Thermo-Viscoelastic Interaction Subjected to Fractional Fourier law with Three-Phase-Lag Effects

Publish Year: 1394
نوع سند: مقاله ژورنالی
زبان: English
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JR_JSMA-7-4_003

تاریخ نمایه سازی: 27 فروردین 1399

Abstract:

In this paper, a new mathematical model of a Kelvin-Voigt type thermo-visco-elastic, infinite thermally conducting medium has been considered in the context of a new consideration of heat conduction having a non-local fractional order due to the presence of periodically varying heat sources. Three-phase-lag thermoelastic model, Green Naghdi models II and III (i.e., the models which predicts thermoelasticity without energy dissipation (TEWOED) and with energy dissipation (TEWED)) are employed to study the thermo-mechanical coupling, thermal and mechanical relaxation effects. In the absence of mechanical relaxations (viscous effect), the results for various generalized theories of thermoelasticity may be obtained as particular cases. The governing equations are expressed in Laplace-Fourier double transform domain. The inversion of the Fourier transform is carried out using residual calculus, where the poles of the integrand are obtained numerically in complex domain by using Laguerre s method and the inversion of the Laplace transform is done numerically using a method based on Fourier series expansion technique. Some comparisons have been shown in the form of the graphical representations to estimate the effect of the non-local fractional parameter and the effect of viscosity is also shown.

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Authors

P Pal

Department of Applied Mathematics, University of Calcutta

A Sur

Department of Applied Mathematics, University of Calcutta

M Kanoria

Department of Applied Mathematics, University of Calcutta

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  • Gross B., 1953, Mathematical Structure of the Theories of Viscoelasticity, ...
  • Staverman A.J., Schwarzl F., 1956, Die Physik der Hochpolymeren, Springer-Verlag, ...
  • Alfery T., Gurnee E.F., 1956, Theory and Applications, Academic Press, ...
  • Ferry J.D., 1970, Viscoelastic Properties of Polymers, John Wiley and ...
  • Bland D.R., 1960, The Theory of Linear Viscoelasticity, Pergamon Press, ...
  • Lakes R.S., 1998, Viscoelastic Solids, CRC Press, New York. ...
  • Biot M.A., 1954, Theory of stress-strain relations in an isotropic ...
  • Biot M.A., 1955, Variational principal in irreversible thermodynamics with application ...
  • Gurtin M.E., Sternberg E., 1962, On the linear theory of ...
  • Iiioushin A.A., Pobedria B.E., 1970, Mathematical Theory of Thermal Viscoelasticity, ...
  • Tanner R.I., 1988, Engineering Rheology, Oxford University Press. ...
  • Freudenthal A.M., 1954, Effect of rheological behaviour on thermal stress, ...
  • Cattaneo C., 1958, Sur une forme de l e quation ...
  • Puri P., Kythe P.K., 1999, Non-classical thermal effects in Stoke ...
  • Caputo M., 1967, Linear models of dissipation whose Q is ...
  • Podlubny I., 1999, Fractional Differential Equations, Academic Press, New York. ...
  • Kiryakova V., 1994, Generalized Fractional Calculus and Applications, In: Pitman ...
  • Miller K.S., Ross B., 1994, An Introduction to the Fractional ...
  • Samko S.G., Kilbas A.A., Marichev O.I., 1993, Fractional Integrals and ...
  • Oldman K.B., Spanier J., 1974, The Fractional Calculus, Academic Press, ...
  • Gorenflo R., Mainardi F., 1997, Fractional Calculus: Integral and Differential ...
  • Hilfer R., 2000, Applications of Fraction Calculus in Physics, World ...
  • Khan M., Anjum A., Fetecau C., Haitao Q., 2010, Exact ...
  • Hyder S., Haitao Q., 2010, Starting solutions for a viscoelastic ...
  • Haitao G., Hui J., 2010, Unsteady helical flows of a ...
  • Saadatmandi A., Dehghan M., 2010, A new operational matrix for ...
  • Kimmich R., 2002, Strange kinetics, porous media, and NMR., Chemical ...
  • Fujita Y., 1990, Integrodifferential equation which interpolates the heat equation ...
  • Povstenko Y.Z., 2004, Fractional heat conductive and associated thermal stress, ...
  • Povstenko Y.Z., 2011, Fractional catteneo-type equations and generalized thermoelasticity, Journal ...
  • Sherief H.H., El-Said A., Abd El-Latief A., 2010, Fractional order ...
  • Lord H., Shulman Y., 1967, A generalized dynamical theory of ...
  • Lebon G., Jou D., Casas-Vázquez J., 2008, Undersyanding Non-equilibrium Thermodynamics: ...
  • Jou D., Casas-Vázquez J., Lebon G., 1988, Extended irreversible thermodynamics, ...
  • Youssef H., 2010, Theory of fractional order generalized thermoelasticity, Journal ...
  • Jumarie G., 2010, Derivation and solutions of some fractional Black-Scholes ...
  • El-Karamany A.S., Ezzat M.A., 2011, Convolutional variational principle, reciprocal and ...
  • El-Karamany A.S., Ezzat M.A., 2011, On the fractional Thermoelasticity, Mathematics ...
  • Ezzat M.A., El Karamany A.S., Fayik M.A., 2012, Fractional order ...
  • El-Karamany A.S., Ezzat M.A., 2011, Fractional order theory of a ...
  • Sur A., Kanoria M., 2012, Fractional order two-temperature thermoelasticity with ...
  • Roychoudhuri S.K., Dutta P.S., 2005, Thermoelastic interaction without energy dissipation ...
  • Tzou D.Y., 1995, A unified field approach for heat conduction ...
  • Ezzat M., 2010, Thermoelectric MHD non-newtonian fluid with fractional derivative ...
  • Honig G., Hirdes U., 1984, A method for the numerical ...
  • Quintanilla R., Racke R., 2008, A note on stability in ...
  • Kanoria M., Mallik S.H., Generalized thermoviscoelastic interaction due to periodically ...
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