Top

Archive of Applied Mechanics

02-04-2024 | Original

Fractional dual-phase-lag hygrothermoelastic model for a sphere subjected to heat-moisture load

Authors: Shahala Sheikh, Lalsingh Khalsa, Gulshan Makkad, Vinod Varghese

Published in: Archive of Applied Mechanics

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

This paper proposes a non-Fourier model of heat and a non-Fick model of moisture diffusion coupling in unification with hygrothermoelasticity theory within the framework of time-fractional calculus theory. The generalized two-temperature theory of hygrothermoelasticity has been used to develop the relevant linearly coupled partial differential equations system. In the context of time-fractional calculus theory, we investigate a hygrothermal elastic problem for a centrally symmetric sphere exposed to physical heat and moisture load at its surface within the limited spherical region. The integral transform approach produces analytical formulas for the transient response of temperature change, moisture distribution, displacement, and stress components in the sphere for pulsed and continuous heat-moisture flux at the sphere’s surface. The Gaver–Stehfest procedure is used to invert the analytical hygrothermal variation solutions that were derived in the Laplace domain. The Kuznetsov convergence criterion has studied the problem’s stability and bounded variations. The effects of fractional order on the hygrothermal fields and hygrothermoelastic stress response are graphically represented and calculated using numerical data. The specific heat and moisture connection, which abides by Fourier heat conduction and Fick’s moisture diffusion, is recovered as a particular case when the fractional-order derivative reduces to the first-order derivative. The study reveals a significant coupling effect between temperature and moisture in composite material T300/5208, with a maximum discrepancy of up to 50%.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

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

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

Benkhedda, A., Tounsi, A., Addabedia, E.A.: Effect of temperature and humidity on transient hygrothermal stresses during moisture desorption in laminated composite plates. Compos. Struct. 82(4), 629–635 (2008)CrossRef

Zenkour, A.: Hygrothermoelastic responses of inhomogeneous piezoelectric and exponentially graded cylinders. Int. J. Press. Vessels Pip. 119, 8–18 (2014)CrossRef

Chiba, R., Sugano, Y.: Transient hygrothermoelastic analysis of layered plates with one-dimensional temperature and moisture variations through the thickness. Compos. Struct. 93(9), 2260–2268 (2011)CrossRef

Ishihara, M., Ootao, Y., Kameo, Y.: Hygrothermal field considering nonlinear coupling between heat and binary moisture diffusion in porous media. J. Therm. Stresses 37(10), 1173–1200 (2014)CrossRef

Mitra, K., Kumar, S., Vedevarz, A., Moallemi, M.K.: Experimental evidence of hyperbolic heat conduction in processed meat. ASME J. Heat Transf. 117(3), 568–573 (1995)CrossRef

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

Hetnarski, R.B., Ignaczak, J.: Generalized thermoelasticity. J. Therm. Stresses 22(4–5), 451–476 (1999)MathSciNet

10.

Lord, H.W., Shulman, Y.: A generalized dynamical theory of thermoelasticity. J. Mech. Phys. Solids 15(5), 299–309 (1967)CrossRef

11.

Green, A., Lindsay, K.: Thermoelasticity. J. Elast. 2(1), 1–7 (1972)CrossRef

12.

Hetnarski, R.B., Ignaczak, J.: Soliton-like waves in a low temperature nonlinear thermoelastic solid. Int. J. Eng. Sci. 34(15), 1767–1787 (1996)MathSciNetCrossRef

13.

Green, A., Naghdi, P.: Thermoelasticity without energy dissipation. J. Elast. 31(3), 189–208 (1993)MathSciNetCrossRef

14.

Tzou, D.Y.: A unified field approach for heat conduction from macro- to micro-scales. ASME J. Heat Transf. 117(1), 8–16 (1995). https://doi.org/10.1115/1.2822329CrossRef

15.

Chandrasekharaiah, D.: Hyperbolic thermoelasticity: a review of recent literature. Appl. Mech. Rev. 51(12), 705–730 (1998)CrossRef

16.

Metzler, R., Klafter, J.: The random walk’s guide to anomalous diffusion: a fractional dynamics approach. Phys. Rep. 339(1), 1–77 (2000)MathSciNetCrossRef

17.

Kimmich, R.: Strange kinetics, porous media, and NMR. Chem. Phys. 284(1–2), 253–285 (2002)CrossRef

18.

Fujita, Y.: Integrodifferential equation which interpolates the heat equation and the wave equation. Osaka J. Math. 27(2), 309–321 (1990)MathSciNet

19.

Luchko, Y., Mainardi, F., Povstenko, Y.: Propagation speed of the maximum of the fundamental solution to the fractional diffusion-wave equation. Comput. Math. Appl. 66(5), 774–784 (2013)MathSciNetCrossRef

20.

Chaves, A.: A fractional diffusion equation to describe Lévy flight. Phys. Lett. A 239(1–2), 13–16 (1998)MathSciNetCrossRef

21.

Zanette, D.H.: Macroscopic current in fractional anomalous diffusion. Phys. A 252(1–2), 159–164 (1998)CrossRef

22.

Gorenflo, R., Mainardi, F., Moretti, D., Paradisi, P.: Time fractional diffusion: a discrete random walk approach. Nonlinear Dyn. 29(1), 129–143 (2002)MathSciNetCrossRef

23.

Povstenko, Y.: Central symmetric solution to the Neumann problem for a time-fractional diffusion-wave equation in a sphere. Nonlinear Anal. Real World Appl. 13(3), 1229–1238 (2012)MathSciNetCrossRef

24.

Povstenko, Y.: Fractional heat conduction equation and associated thermal stress. J. Therm. Stresses 28(1), 83–102 (2004)MathSciNetCrossRef

25.

Sherief, H.H., El-Sayed, A., El-Latief, A.A.: Fractional order theory of thermoelasticity. Int. J. Solids Struct. 47(2), 269–275 (2010)CrossRef

26.

Youssef, H.M.: Theory of fractional order generalized thermoelasticity. ASME J. Heat Transf. 132(6), 061301 (2010)CrossRef

27.

Ezzat, M.A., El Karamany, A.S.: Theory of fractional order in electro-thermoelasticity. Eur. J. Mech. A. Solids 30(4), 491–500 (2011)CrossRef

28.

Jumarie, G.: Derivation and solutions of some fractional Black-Scholes equations in coarse-grained space and time—application to Merton’s optimal portfolio. Comput. Math. Appl. 59(3), 1142–1164 (2010)MathSciNetCrossRef

29.

Povstenko, Y.: Time-fractional thermoelasticity problem for a sphere subjected to the heat flux. Appl. Math. Comput. 257, 327–334 (2015)MathSciNet

30.

Andarwa, S., Tabrizi, H.B.: Non-Fourier effect in the presence of coupled heat and moisture transfer. Int. J. Heat Mass Transfer 53(15–16), 3080–3087 (2010)CrossRef

31.

Silva, F.R., Gonçalves, G., Lenzi, M.K., Lenzi, E.K.: An extension of the linear Luikov system equations of heat and mass transfer. Int. J. Heat Mass Transfer 63, 233–238 (2013)CrossRef

32.

Zhang, X.Y., Li, X.F.: Transient response of a hygrothermoelastic cylinder based on fractional diffusion wave theory. J. Therm. Stresses 40(12), 1575–1594 (2017)CrossRef

33.

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 Transfer 126, 1094–1103 (2018)CrossRef

34.

Hartranft, R.J., Sih, G.C.: The influence of the Soret and Dufour effects on the diffusion of heat and moisture in solids. Int. J. Eng. Sci. 18, 1375–1383 (1980). https://doi.org/10.1016/0020-7225(80)90094-4CrossRef

35.

Ignaczak, J., Ostoja-Starzewski, M.: Thermoelasticity with finite wave speeds. Oxford University Press, Oxford (2010). https://doi.org/10.1093/acprof:oso/9780199541645.001.0001CrossRef

36.

Quintanilla, R.: A well-posed problem for the dual-phase-lag heat conduction. J. Therm. Stress 31(3), 260–269 (2008). https://doi.org/10.1080/01495730701738272CrossRef

37.

Chen, P.J., Gurtin, M.E.: On a theory of heat conduction involving two temperatures. Z. Angew. Math. Phys. 19, 559–577 (1968). https://doi.org/10.1007/BF01594969CrossRef

38.

Sugano, Y., Chuuman, Y.: Analytic solution of transient hygrothermoelastic problem due to coupled heat and moisture diffusion in a hollow circular cylinder. Trans. Jpn Soc. Mech. Eng. 59(564), 1956–1963 (1993)CrossRef

39.

Zhang, X.Y., Peng, Y., Li, X.F.: Time-fractional hygrothermoelastic problem for a sphere subjected to heat and moisture flux. J. Heat Transfer 140(12), 122002 (2018). https://doi.org/10.1115/1.4041419CrossRef

40.

Mukhopadhyay, S., Prasad, R., Kumar, R.: On the theory of two-temperature thermoelasticity with two phase-lags. J. Therm. Stress 34(4), 352–365 (2011). https://doi.org/10.1080/01495739.2010.550815CrossRef

41.

Noda, N., Hetnarski, R.B., Tanigawa, Y.: Thermal stresses, 2nd edn. Routledge, London (2003). https://doi.org/10.1201/9780203735831CrossRef

42.

Chen, I.I.H.: Modified Fourier-Bessel series and finite spherical Hankel transform. Int. J. Math. Educ. Sci. Technol. 13(3), 281–283 (1982). https://doi.org/10.1080/0020739820130307MathSciNetCrossRef

43.

Abramowitz, M., Stegun, I.A.: Handbook of mathematical functions, p. 485. National Bureau of Standards, Washington, D. C. (1965)

44.

Gaver, D.P.: Observing stochastic processes and approximate transform inversion. Oper. Res. 14(3), 444–459 (1966). https://doi.org/10.1287/opre.14.3.444MathSciNetCrossRef

45.

Stehfest, H.: Algorithm 368, numerical inversion of Laplace transforms. Comm. Assn. Comp. Mach. 13(1), 47–49 (1970). https://doi.org/10.1145/361953.361969CrossRef

46.

Stehfest, H.: Remark on algorithm 368: numerical inversion of Laplace transforms. Commun. Assn. Comput. Mach. 13(10), 624 (1970). https://doi.org/10.1145/355598.362787CrossRef

47.

Kuznetsov, A.: On the convergence of the Gaver–Stehfest algorithm. SIAM J. Num. Anal. 51(6), 2984–2998 (2013). https://doi.org/10.1137/13091974XMathSciNetCrossRef

48.

Calvo, I., et al.: Fractional generalization of Fick’s law: a microscopic approach. Phys. Rev. Lett. 99(23), 230603 (2007). https://doi.org/10.1103/PhysRevLett.99.230603CrossRef

49.

Xu, G., Wang, J.: Analytical solution of time fractional Cattaneo heat equation for finite slab under pulse heat flux. Appl. Math. Mech. Engl. Ed. 39, 1465–1476 (2018). https://doi.org/10.1007/s10483-018-2375-8MathSciNetCrossRef

50.

Caputo, M.: Linear models of dissipation whose q is almost frequency independent, part II. Geophys. J. Roy. Astron. Soc. 13, 529–539 (1967)CrossRef

51.

Caputo, M.: Elasticita e Dissipazione. Zanichelli, Bologna (1969)

52.

Zenkour, A.M., Abouelregal, A.E.: Non-simple magneto-thermoelastic solid cylinder with variable thermal conductivity due to harmonically varying heat. Earthq. Struct. 10(3), 681–697 (2016). https://doi.org/10.12989/eas.2016.10.3.681CrossRef

53.

Benkhedda, A., Tounsi, A., Adda Bedia, E.A.: Effect of temperature and humidity on transient hygrothermal stresses during moisture desorption in laminated composite plates. Compos. Struct. 82(4), 629–635 (2008). https://doi.org/10.1016/j.compstruct.2007.04.013CrossRef

54.

Cattaneo, C.: Sur uneForme de I’equation de la Chaleur eliminant le paradoxed’une propagation instantanee’. C. R. Acad. Sci. 247, 431–433 (1958)

55.

Vernotte, P.: Les paradoxes de la théorie continue de l’équation de la chaleur. C. R. Acad. Sci. 246, 3154–3155 (1958)MathSciNet

56.

Ezzat, M.A.: Magneto-thermoelasticity with thermoelectric properties and fractional derivative. Heat Transf. Phys. B 406, 30–35 (2011)

57.

Lotfy, K., Hassan, W.: Normal mode method for two-temperature generalized thermoelasticity under thermal shock problem. J. Therm. Stresses 37(5), 545–560 (2014). https://doi.org/10.1080/01495739.2013.869145CrossRef

58.

Lotfy, K., El-Bary, A.A., Tantawi, R.S.: Effects of variable thermal conductivity of a small semiconductor cavity through the fractional order heat-magneto-photothermal theory. Eur. Phys. J. Plus 134(6), 280 (2019)CrossRef

59.

Lotfy, K., Elidy, E.S., Tantawi, R.S.: Piezo-photo-thermoelasticity transport process for hyperbolic two-temperature theory of semiconductor material. Int. J. Mod. Phys. C 32(7), 2150088 (2021)MathSciNetCrossRef

60.

Abo-Dahab, S.M., Lotfy, Kh., Gohaly, A.: Rotation and magnetic field effect on surface waves propagation in an elastic layer lying over a generalized thermoelastic diffusive half-space with imperfect boundary. Math. Probl. Eng. 2015, 671783 (2015)MathSciNetCrossRef

Title: Fractional dual-phase-lag hygrothermoelastic model for a sphere subjected to heat-moisture load
Authors: Shahala Sheikh
Lalsingh Khalsa
Gulshan Makkad
Vinod Varghese
Publication date: 02-04-2024
Publisher: Springer Berlin Heidelberg
Published in: Archive of Applied Mechanics
Print ISSN: 0939-1533
Electronic ISSN: 1432-0681
DOI: https://doi.org/10.1007/s00419-024-02583-9

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Premium Partners