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Basic Problems of Non-Fourier Heat Conduction

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Advanced Thermal Stress Analysis of Smart Materials and Structures

Part of the book series: Structural Integrity ((STIN,volume 10))

Abstract

In this chapter, the non-Fourier heat conduction equations along with the boundary and initial conditions are solved for one-dimensional (1D) media with semi-infinite or finite dimensions in Cartesian, cylindrical, and spherical coordinates.

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References

  1. Tzou D, Guo Z-Y (2010) Nonlocal behavior in thermal lagging. Int J Therm Sci 49(7):1133–1137

    Article  Google Scholar 

  2. Tzou D (2011) Nonlocal behavior in phonon transport. Int J Heat Mass Transf 54(1):475–481

    Article  MathSciNet  Google Scholar 

  3. Tzou DY (2014) Macro-to microscale heat transfer: the lagging behavior. Wiley

    Google Scholar 

  4. Akbarzadeh A, Fu J, Chen Z (2014) Three-phase-lag heat conduction in a functionally graded hollow cylinder. Trans Can Soc Mech Eng 38(1):155

    Article  Google Scholar 

  5. Youssef HM (2010) Theory of fractional order generalized thermoelasticity. J Heat Transf 132(6):061301

    Article  Google Scholar 

  6. Ezzat MA, El Karamany AS, Fayik MA (2012) Fractional order theory in thermoelastic solid with three-phase lag heat transfer. Arch Appl Mech 82(4):557–572

    Article  Google Scholar 

  7. Akbarzadeh A, Cui Y, Chen Z (2017) Thermal wave: from nonlocal continuum to molecular dynamics. RSC Adv 7(22):13623–13636

    Article  Google Scholar 

  8. Akbarzadeh A, Pasini D (2014) Phase-lag heat conduction in multilayered cellular media with imperfect bonds. Int J Heat Mass Transf 75:656–667

    Article  Google Scholar 

  9. Plimpton S (1995) Fast parallel algorithms for short-range molecular dynamics. J Comput Phys 117(1):1–19

    Article  Google Scholar 

  10. Nosé S (1984) A unified formulation of the constant temperature molecular dynamics methods. J Chem Phys 81(1):511–519

    Article  Google Scholar 

  11. Foiles S, Baskes M, Daw M (1986) Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. Phys Rev B 33(12):7983

    Article  Google Scholar 

  12. Liu Q, Jiang P, Xiang H (2008) Molecular dynamics simulations of non-Fourier heat conduction. Progr Nat Sci 18(8):999–1007

    Article  Google Scholar 

  13. Tan T et al (2011) Mechanical properties of functionally graded hierarchical bamboo structures. Acta Biomater 7(10):3796–3803

    Article  Google Scholar 

  14. Rahbar N, Soboyejo W (2011) Design of functionally graded dental multilayers. Fatigue Fract Eng Mater Struct 34(11):887–897

    Article  Google Scholar 

  15. Miserez A et al (2008) The transition from stiff to compliant materials in squid beaks. Science 319(5871):1816–1819

    Article  Google Scholar 

  16. Reddy J, Chin C (1998) Thermomechanical analysis of functionally graded cylinders and plates. J Therm Stresses 21(6):593–626

    Article  Google Scholar 

  17. Vel SS, Batra R (2003) Three-dimensional analysis of transient thermal stresses in functionally graded plates. Int J Solids Struct 40(25):7181–7196

    Article  Google Scholar 

  18. Guo L, Wang Z, Noda N (2012) A fracture mechanics model for a crack problem of functionally graded materials with stochastic mechanical properties. Proc R Soc A 468(2146), 2939–2961. The Royal Society

    Article  MathSciNet  Google Scholar 

  19. Kieback B, Neubrand A, Riedel H (2003) Processing techniques for functionally graded materials. Mater Sci Eng, A 362(1):81–106

    Article  Google Scholar 

  20. Overvelde JT et al (2016) A three-dimensional actuated origami-inspired transformable metamaterial with multiple degrees of freedom. Nat Commun 7:10929

    Article  Google Scholar 

  21. Bartlett NW et al (2015) A 3D-printed, functionally graded soft robot powered by combustion. Science 349(6244):161–165

    Article  Google Scholar 

  22. Akbarzadeh A, Abedini A, Chen Z (2015) Effect of micromechanical models on structural responses of functionally graded plates. Compos Struct 119:598–609

    Article  Google Scholar 

  23. Akbarzadeh A, Chen Z (2013) Heat conduction in one-dimensional functionally graded media based on the dual-phase-lag theory. Proc Inst Mech Eng Part C J Mech Eng Sci 227(4):744–759

    Article  Google Scholar 

  24. Babaei M, Chen Z (2008) Hyperbolic heat conduction in a functionally graded hollow sphere. Int J Thermophys 29(4):1457–1469

    Article  Google Scholar 

  25. Choudhuri SR (2007) On a thermoelastic three-phase-lag model. J Therm Stresses 30(3):231–238

    Article  Google Scholar 

  26. Ramadan K (2009) Semi-analytical solutions for the dual phase lag heat conduction in multilayered media. Int J Therm Sci 48(1):14–25

    Article  Google Scholar 

  27. Akbarzadeh A, Chen Z (2013) On the harmonic magnetoelastic behavior of a composite cylinder with an embedded polynomial eigenstrain. Compos Struct 106:296–305

    Article  Google Scholar 

  28. Chen T (2001) Thermal conduction of a circular inclusion with variable interface parameter. Int J Solids Struct 38(17):3081–3097

    Article  Google Scholar 

  29. Wang M, Pan N (2008) Modeling and prediction of the effective thermal conductivity of random open-cell porous foams. Int J Heat Mass Transf 51(5):1325–1331

    Article  Google Scholar 

  30. Arabnejad S, Pasini D (2013) Mechanical properties of lattice materials via asymptotic homogenization and comparison with alternative homogenization methods. Int J Mech Sci 77:249–262

    Article  Google Scholar 

  31. Akbarzadeh A et al (2016) Electrically conducting sandwich cylinder with a planar lattice core under prescribed eigenstrain and magnetic field. Compos Struct 153:632–644

    Article  MathSciNet  Google Scholar 

  32. Mirabolghasemi A, Akbarzadeh AH, Rodrigue D, Therriault D (2019) Thermal conductivity of architected cellular metamaterials. Acta Materialia 174:61–80

    Article  Google Scholar 

  33. Ashby MF, Cebon D (1993) Materials selection in mechanical design. Le Journal de Physique IV 3(C7):C7-1–C7-9

    Google Scholar 

  34. Akbarzadeh A, Chen Z (2012) Transient heat conduction in a functionally graded cylindrical panel based on the dual phase lag theory. Int J Therm 33(6):1100–1125

    Article  Google Scholar 

  35. Quintanilla R, Racke R (2006) A note on stability in dual-phase-lag heat conduction. Int J Heat Mass Transf 49(7):1209–1213

    Article  Google Scholar 

  36. Akbarzadeh AH, Chen ZT (2014) Dual phase lag heat conduction in functionally graded hollow spheres. Int J Appl Mech 6(1):1450002

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Alberta, Edmonton, Canada

    Prof. Dr. Zengtao Chen

  2. Department of Bioresource Engineering, McGill University, Island of Montreal, QC, H9X 3V9, Canada

    Dr. Abdolhamid Akbarzadeh

  3. Department of Mechanical Engineering, McGill University, Montreal, QC, H3A 0C3, Canada

    Dr. Abdolhamid Akbarzadeh

Authors
  1. Prof. Dr. Zengtao Chen
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  2. Dr. Abdolhamid Akbarzadeh
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Corresponding author

Correspondence to Zengtao Chen .

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Chen, Z., Akbarzadeh, A. (2020). Basic Problems of Non-Fourier Heat Conduction. In: Advanced Thermal Stress Analysis of Smart Materials and Structures. Structural Integrity, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-030-25201-4_2

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  • DOI: https://doi.org/10.1007/978-3-030-25201-4_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-25200-7

  • Online ISBN: 978-3-030-25201-4

  • eBook Packages: EngineeringEngineering (R0)

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