Skip to main content
SpringerLink
Log in

Magneto-thermoelastic interaction in a reinforced medium with cylindrical cavity in the context of Caputo–Fabrizio heat transport law

  • Original Paper
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

This present work is devoted to the investigation of the transient phenomena for a fiber-reinforced medium with a cylindrical cavity in the context of the three-phase-lag model of generalized thermoelasticity with a new form of derivative of the Caputo–Fabrizio (CF) type in the heat transport equation, where the medium is under the action of an induced magnetic field. The Laplace transform is incorporated as a tool for the solution of the problem when the boundary of the cavity is exposed to harmonically varying heat with a constant angular frequency of thermal vibration. The numerical inversion of the Laplace transforms is computed using the Zakian method. Excellent predictive capability is demonstrated due to the presence of reinforcement, the angular frequencies on thermal vibrations, CF fractional parameter and magnetic field.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Sul, J.H., Gangadhara, P.B., Ray, T.: Prediction of low cycle fatigue life of short fibre composites at elevated temperatures using surrogate modelling. Compos. Part B. Eng. 42, 1453–1460 (2011). https://doi.org/10.1016/j.compositesb.2011.04.047

    Article  Google Scholar 

  2. Lam, C.K., Cheung, H., Lau, K., Zhou, L., Ho, M., Hui, D.: Cluster size effect in hardness of nanoclay/epoxy composites. Compos. Part B. Eng. 36, 263–269 (2005). https://doi.org/10.1016/j.compositesb.2004.09.006

    Article  Google Scholar 

  3. Chaudhry, M.S., Czekanski, A., Zhu, Z.H.: Characterization of carbon nanotube enhanced interlaminar fracture toughness of woven carbon fiber reinforced polymer composites. Int. J. Mech. Sci. 480, 131–132 (2017). https://doi.org/10.1016/j.ijmecsci.2017.06.016

    Article  Google Scholar 

  4. Sur, A., Kanoria, M.: Fibre-reinforced magneto-thermoelastic rotating medium with fractional heat conduction. Procedia Eng. 127, 605–612 (2015)

    Article  Google Scholar 

  5. Sur, A., Kanoria, M.: Modeling of fibre-reinforced magneto-thermoelastic plate with heat sources. Procedia Eng. 173, 875–882 (2017)

    Article  Google Scholar 

  6. Padture, N.P., Gell, M., Jordan, E.H.: Thermal barrier coatings for gas-turbine engine applications. Science 296, 280–284 (2017)

    Article  Google Scholar 

  7. Zoby, E., Thompson, R., Wurster, K.: Aeroheating design issues for reusable launch vehicles a perspective. In: Proceedings of Thirty Fourth AIAA Fluid Dynamics Conference Exhibit, pp. 25–35 (2004)

  8. Li, T.Q., Xu, Z.H., Hu, Z.J., Yang, X.G.: Application of a high thermal conductivity c/c composite in a heat-redistribution thermal protection system. Carbon 48(3), 924–925 (2010)

    Article  Google Scholar 

  9. Mondal, S., Sur, A., Kanoria, M.: A memory response in the vibration of a microscale beam induced by laser pulse. J. Therm. Stress. (2019). https://doi.org/10.1080/01495739.2019.1629854

    Article  Google Scholar 

  10. Landau, L.: The theory of superfluidity of helium II. J. Phys. 5, 71 (1941)

    MATH  Google Scholar 

  11. Sur, A., Paul, S., Kanoria, M.: Modeling of memory-dependent derivative in a functionally graded plate. Waves Random Complex Media (2019). https://doi.org/10.1080/17455030.2019.1606962

    Article  Google Scholar 

  12. Purkait, P., Sur, A., Kanoria, M.: Elasto-thermodiffusive response in a spherical shell subjected to memory-dependent heat transfer. Waves Random Complex Media (2019). https://doi.org/10.1080/17455030.2019.1599464

    Article  Google Scholar 

  13. Mondal, S., Sur, A., Kanoria, M.: Transient response in a piezoelastic medium due to the influence of magnetic field with memory dependent derivative. Acta Mech. (2019). https://doi.org/10.1007/s00707-019-02380-4

    Article  MathSciNet  Google Scholar 

  14. Sur, A., Kanoria, M.: Thermoelastic interaction in a three dimensional layered sandwich structure. Mech. Adv. Compos. Struct. 5, 187–198 (2018)

    Google Scholar 

  15. Sur, A., Kanoria, M.: Propagation of thermal waves in a functionally graded thick plate. Math. Mech. Solids 22(4), 718–736 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  16. Sur, A., Kanoria, M.: Thermoelastic interaction in a functionally graded half-space subjected to a Mode-I crack. Int. J. Adv. Appl. Math. Mech. 3(2), 33–44 (2015)

    MathSciNet  MATH  Google Scholar 

  17. Pal, P., Sur, A., Kanoria, M.: Thermo-viscoelastic interaction subjected to fractional Fourier law with three-phase-lag effects. J. Solid Mech. 7(4), 400–415 (2015)

    Google Scholar 

  18. Sur, A., Kanoria, M.: Three-phase-lag elasto-thermodiffusive response in a elastic solid under hydrostatic pressure. Int. J. Adv. Appl. Math. Mech. 3(2), 121–137 (2015)

    MathSciNet  MATH  Google Scholar 

  19. Sur, A., Kanoria, M.: Three dimensional viscoelastic medium under thermal shock. Eng. Solid Mech. 4, 187–200 (2016)

    Article  Google Scholar 

  20. Sur, A., Kanoria, M.: Thermoelastic interaction in a viscoelastic functionally graded half-space under three phase lag model. Eur. J. Comput. Mech. 23, 179–198 (2014)

    Article  Google Scholar 

  21. Das, P., Kanoria, M.: Study of finite thermal wavs in a magneto-thermo-elastic rotating medium. J. Therm. Stress. 37, 405–428 (2014)

    Article  Google Scholar 

  22. Das, P., Kar, A., Kanoria, M.: Analysis of magneto-thermoelastic response in a transversely isotropic hollow cylinder under thermal shock with three-phase-lag effect. J. Therm. Stress. 36, 239–258 (2013)

    Article  Google Scholar 

  23. Sur, A., Pal, P., Kanoria, M.: Modeling of memory-dependent derivative in a fibre-reinforced plate under gravitational effect. J. Therm. Stress. 41(8), 973–992 (2018)

    Article  Google Scholar 

  24. Karmakar, R., Sur, A., Kanoria, M.: Generalized thermoelastic problem of an infinite body with a spherical cavity under dual-phase-lags. J. Appl. Mech. Tech. Phys. 57(4), 652–665 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  25. Sur, A., Kanoria, M.: Finite thermal wave propagation in a half-space due to variable thermal loading. Appl. Appl. Math. Int. J. 9(1), 94–120 (2014)

    MathSciNet  MATH  Google Scholar 

  26. Roy Choudhuri, S.K.: On a thermoelastic three-phase-lag model. J. Therm. Stress. 30, 231–238 (2007)

    Article  Google Scholar 

  27. Chakravorty, S., Ghosh, S., Sur, A.: Thermo-viscoelastic interaction in a three-dimensional problem subjected to fractional heat conduction. Procedia Eng. 173, 851–858 (2017)

    Article  Google Scholar 

  28. Sur, A., Kanoria, M.: Fractional order generalized thermoelastic functionally graded solid with variable material properties. J. Solid Mech. 6, 54–69 (2014)

    Google Scholar 

  29. Sur, A., Kanoria, M.: Three dimensional thermoelastic problem under two-temperature theory. Int. J. Comput. Method 14(2), 1–17 (2016). https://doi.org/10.1142/S021987621750030X

    Article  MathSciNet  MATH  Google Scholar 

  30. Caputo, M.: Linear models of dissipation whose Q is almost frequency independent II. Geophys. J. R. Astron. Soc. 3, 529–539 (1967)

    Article  Google Scholar 

  31. Caputo, M., Mainardi, F.: Linear model of dissipation in anelastic solids. Rivis. ta. el. Nuovo. cimento 1, 161–198 (1971)

    Article  Google Scholar 

  32. Gómez-Aguilar, J., López-López, M., Alvarado-Martínez, V., Reyes-Reyes, J., Adam-Medina, M.: Modeling diffusive transport with a fractional derivative without singular kernel. Phys. A Stat. Mech. Appl. 447, 467–481 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  33. Anh, V.V., Leonenko, N.N.: Spectral analysis of fractional kinetic equations with random data. J. Stat. Phys. 104, 1349–1387 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  34. Meerschaert, M.M., Sikorskii, A.: Stochastic Models for Fractional Calculus. De Gruyter Studies in Mathematics, vol. 43. De Gruyter, Berlin (2012)

    MATH  Google Scholar 

  35. Leonenko, N.N., Meerschaert, M.M., Sikorskii, A.: Fractional Pearson diffusions. J. Math. Anal. Appl. 403(2), 532–546 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  36. Atangana, A.: Fractional Operators with Constant and Variable Order with Application to Geo-Hydrology. Academic Press, London (2018). ISBN: 978-0-12-809670-3

    MATH  Google Scholar 

  37. Caputo, M., Fabrizio, M.: A new definition of fractional derivative without singular kernel. Prog. Frac. Differ. Appl. 1(2), 73–85 (2015)

    Google Scholar 

  38. Aydogan, S.M., Baleanu, D., Mousalou, A., Rezapour, S.: On approximate solutions for two higher-order Caputo–Fabrizio fractional integro-differential equations. Adv. Differ. Equ. (2017). https://doi.org/10.1186/s13662-017-1258-3

    Article  MathSciNet  MATH  Google Scholar 

  39. Losada, J., Nieto, J.J.: Properties of a new fractional derivative without singular kernel. Prog. Fract. Differ. Appl. 1(2), 87–92 (2015)

    Google Scholar 

  40. Caputo, M., Fabrizio, M.: Applications of new time and spatial fractional derivatives with exponential kernels. Prog. Fract. Differ. Appl. 2(1), 1–11 (2016)

    Article  Google Scholar 

  41. Atangana, A., Alkahtani, B.S.T.: Analysis of the Keller–Segel model with a fractional derivative without singular kernel. Entropy 17(6), 4439–4453 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  42. Atangana, A., Alkahtani, B.S.T.: New model of groundwater flowing within a confine aquifer: application of Caputo-Fabrizio derivative. Arab. J. Geosci. (2015). https://doi.org/10.1007/s12517-015-2060-8

    Article  Google Scholar 

  43. Atangana, A., Baleanu, D.: Caputo–Fabrizio derivative applied to groundwater flow within confined aquifer. J. Eng. Mech. (2017). https://doi.org/10.1061/(ASCE)EM.1943-7889.0001091

    Article  Google Scholar 

  44. Shah, N.A., Khan, I.: Heat transfer analysis in a second grade fluid over and oscillating vertical plate using fractional Caputo–Fabrizio derivatives. Eur. Phys. J. C (2016). https://doi.org/10.1140/epjc/s10052-016-4209-3

    Article  Google Scholar 

  45. Sheikh, N.A., Ali, F., Khan, I., Saqib, M.: A modern approach of Caputo–Fabrizio time-fractional derivative to MHD free convection flow of generalized second-grade fluid in a porous medium. Neural Comput. Appl. (2016). https://doi.org/10.1007/s00521-016-2815-5

    Article  Google Scholar 

  46. Khan, I., Ali-Shah, N., Mahsud, Y., Vieru, D.: Heat transfer analysis in a Maxwell fluid over an oscillating vertical plate using fractional Caputo–Fabrizio derivatives. Eur. Phys. J. Plus (2017). https://doi.org/10.1140/epjp/i2017-11456-2

    Article  Google Scholar 

  47. Atangana, A., Alkahtani, S.T.A.: Extension of the RLC electrical circuit to fractional derivative without singular kernel. Adv. Mech. Eng. 7, 1–6 (2015)

    Google Scholar 

  48. Atangana, A., Nieto, J.J.: Numerical solution for the model of RLC circuit via the fractional derivative without singular kernel. Adv. Mech. Eng. 7, 1–7 (2015)

    Google Scholar 

  49. Alsaedi, A.: On coupled systems of time-fractional differential problems by using a new fractional derivative. J. Funct. Spaces (2016). https://doi.org/10.1155/2016/4626940

    Article  MathSciNet  MATH  Google Scholar 

  50. Gómez-Aguilar, J.F., Yépez-Martnez, H., Calderón-Ramón, C., Cruz-Orduña, I., Fabricio, R., Jiménez, E., Olivares-Peregrino, V.H.: Modeling of a mass-spring-damper system by fractional derivatives with and without a singular kernel. Entropy 17(9), 6289–6303 (2005)

    MathSciNet  MATH  Google Scholar 

  51. Sherief, H.H., Helmy, A.K.: A two dimensional problem for a half-space in magneto-thermoelasticity with thermal relaxation. Int. J. Eng. Sci. 40, 587–604 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  52. Othman, M.I.A.: Generalized electromagneto-thermoelastic plane waves by thermal shock problem in a finite conductivity half-space with one relaxation time. Multidiscipl. Model. Mater. Struct. 1, 231–250 (2005)

    Article  Google Scholar 

  53. Othman, M.I.A., Zidan, M.E.M., Hilal, M.I.M.: The effect of magnetic field on a rotating thermoelastic medium with voids under thermal loading due to laser pulse with energy dissipation. Can. J. Phys. 92, 1359–1371 (2014)

    Article  Google Scholar 

  54. Sur, A., Kanoria, M.: Modeling of memory-dependent derivative in a fibre-reinforced plate. Thin Walled Struct. (2017). https://doi.org/10.1016/j.tws.2017.05.005

    Article  MATH  Google Scholar 

  55. Halsted, D.J., Brown, D.E.: Zakian’s technique for inverting Laplace transforms. Chem. Eng. J. 3, 312–313 (1972)

    Article  Google Scholar 

  56. Othman, M.I.A.: Generalized electro-magneto-thermoelasticity in case of thermal shock plane waves for a finite conducting half-space with two relaxation time. Mech. Mech. Eng. 14(1), 5–30 (2010)

    Google Scholar 

  57. Nowacki, W.: Dynamic Problem of Thermoelasticity, vol. 399. Noordhoff International, Leyden (1975)

    MATH  Google Scholar 

  58. Spencer, A.J.M.: Continuum Theory of the Mechanics of Fibre-Reinforced Composites. Springer, Berlin (1984). ISBN: 978-3-7091-4336-0

    Book  MATH  Google Scholar 

  59. Dhaliwal, R.S., Singh, A.: Dynamic Coupled Thermoelasticity. Hindustan Publishing Corporation, New Delhi (1980)

    Google Scholar 

  60. Youssef, H.M., Al-Lehaibi, E.A.: Fractional order generalized thermoelastic infinite medium with cylindrical cavity subjected to harmonically varying heat. Engineering 3, 32–37 (2011)

    Article  Google Scholar 

  61. Mondal, S., Pal, P., Kanoria, M.: Transient response in a thermoelastic half-space solid due to a laser pulse under three theories with memory-dependent derivative. Acta Mech. 230(1), 179–199 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  62. Tiwari, R., Mukhopadhyay, S.: Analysis of wave propagation in the presence of a continuous line heat source under heat transfer with memory dependent derivatives. Math. Mech. Solids (2017). https://doi.org/10.1177/1081286517692020

    Article  MATH  Google Scholar 

  63. Sur, A., Pal, P., Mondal, S., Kanoria, M.: Finite element analysis in a fibre-reinforced cylinder due to memory-dependent heat transfer. Acta Mech. (2019). https://doi.org/10.1007/s00707-018-2357-2

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the editor and the anonymous referees for their comments and suggestions on this paper.

Funding

The author received no financial support for the research.

Author information

Authors and Affiliations

  1. Department of Mathematics, Basirhat College, North 24 Parganas, West Bengal, 743412, India

    Sudip Mondal

  2. Department of Mathematics, Sister Nivedita University, Newtown, Kolkata, West Bengal, 700156, India

    Abhik Sur & M. Kanoria

  3. Department of Applied Mathematics, University of Calcutta, 92 A.P.C. Road, Kolkata, West Bengal, 700009, India

    M. Kanoria

Authors
  1. Sudip Mondal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Abhik Sur
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Kanoria
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Abhik Sur.

Ethics declarations

Conflict of interest

The author declares that there is no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mondal, S., Sur, A. & Kanoria, M. Magneto-thermoelastic interaction in a reinforced medium with cylindrical cavity in the context of Caputo–Fabrizio heat transport law. Acta Mech 230, 4367–4384 (2019). https://doi.org/10.1007/s00707-019-02498-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-019-02498-5

Search

Navigation