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Coupled Problems in Thermodynamics

  • Elena A. IvanovaEmail author
  • Dmitry V. Matias
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 100)

Abstract

We consider three basic methods adopted in modern thermodynamics. We discuss the state of the art, current problems and development prospects. We also discuss the possibility and necessity of constructing mechanical models of thermal processes and models of other processes of “non-mechanical nature”. Next, we consider one of the possible mechanical models of thermal and electromagnetic processes. In order to illustrate the consequences of this model, we analyze the mutual influence of thermal and electromagnetic waves at the interface between two materials.

Keywords

Micropolar continuum Cosserat continuum Rotational degrees of freedom Thermodynamics Electrodynamics Wave propagation 

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References

  1. Ananth P, Dinesh A, Sugunamma V, Sandeep N (2015) Effect of nonlinear thermal radiation on stagnation flow of a casson fluid towards a stretching sheet. Ind Eng Lett 5(8):70–79Google Scholar
  2. Babenkov MB, Ivanova EA (2014) Analysis of the wave propagation processes in heat transfer problems of the hyperbolic type. Continuum Mech Thermodyn 26(4):483–502Google Scholar
  3. Babenkov MB, Vitokhin EY (2018) Thermoelastic waves in a medium with heat-flux relaxation. In: Altenbach, H and Öchsner, A (ed) Encyclopedia of Continuum Mechanics, Springer, Berlin, HeidelbergGoogle Scholar
  4. Baik C, Lavine AS (1995) On hyperbolic heat conduction equation and the second law of thermody- namics. Trans ASME J Heat Transf 117:256 – 263Google Scholar
  5. Bardeen J, Cooper LN, Schrieffer JR (1957) Micromorphic theory of superconductivity. The Phys Rev 106(1):162–164Google Scholar
  6. Barletta A, Zanchini E (1997) Hyperbolic heat conduction and local equilibrium: A second law analysis. Int J Heat Mass Transf 40(5):1007 – 1016Google Scholar
  7. Biot MA (1970) Variational Principles in Heat Transfer: A Unified Lagrangian Analysis of Dissipative Phenomena. Oxford Mathematical Monographs, Clarendon Press, OxfordGoogle Scholar
  8. Biot MA (1984) New variational-Lagrangian irreversible thermodynamics with application to viscous flow, reaction–diffusion, and solid mechanics. Advances in Applied Mechanics 24:1 – 91Google Scholar
  9. Boltzmann L (1974) Theoretical Physics and Philosophical Problems: Selected Writings. D. Reidel Publishing Company, BostonGoogle Scholar
  10. Campo A (1982) Estimate of the transient conduction of heat in materials with linear thermal properties based on the solution for constant properties. Heat and Mass Transf 17(1):1–9Google Scholar
  11. Čápek V, Sheehan DP (2005) Challenges to the Second Law of Thermodynamics. Theory and Experiment. SpringerGoogle Scholar
  12. Cataneo C (1958) A form of heat conduction equation which eliminates the paradox of instantaneous propagation. Compte Rendus 247:431–433Google Scholar
  13. Chaibi M, Fernández T, Mimouni A, Rodriguez-Tellez J, Tazón A, Mediavilla A (2012) Nonlinear modeling of trapping and thermal effects on GaAs and GaN MESFET/HEMT devices. Progr Electromagn Res 124:163–186Google Scholar
  14. Chandrasekharaiah DS (1998) Hyperbolic thermoelasticity: A review of recent literature. Appl Mech Rev 51:705–729Google Scholar
  15. De Groot SR (1951) Thermodynamics of Irreversible Processes. North Holland, AmsterdamGoogle Scholar
  16. Dixon RC, Eringen AC (1964) A dynamical theory of polar elastic dielectrics — I. Int J Engng Sci 2:359–377Google Scholar
  17. Dixon RC, Eringen AC (1965) A dynamical theory of polar elastic dielectrics — II. Int J Engng Sci 3:379–398Google Scholar
  18. Dugdale JS (1996) Entropy and its Physical Meaning. Taylor & Francis, LondonGoogle Scholar
  19. Duhem P (1954) The Aim and Structure of Physical Theory. Princeton Univercity Press, Princeton, New JerseyGoogle Scholar
  20. Ebadian A, Darania P (2008) Study of exact solutions of nonlinear heat equations. Comput Appl Math 27(2):107–121Google Scholar
  21. Eisenschitz R (1958) Statistical Theory of Irreversible Processes. Oxford University Press, LondonGoogle Scholar
  22. Eringen AC (2003) Continuum theory of micromorphic electromagnetic thermoelastic solids. Int J Engng Sci 41:653–665Google Scholar
  23. Eringen AC, Maugin GA (1990) Electrodynamics of Continua. Springer–Verlag, New YorkGoogle Scholar
  24. Feynman RP, Leighton RB, Sands M (1963) The Feynman Lectures on Physics. Mainly Mechanics, Radiation, and Heat, vol 1. Addison Wesley Publishing Company, LondonGoogle Scholar
  25. Fomethe A, Maugin GA (1996) Material forces in thermoelastic ferromagnets. Continuum Mech Thermodyn 8:275–292Google Scholar
  26. Fong E, Lam TT, Davis SE (2010) Nonlinear heat conduction in isotropic and orthotropic materials with laser heat source. J Thermophys Heat Transf 24(1):104–111Google Scholar
  27. Galeş C, Ghiba ID, Ignătescu I (2011) Asymptotic partition of energy in micromorphic thermopiezo-electricity. Journal of Thermal Stresses 34:1241–1249Google Scholar
  28. Gay-Balmaz F, Yoshimura H (2019) From Lagrangian mechanics to nonequilibrium thermodynamics: A variational perspective. Entropy 21(1), doi: https://doi.org/10.3390/e21010008, 8
  29. Grekova E, Zhilin P (2001) Basic equations of Kelvin’s medium and analogy with ferromagnets. Journal of Elasticity 64:29–70Google Scholar
  30. Grekova EF (2001) Ferromagnets and Kelvin’s medium: Basic equations and wave processes. Journal of Computational Acoustics 9(2):427–446Google Scholar
  31. Grudinin I, Lee H, Chen T, Vahala K (2011) Compensation of thermal nonlinearity effect in optical resonators. Opt Express 19(8):7365–7372Google Scholar
  32. Habibi M, Oloumi M, Hosseinkhani H, Magidi S (2015) Numerical investigation into the highly nonlinear heat transfer equation with Bremsstrahlung emission in the inertial confinement fusion plasmas. Contrib Plasma Phys 55(9):677–684Google Scholar
  33. Huang C, Fan J, Zhu L (2012) Dynamic nonlinear thermal optical effects in coupled ring resonators. AIP Adv 2(032131):1–8Google Scholar
  34. Huang K (1963) Statistical Mechanics. John Wiley and Sons, New YorkGoogle Scholar
  35. Ignaczak J, Ostoja-Starzewski M (2009) Thermoelasticity with Finite Wave Speeds. Oxford Science Publications, OxfordGoogle Scholar
  36. Ivanova EA (2010) Derivation of theory of thermoviscoelasticity by means of two-component medium. Acta Mech 215:261–286Google Scholar
  37. Ivanova EA (2011) On one model of generalized continuum and its thermodynamical interpretation. In: Altenbach H, Maugin GA, Erofeev V (eds) Mechanics of Generalized Continua, Springer, Berlin, Heidelberg, Advanced Structured Materials, vol 7, pp 151–174Google Scholar
  38. Ivanova EA (2012) Derivation of theory of thermoviscoelasticity by means of two-component Cosserat continuum. Tech Mech 32:273–286Google Scholar
  39. Ivanova EA (2014) Description of mechanism of thermal conduction and internal damping by means of two-component Cosserat continuum. Acta Mech 225:757–795Google Scholar
  40. Ivanova EA (2015) A new model of a micropolar continuum and some electromagnetic analogies. Acta Mech 226:697–721Google Scholar
  41. Ivanova EA (2017) Description of nonlinear thermal effects by means of a two-component Cosserat continuum. Acta Mech 228:2299–2346Google Scholar
  42. Ivanova EA (2018) Thermal effects by means of two-component cosserat continuum. In: Altenbach H, Öchsner A (eds) Encyclopedia of Continuum Mechanics, Springer, Berlin, pp 1–12Google Scholar
  43. Ivanova EA (2019a) On micropolar continuum approach to some problems of thermo- and electrodynamics. Acta Mech 230:1685–1715Google Scholar
  44. Ivanova EA (2019b) Towards micropolar continuum theory describing some problems of thermo- and electrodynamics. In: Altenbach H, Irschik H, Metveenko V (eds) Contributions to Advanced Dynamics and Continuum Mechanics, Springer, Cham, Advanced Structured Materials, vol 114, pp 1–19Google Scholar
  45. Ivanova EA, Kolpakov YE (2013) Piezoeffect in polar materials using moment theory. J Appl Mech Tech Phys 54(6):989–1002Google Scholar
  46. Ivanova EA, Kolpakov YE (2016) A description of piezoelectric effect in non-polar materials taking into account the quadrupole moments. Z Angew Math Mech 96(9):1033–1048Google Scholar
  47. Jordan A, Khaldi S, Benmouna M, Borucki A (1987) Study of non-linear heat transfer problems. Revue de Physique Appliqueé 22(1):101–105Google Scholar
  48. Jou D, Casas-Vazquez J, Lebon G (2001) Extended Irreversible Thermodynamics. Springer, BerlinGoogle Scholar
  49. Khandekar C, Pick A, Johnson SG, Rodriguez AW (2015) Radiative heat transfer in nonlinear Kerr media. Phys Rev B 91(115406):1–9Google Scholar
  50. Kittel C (1970) Thermal Physics. John Wiley and Sons, New YorkGoogle Scholar
  51. Kondepudi D, Prigogine I (1998) Modern Thermodynamics: From Heat Engines to Dissipative Structures. Wiley, ChichesterGoogle Scholar
  52. Krylov NS (2003) Works on the Substantiation of Statistical Physics (in Russ.). Editorial URSS, MoscowGoogle Scholar
  53. Kubo R (1965) Statistical Mechanics. Elsevier Science Publishers B.V., AmsterdamGoogle Scholar
  54. Lebon G, Casas-Vazquez J (1974) Lagrangian formulation of unsteady non-linear heat transfer problems. J Enging Math 8(1):31 – 44Google Scholar
  55. Lebon G, Dauby PC (1990) Heat transport in dielectric crystals at low temperature: a variational formulation based on extended irreversible thermodynamics. Phys Rev A 42:4710 – 4715Google Scholar
  56. LeMesurier B (2008) Modeling thermal effects on nonlinear wave motion in biopolymers by a stochastic discrete nonlinear Schrödinger equation with phase damping. Discrete and Contin Dyn Syst S 1(2):317–327Google Scholar
  57. Lieb EH, Yngvason J (1997) A guide to entropy and the second law of thermodynamics. Notices of the AMS (May):571 – 581Google Scholar
  58. Markides CN, Osuolale A, Solanki R, Stan GBV (2013) Nonlinear heat transfer processes in a two-phase thermofluidic oscillator. Appl Energy 104:958–977Google Scholar
  59. Maugin GA (1988) Continuum Mechanics of Electromagnetic Solids. Elsevier Science Publishers, OxfordGoogle Scholar
  60. Mottaghy D, Rath V (2006) Latent heat effects in subsurface heat transport modeling and their impact on palaeotemperature reconstructions. Geophys J Int 164:236–245Google Scholar
  61. Müller I (2007) A History of Thermodynamics. The Doctrine of Energy and Entropy. Springer, Berlin, Heidelberg, doi: https://doi.org/10.1007/978-3-540-46227-9
  62. Ostoja-Starzewski M (2016) Second law violations, continuum mechanics, and permeability. Continuum Mechanics and Thermodynamics 28(1-2):489–501, doi: https://doi.org/10.1007/s00161-015-0451-4
  63. Ostoja-Starzewski M (2017) Admitting spontaneous violations of the second law in continuum thermomechanics. Entropy 19(78):1–10, doi: https://doi.org/10.3390/e19020078
  64. Polyanin AD, Zhurov AI, Vyaz’min AV (2000) Exact solutions of nonlinear heat- and mass-transfer equations. Theor Found of Chem Eng 34(5):403–415Google Scholar
  65. Prigogine I (1955) Introduction to Thermodynamics of Irreversible Processes. Charles C. Thomas Publishers, SpringfieldGoogle Scholar
  66. Reif F (1967) Berkeley Physics Course, vol 5. Statistical Physics. McGraw-Hill Book Company, New YorkGoogle Scholar
  67. Röpke G (2013) Nonequilibrium Statistical Physics. Wiley-VCH, WeinheimGoogle Scholar
  68. Rubin MB (1992) Hyperbolic heat conduction and the second law. Int J Eng Sci 30(11):1665 – 1676Google Scholar
  69. Ruelle D (1978) Thermodynamic Formalism. The Mathematical Structures of Classical Equilibrium Statistical Mechanics. Addison-Wesley Publishing Company, LondonGoogle Scholar
  70. Shliomis MI, Stepanov VI (1993) Rotational viscosity of magnetic fluids: contribution of the Brownian and Néel relaxational processes. J Magnetism Magnetic Mat 122:196–199Google Scholar
  71. Straughan B (2011) Heat Waves, Applied Mathematical Sciences, vol 177. Springer, New YorkGoogle Scholar
  72. Tiersten HF (1964) Coupled magnetomechanical equations for magnetically saturated insulators. J Math Phys 5(9):1298–1318Google Scholar
  73. Treugolov IG (1989) Moment theory of electromagnetic effects in anisotropic solids. Journal of Applied Mathematics and Mechanics 53(6):786–790Google Scholar
  74. Vitokhin EY, Ivanova EA (2017) Dispersion relations for the hyperbolic thermal conductivity, thermoelasticity and thermoviscoelasticity. Continuum Mech Thermodyn 29(6):1219–1240Google Scholar
  75. Zanchini E (1999) Hyperbolic heat conduction theories and nondecreasing entropy. Phys Rev B Condens Matter Mater Phys 60(2):991 — 997Google Scholar
  76. Zhilin PA (2006a) Advanced Problems in Mechanics, vol 2. Institute for Problems in Mechanical Engineering, St. PetersburgGoogle Scholar
  77. Zhilin PA (2006b) Advanced Problems in Mechanics (In Russ.), vol 1. Institute for Problems in Mechanical Engineering, St. PetersburgGoogle Scholar
  78. Zhilin PA (2012) Rational Continuum Mechanics (in Russ.). Polytechnic University Publishing House, St. PetersburgGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Peter the Great St. Petersburg Polytechnic University, Department of Theoretical Mechanics, Institute of Applied Mathematics and MechanicsSt. PetersburgRussia
  2. 2.Laboratory of MechatronicsInstitute for Problems in Mechanical Engineering of Russian Academy of SciencesSt. PetersburgRussia

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