scopus 로고    scopus 로고
    • Fractional heat conduction equation and associated thermal stress
    • Povstenko Y. Z.: Fractional heat conduction equation and associated thermal stress. J. Therm. Stress. 28, 83-102 (2005).
    • (2005) J. Therm. Stress. , vol.28 , pp. 83-102
    • Povstenko, Y.Z.1
  • 52
    • 77955283494 scopus 로고    scopus 로고
    • Theory of fractional order generalized thermoelasticity
    • Youssef H.: Theory of fractional order generalized thermoelasticity. J. Heat Transf. 132, 1-7 (2010).
    • (2010) J. Heat Transf. , vol.132 , pp. 1-7
    • Youssef, H.1
  • 53
    • 77957168518 scopus 로고    scopus 로고
    • Thermoelectric MHD non-Newtonian fluid with fractional derivative heat transfer
    • Ezzat M. A.: Thermoelectric MHD non-Newtonian fluid with fractional derivative heat transfer. Phys. B 405, 4188-4194 (2010).
    • (2010) Phys. B , vol.405 , pp. 4188-4194
    • Ezzat, M.A.1
  • 54
    • 78349303958 scopus 로고    scopus 로고
    • Magneto-thermoelasticity with thermoelectric properties and fractional derivative heat transfer
    • Ezzat M. A.: Magneto-thermoelasticity with thermoelectric properties and fractional derivative heat transfer. Phys. B 406, 30-35 (2011).
    • (2011) Phys. B , vol.406 , pp. 30-35
    • Ezzat, M.A.1
  • 55
    • 74249118189 scopus 로고    scopus 로고
    • Derivation and solutions of some fractional Black_Scholes equations in coarse-grained space and time. Application to Merton's optimal portfolio
    • Jumarie G.: Derivation and solutions of some fractional Black_Scholes equations in coarse-grained space and time. Application to Merton's optimal portfolio. Comput. Math. Appl. 59, 1142-1164 (2010).
    • (2010) Comput. Math. Appl. , vol.59 , pp. 1142-1164
    • Jumarie, G.1
  • 56
    • 79551523032 scopus 로고    scopus 로고
    • Convolutional variational principle, reciprocal and uniqueness theorems in linear fractional two-temperature thermoelasticity
    • El-Karamany A. S., Ezzat M. A.: Convolutional variational principle, reciprocal and uniqueness theorems in linear fractional two-temperature thermoelasticity. J. Therm. Stress. 34(3), 264-284 (2011).
    • (2011) J. Therm. Stress. , vol.34 , Issue.3 , pp. 264-284
    • El-Karamany, A.S.1    Ezzat, M.A.2
  • 57
    • 79956121976 scopus 로고    scopus 로고
    • On the Fractional Thermoelasticity
    • Published online 8 March, doi: 10.1177/1081286510397228
    • El-Karamany, A. S., Ezzat, M. A.: On the Fractional Thermoelasticity. Mathematics and Mechanics of Solid. Published online 8 March 2011, doi: 10. 1177/1081286510397228.
    • (2011) Mathematics and Mechanics of Solid
    • El-Karamany, A.S.1    Ezzat, M.A.2
  • 58
    • 79953232071 scopus 로고    scopus 로고
    • Fractional order theory of a perfect conducting thermoelastic medium
    • Ezzat M. A., El-Karamany A. S.: Fractional order theory of a perfect conducting thermoelastic medium. Can. J. Phys. 89(3), 311-318 (2011).
    • (2011) Can. J. Phys. , vol.89 , Issue.3 , pp. 311-318
    • Ezzat, M.A.1    El-Karamany, A.S.2
  • 59
    • 0021375050 scopus 로고
    • A method for the numerical inversion of the Laplace transform
    • Honig G., Hirdes U.: A method for the numerical inversion of the Laplace transform. J. Comp. Appl. Math. 10, 113-132 (1984).
    • (1984) J. Comp. Appl. Math. , vol.10 , pp. 113-132
    • Honig, G.1    Hirdes, U.2
  • 60
    • 36849124387 scopus 로고
    • Thermoelasticity and irreversible thermodynamics
    • Biot M.: Thermoelasticity and irreversible thermodynamics. J. Appl. Phys. 27, 240-253 (1956).
    • (1956) J. Appl. Phys. , vol.27 , pp. 240-253
    • Biot, M.1
  • 61
    • 70449561139 scopus 로고    scopus 로고
    • State space approach of two-temperature magneto-viscoelasticity with thermal relaxation in a medium of perfect conductivity
    • Ezzat M. A., El-Karamany A. S.: State space approach of two-temperature magneto-viscoelasticity with thermal relaxation in a medium of perfect conductivity. J. Therm. Stress. 32, 819-838 (2009).
    • (2009) J. Therm. Stress. , vol.32 , pp. 819-838
    • Ezzat, M.A.1    El-Karamany, A.S.2
  • 62
    • 77954200110 scopus 로고    scopus 로고
    • Electro-magneto-thermoelastic plane waves in micropolar solid involving two temperatures
    • Ezzat M. A., Farid H., Emad A.: Electro-magneto-thermoelastic plane waves in micropolar solid involving two temperatures. Acta Mech. Solida Sin. 23, 200-212 (2010).
    • (2010) Acta Mech. Solida Sin. , vol.23 , pp. 200-212
    • Ezzat, M.A.1    Farid, H.2    Emad, A.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.