Meccanica

, Volume 51, Issue 5, pp 1127–1133 | Cite as

An approach of a heat-flux dependent theory for micropolar porous media

Article
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Abstract

This study is dedicated to a micropolar porous body, including voidage time derivative among the independent constitutive variables. We formulate a heat-flux theory in this context taking into account a new set of state variables that includes the heat-flux vector and an evolution equation for it. The mixed initial boundary value problems have the specific feature that the governing system of equations consists of hyperbolic field equations only. Consistency of the theory is supported by a result of uniqueness.

Keywords

Micropolar Voids Thermoelastic body Heat-flux 
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Notes

Acknowledgments

Author is very thankful to the referees for their valuable criticism, comments and help in improvement of the manuscript.

References

  1. 1.
    Nunziato JW, Cowin SC (1979) A nonlinear theory of elastic materials with voids. Arch Ration Mech Anal 72:175–201MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Cowin SC, Nunziato JW (1983) Linear elastic materials with voids. J Elast 13:125–147CrossRefMATHGoogle Scholar
  3. 3.
    Iesan D (1984) A theory of thermoelastic materials with voids. Acta Mech 60:67–89CrossRefGoogle Scholar
  4. 4.
    Eringen AC (2003) Micropolar mixture theory of porous media. J Appl Phys 94(6):4184–4190ADSCrossRefGoogle Scholar
  5. 5.
    Iesan D, Quintanilla R (2013) Non-linear deformations of porous elastic solids Int. J Non-Linear Mech 49:57–65CrossRefGoogle Scholar
  6. 6.
    Marin M (2009) On the minimum principle for dipolar materials with stretch. Nonlinear Anal R W A 10(3):1572–1578MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Marin M, Stan G (2013) Weak solutions in elasticity of dipolar bodies with stretch. Carpath J Math 29(1):33–40MathSciNetMATHGoogle Scholar
  8. 8.
    Marin M, Agarwal RP, Mahmoud SR (2013) Nonsimple material problems addressed by the Lagrange’s identity boundary value problems, 2013. Art. Id. 135: doi: 10.1186/1687-2770-2013-135
  9. 9.
    Marin M, Agarwal RP, Mahmoud SR (2013) Modeling a microstretch thermoelastic body with two temperatures, Abst Appl Anal, ID 583464, 7 p., doi: 10.1155/2013/583464 (2013)
  10. 10.
    Marin M, Florea O (2014) On temporal behaviour of solutions in thermoelasticity of porous micropolar bodies. Ann Sci Univ Ovidius Ser Math 22(1):169–188MathSciNetMATHGoogle Scholar
  11. 11.
    Sharma K, Marin M (2014) Reflection and transmission of waves from imperfect boundary between two heat conducting micropolar thermoelastic solids. Ann Sci Univ Ovidius Ser Math 22(2):151–175MathSciNetMATHGoogle Scholar
  12. 12.
    Singh SS (2013) Transverse wave at a plane interface in thermo-elastic materials with voids. Meccanica 48(1):617–630MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Mller I, Ruggeri T (1998) Rational extended thermodynamics. Springer, New YorkCrossRefGoogle Scholar
  14. 14.
    Jou D, Casas-Vazquez J, Lebon G (2010) Extended irreversible thermodynamics, 4th edn. Springer, BerlinCrossRefMATHGoogle Scholar
  15. 15.
    Lebon G, Jou D, Casas-Vazquez J (2008) Understanding nonequilibrium thermodynamics: foundations, applications, frontiers. Springer, BerlinCrossRefMATHGoogle Scholar
  16. 16.
    Lebon G (1982) A generalized theory of thermoelasticity. J Tech Phys. 23:37–46MATHGoogle Scholar
  17. 17.
    Lebon G (2014) Heat conduction ant micro and nano scales: a review through the prism of extended irreversible thermodynamics. J Non-Equilib Thermodyn 39:35–58CrossRefGoogle Scholar
  18. 18.
    Cimmelli VA (2009) Different thermodynamic theories and different heat conduction laws. J Non-Equilib Thermodyn 34:299–333ADSCrossRefMATHGoogle Scholar
  19. 19.
    Alvarez FX, Jou D, Sellitto A (2010) Pore-size dependence of the thermal conductivity of porous silicon: a phonon-hydrodynamic approach. Appl Phys Lett 97:033103ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of MathematicsTransilvania University of BrasovBrasovRomania

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