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Hygrothermoelastic response in a hollow cylinder considering dual-phase-lag heat-moisture coupling

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Abstract

With the development of micro/nanoscale electromechanical systems and the wide applications of ultrashort pulse lasers, the classical and hyperbolic hygrothermal coupled models fail to predict the micro/nanoscale hygrothermoelastic responses. This paper presents a dual-phase-lag hygrothermal coupled model to analyze the transient responses of an infinitely long hollow cylinder subjected to hygrothermal loadings at the inner surface. By using the method of separating variables and the Laplace transform, the closed form solutions of temperature, moisture, displacement and stresses are obtained. The effects of the phase-lags of heat flux, moisture flux, temperature gradient and concentration gradient on the responses are calculated and displayed graphically. The present results are also compared with those based on the classical and hyperbolic models, which can be viewed as two special cases of the dual-phase-lag model. It can be shown that the phase-lags parameters play an essential role in controlling the heat and moisture transfer process.

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References

  1. Sih, G.C., Shih, M.T.: Transient hygrothermal stresses in composites: coupling of moisture and heat with temperature varying diffusivity. Int. J. Eng. Sci. 18(1), 19–42 (1980)

    Article  Google Scholar 

  2. Chang, W.J., Chen, T.C., Weng, C.I.: Transient hygrothermal stresses in an infinitely long annular cylinder: coupling of heat and moisture. J. Therm. Stress. 14(4), 439–454 (1991)

    Article  Google Scholar 

  3. Chang, W.J.: Transient hygrothermal responses in a solid cylinder by linear theory of coupled heat and moisture. Appl. Math. Model. 18(8), 467–473 (1994)

    Article  Google Scholar 

  4. Chen, T.C., Weng, C.I., Chang, W.J.: Transient hygrothermal stresses induced in general plane problems by theory of coupled heat and moisture. J. Appl. Mech. Trans. ASME 59(2S), S10–6 (1992)

    Article  Google Scholar 

  5. Chen, T.C., Hwang, B.H.: Transient hygrothermal stresses induced in two dimensional problems by nonlinear theory of coupled heat and moisture. J. Appl. Mech. Trans. ASME 61(4), 938–943 (1994)

    Article  Google Scholar 

  6. Sobhy, M.: An accurate shear deformation theory for vibration and buckling of FGM sandwich plates in hygrothermal environment. Int. J. Mech. Sci. 110, 62–77 (2016)

    Article  Google Scholar 

  7. Ebrahimi, F., Barati, M.R.: Hygrothermal effects on vibration characteristics of viscoelastic FG nanobeams based on nonlocal strain gradient theory. Compos. Struct. 159, 433–444 (2017)

    Article  Google Scholar 

  8. Xu, M.T., Guo, J.F., Wang, L.Q., Cheng, L.: Thermal wave interference as the origin of the overshooting phenomenon in dual-phase-lagging heat conduction. Int. J. Therm. Sci. 50(5), 825–830 (2011)

    Article  Google Scholar 

  9. Qiu, T.Q., Tien, C.L.: Short-pulse laser heating on metals. Int. J. Heat Mass Transf. 35(3), 719–726 (1992)

    Article  Google Scholar 

  10. Joseph, D.D., Preziosi, L.: Heat waves. Rev. Mod. Phys. 61, 41–73 (1989)

    Article  MathSciNet  Google Scholar 

  11. Chester, M.: Second sound in solids. Phys. Rev. 131, 2013–2015 (1963)

    Article  Google Scholar 

  12. Zhang, X.Y., Peng, Y., Xie, Y.J., Li, X.F.: Hygrothermoelastic response of a hollow cylinder based on a coupled time-fractional heat and moisture transfer model. Z. Angew. Math. Phys. 70(2), 1–21 (2019)

    MathSciNet  MATH  Google Scholar 

  13. Cattaneo, C.: A form of heat conduction equation which eliminates the paradox of instantaneous propagation. Comp. Rend. 247(4), 431–433 (1958)

    MATH  Google Scholar 

  14. Vernotte, P.: Paradoxes in the continuous theory of the heat conduction. Comp. Rend. 246, 3154–3155 (1958)

    MathSciNet  MATH  Google Scholar 

  15. Yang, W.Z., Chen, Z.T.: Investigation of the thermal-elastic problem in cracked semi-infinite FGM under thermal shock using hyperbolic heat conduction theory. J. Therm. Stress. 42(8), 993–1010 (2019)

    Article  Google Scholar 

  16. Lee, H.L., Chen, W.L., Chang, W.J., Yang, Y.C.: Estimation of surface heat flux and temperature distributions in a multilayer tissue based on the hyperbolic model of heat conduction. Comput. Methods Biomech. Biomed. Eng. 18(14), 1525–1534 (2015)

    Article  Google Scholar 

  17. Xue, Z.N., Chen, Z.T., Tian, X.G.: Transient thermal stress analysis for a circumferentially cracked hollow cylinder based on memory-dependent heat conduction model. Theor. Appl. Fract. Mech. 96, 123–133 (2018)

    Article  Google Scholar 

  18. Xue, Z.N., Chen, Z.T., Tian, X.G.: Thermoelastic analysis of a cracked strip under thermal impact based on memory-dependent heat conduction model. Eng. Fract. Mech. 200, 479–498 (2018)

    Article  Google Scholar 

  19. Peng, Y., Zhang, X.Y., Xie, Y.J., Li, X.F.: Transient hygrothermoelastic response in a cylinder considering non-Fourier hyperbolic heat-moisture coupling. Int. J. Heat Mass Transf. 126, 1094–1103 (2018)

    Article  Google Scholar 

  20. Xue, Z.N., Tian, X.G., Liu, J.L.: Non-classical hygrothermal fracture behavior of a hollow cylinder with a circumferential crack. Eng. Fract. Mech. 224, 106805 (2020)

    Article  Google Scholar 

  21. Majumdar, A.: Microscale heat conduction in dielectric thin films. J. Heat Transf. Trans. ASME 115(1), 7–16 (1993)

    Article  Google Scholar 

  22. Moshi, A.A., Majumdar, A.: Transient ballistic and diffusive phonon heat transport in thin films. J. Appl. Phys. 74(1), 31–39 (1993)

    Article  Google Scholar 

  23. Tzou, D.Y.: A unified field approach for heat conduction from macro-to micro-scales. J. Heat Transf. Trans. ASME 117(1), 8–16 (1995)

    Article  Google Scholar 

  24. Tzou, D.Y.: Experimental support for the lagging behavior in heat propagation. J. Thermophys. Heat Transf. 9(4), 686–693 (1995)

    Article  Google Scholar 

  25. Liu, K.C., Chen, H.T.: Investigation for the dual phase lag behavior of bio-heat transfer. Int. J. Therm. Sci. 49(7), 1138–1146 (2010)

    Article  Google Scholar 

  26. Liu, K.C., Lin, C.T.: Solution of an inverse heat conduction problem in bi-layer spherical tissue. Numer. Heat Transf. A Appl. 58(10), 802–818 (2010)

    Article  Google Scholar 

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

    Article  Google Scholar 

  28. Zhou, J.H., Zhang, Y.W., Chen, J.K.: An axisymmetric dual-phase-lag bioheat model for laser heating of living tissues. Int. J. Therm. Sci. 48(8), 1477–1485 (2009)

    Article  Google Scholar 

  29. Liu, K.C., Wang, Y.N., Chen, Y.S.: Investigation on the bio-heat transfer with the dual-phase-lag effect. Int. J. Therm. Sci. 58, 29–35 (2012)

    Article  Google Scholar 

  30. Guo, S.L., Wang, B.L., Li, J.E.: Surface thermal shock fracture and thermal crack growth behavior of thin plates based on dual-phase-lag heat conduction. Theor. Appl. Fract. Mech. 96, 105–113 (2018)

    Article  Google Scholar 

  31. Majchrzak, E., Mochnacki, B.: Dual-phase lag model of thermal processes in a multi-layered microdomain subjected to a strong laser pulse using the implicit scheme of FDM. Int. J. Therm. Sci. 133, 240–251 (2018)

    Article  Google Scholar 

  32. Borjalilou, V., Asghari, M., Bagheri, E.: Small-scale thermoelastic damping in microbeams utilizing the modified couple stress theory and the dual-phase-lag heat conduction model. J. Therm. Stress. 5, 1–14 (2019)

    Google Scholar 

  33. Chang, W.J., Weng, C.I.: An analytical solution of a transient hygrothermal problem in an axisymmetric double-layer annular cylinder by linear theory of coupled heat and moisture. Appl. Math. Model. 21, 721–734 (1997)

    Article  Google Scholar 

  34. Jiang, F.M., Liu, D.Y.: Transient thin layer model for heat and mass transfer processes. J. Grad. Sch. Chin. Acad. Sci. 17(1), 28–35 (2000) (in Chinese)

  35. Brancik, L.: Programs for fast numerical inversion of Laplace transforms in MATLAB language environment. In: Proceedings of the 7th Conference MATLAB’99, Czech Republic, Prague, pp. 27–39 (1999)

  36. Brancık, L.: Utilization of quotient-difference algorithm in FFT-based numerical ILT method. In: Proceedings of the 11th International Czech-Slovak Scientific Conference Radioelektronika, Czech Republic, Brno, pp. 352–355 (2001)

  37. Sih, G.C., Michopoulos, J., Chou, S.C.: Hygrothermoelasticity. Martinus Niijhoof Publishing, Dordrecht (1986)

    Book  Google Scholar 

  38. Loh, J.S., Azid, I.A., Seetharamu, K.N., Quadir, G.A.: Fast transient thermal analysis of Fourier and non-Fourier heat conduction. Int. J. Heat Mass Transf. 50(21–22), 4400–4408 (2007)

    Article  Google Scholar 

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Acknowledgements

This study is supported by the National Natural Science Foundation of China (11972375, 11732007), China Postdoctoral Science Foundation funded project (2019TQ0355), Qingdao Postdoctoral Applied Research Program (qd20190007), and Open Projects of State Key Laboratory for Strength and Vibration of Mechanical Structures (SV2020-KF-12).

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Authors and Affiliations

  1. Department of Engineering Mechanics, College of Pipeline and Civil Engineering, China University of Petroleum (East China), Qingdao, 266580, China

    Zhangna Xue & Jianlin Liu

  2. State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an, 710049, China

    Xiaogeng Tian

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  1. Zhangna Xue
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  2. Xiaogeng Tian
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  3. Jianlin Liu
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Correspondence to Zhangna Xue or Jianlin Liu.

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Appendix

Appendix

$$\begin{aligned} d= & {} \eta \lambda \chi a_{1} ,\;\;e_{1} =\left( {1+\tau _{Th} s} \right) k_{1}^{2} -a_{1} ,\;\;e_{2} =\left( {1+\tau _{Th} s} \right) k_{2}^{2} -a_{1} \\ f= & {} -e_{2} \bar{{\varphi }}_{0}^{*} \left( s \right) -d\bar{{\psi }}_{0}^{*} \left( s \right) \\ f_{1}= & {} \left( {de_{2} -de_{1} } \right) I_{0} \left( {k_{1} } \right) \;\;f_{2} =\left( {de_{2} -de_{1} } \right) K_{0} \left( {k_{1} } \right) \\ h_{1}= & {} I_{1} \left( {k_{1} \rho _{2} } \right) ,\;\;h_{2} =K_{1} \left( {k_{1} \rho _{2} } \right) \\ g_{1}= & {} e_{1} k_{2} I_{0} \left( {k_{1} } \right) K_{1} \left( {k_{2} \rho _{2} } \right) +e_{2} k_{1} I_{1} \left( {k_{1} \rho _{2} } \right) K_{0} \left( {k_{2} } \right) \\ g_{2}= & {} e_{1} k_{2} K_{0} \left( {k_{1} } \right) K_{1} \left( {k_{2} \rho _{2} } \right) -e_{2} k_{1} K_{0} \left( {k_{2} } \right) K_{1} \left( {k_{1} \rho _{2} } \right) \\ g_{3}= & {} e_{2} k_{2} I_{0} \left( {k_{2} } \right) K_{1} \left( {k_{2} \rho _{2} } \right) +e_{2} k_{2} I_{1} \left( {k_{2} \rho _{2} } \right) K_{0} \left( {k_{2} } \right) \\ g_{4}= & {} k_{2} K_{1} \left( {k_{2} \rho _{2} } \right) \bar{{\psi }}_{0}^{*} \left( s \right) \end{aligned}$$

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Xue, Z., Tian, X. & Liu, J. Hygrothermoelastic response in a hollow cylinder considering dual-phase-lag heat-moisture coupling. Z. Angew. Math. Phys. 71, 23 (2020). https://doi.org/10.1007/s00033-019-1246-4

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