Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Modeling of memory-dependent derivative in a rotating magneto-thermoelastic diffusive medium with variable thermal conductivity

  • Said, Samia M. (Department of Mathematics, Faculty of Science, Zagazig University) ;
  • Abd-Elaziz, Elsayed M. (Ministry of Higher Education, Zagazig Higher Institute of Eng. & Tech.) ;
  • Othman, Mohamed I.A. (Department of Mathematics, Faculty of Science, Zagazig University)
  • Received : 2020.05.15
  • Accepted : 2020.08.28
  • Published : 2020.09.25
⟨ Previous Next ⟩

Abstract

The purpose of this paper is to depict the effect of rotation and initial stress on a magneto-thermoelastic medium with diffusion. The problem discussed within memory-dependent derivative in the context of the three-phase-lag model (3PHL), Green-Naghdi theory of type III (G-N III) and Lord and Shulman theory (L-S). Analytical expressions of the considered variables are obtained by using Laplace-Fourier transforms technique. Numerical results for the field quantities given in the physical domain and illustrated graphically in the absence and presence of a magnetic field, initial stress as well as the rotation. The differences in variable thermal conductivity are also presented at different parameter of thermal conductivity. The numerical results of the field variables are presented graphically to discuss the effect of various parameters of interest. Some special cases are also deduced from the present investigation.

Keywords

Acknowledgement

The authors received no financial support for the research, authorship, and/or publication of this article.

References

  1. Abd-Elaziz, E.M., Marin, M. and Othman, M.I.A. (2019), "On the solid under GN electromagnetic theory", Symmetry, 11(3), 413-430. https://doi.org/10.3390/sym11030413.
  2. Al-Jamel, A., Al-Jamal, M.F. and El-Karamany, A.S. (2018), "A memory-dependent derivative model for damping in oscillatory systems", J. Vib. Control, 24(11), 2221-2229. https://doi.org/10.1177/1077546316681907.
  3. Bhatti, M.M., Ellahi, R., Zeeshan, A., Marin, M. and Ijaz, N. (2019), "Numerical study of heat transfer and Hall current impact on peristaltic propulsion of particle-fluid suspension with compliant wall properties", Mod. Phys. Lett. B, 33(35), Art. No. 1950439. DOI: 10.1142/S0217984919504396.
  4. Caputo, M. (1971a), "Vibrations on an infinite viscoelastic layer with a dissipative memory", J. Acoust. Soc. Am., 56, 897-904. https://doi.org/10.1121/1.1903344
  5. Caputo, M. and Mainardi, F. (1971b), "A new dissipation model based on memory mechanism", Pure Appl. Geophys., 91, 134-147. https://doi.org/10.1007/BF00879562
  6. Caputo, M. and Mainardi, F. (1971c), "Linear model of dissipation in an elastic solid", La Rivista del Nuovo Cimento, 1, 161-198. https://doi.org/10.1007/BF02820620
  7. Deswal, S. and Kalkal, K.K. (2014), "Plane waves in a fractional order micropolar magneto-thermoelastic half-space", Wave Motion, 51(1), 100-113. https://doi.org/10.1016/j.wavemoti.2013.06.009.
  8. Dogonchi, A.S. and Ganji, D.D. (2016), "Convection-radiationheat transfer study of moving fin with temperaturedependent thermal conductivity, heat transfer coefficient and heat generation", Appl. Therm. Eng., 103, 705-712. https://doi.org/10.1016/j.applthermaleng.2016.04.121.
  9. Gholinia, M., Hosseinzadeh, Kh. and Ganji, D.D. (2020), "Investigation of different base fluids suspend by CNTs hybrid nanoparticle over a vertical circular cylinder with sinusoidal radius", Case Studies in Therm. Eng., 21, 100666, https://doi.org/10.1016/j.csite.2020.100666.
  10. Hendy, M.H., El-Attar, S.I. and Ezzat, M.A. (2020), "On thermoelectric materials with memory-dependent derivative and subjected to a moving heat source", Microsys. Tech., 26, 595-608. https://doi.org/10.1007/s00542-019-04519-8.
  11. Hosseinzadeh, Kh., Asadi, A., Mogharrebi, A.R., Khalesi, J., Mousavisani, S. and Ganji, D.D. (2019), "Entropy generation analysis of (CH2OH)2containing CNTs nanofluid flow under effect of MHD and thermal radiation", Case Studies in Therm. Eng., 14, 100482. https://doi.org/10.1016/j.csite.2019.100482.
  12. Hosseinzadeh, Kh., Roghani, So., Asadi, A., Mogharrebi, A.R. and Ganji, D.D. (2020a), "Investigation of micropolar hybrid ferrofluid flow over a vertical plate by considering various base fluid and nanoparticle shape factor", Int. J. Numer. Method. Heat Fluid Fl., DOI 10.1108/HFF-02-2020-0095.
  13. Hosseinzadeh, Kh., Roghani, So., Mogharrebi, A.R., Asadi, A., Waqas, M. and Ganji, D.D. (2020b), "Investigation of crossfluid flow containing motile gyrotactic micro-organisms and nanoparticles over a three-dimensional cylinder", Alex. Eng. J., https://doi.org/10.1016/j.aej.2020.04.037.
  14. Hosseinzadeh, Kh., Asadi, A., Mogharrebi, A.R., Azari, M.E. and Ganji, D.D. (2020), "Investigation of mixture fluid suspended by hybrid nanoparticles over vertical cylinder by considering shape factor effect", J. Therm. Anal. Calorimetry, 1-15. DOI 10.1007/s10973-020-09347-x
  15. Hosseinzadeh, Kh., Mogharrebi, A.R., Asadi, A., Sheikhshahrokhdehkordi, M., Mousavisani, S. and Ganji, D.D. (2019), "Entropy generation analysis of mixture nanofluid (H2O/c2H6O2)-Fe3O4 flow between two stretching rotating disks under the effect of MHD and nonlinear thermal radiation", Int. J. Ambient Energy, 1-13. https://doi.org/10.1080/01430750.2019.1681294.
  16. Hetnaraski, R.B. (1986), "Thermal Stresses", North-Holland, Amsterdam, 1, 391-396.
  17. Kumar, R. and L. Rani. (2005), "Deformation due to inclined load in thermoelastic half- space with voids", Arch. of Mech., 57, 7-24.
  18. Marin, M., Craciun, E.M. and Pop, N. (2016), "Considerations on mixed initial-boundary value problems for micropolar porous bodies", Dyn. Syst. Appl., 25(1-2), 175-196.
  19. Medani, M., Benahmed, A., Zidour, M., Heireche, H., Tounsi, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2019), "Static and dynamic behavior of (FG-CNT) reinforced porous sandwich plate", Steel Compos. Struct., 32(5), 595-610. https://doi.org/10.12989/scs.2019.32.5.595.
  20. Mondal, S., Sur, A. and Kanoria, M. (2019), "Tranient response in a piezoelastic medium due to the influence of magnetic field with memory-dependent derivative", Acta Mechanica, 230, 2325-2338. https://doi.org/10.1007/s00707-019-02380-4.
  21. Othman, M.I.A. (2005), "Generalized electromagneto-thermoelastic plane waves by thermal shock problem in a finite conductivity half-space with one relaxation time", Multi. Model. Mater. Struct., 1(3), 231-250. http://dx.doi.org/10.1163/157361105774538557.
  22. Othman, M.I.A. and Song, Y.Q. (2009), "The effect of rotation on 2-D thermal shock problems for a generalized magneto-thermoelasticity half-space under three theories", Multi. Model. Mater. Struct., 5(1), 43-58. https://doi.org/10.1108/15736105200900003
  23. Othman, M.I.A. and Said, S.M. (2012), "The effect of rotation on two-dimensional problem of a fibre-reinforced thermoelastic with one relaxation time", Int. J. Thermophys., 33(2) 160-171. DOI 10.1007/s10765-011-1109-5.
  24. Othman, M.I.A. and Said, S.M. (2013), "Plane waves of a fiber-reinforcement magneto-thermoelastic comparison of three different theories", Int. J. Thermophys., 34, 366-383. DOI 10.1007/s10765-013-1417-z.
  25. Othman, M.I.A., Sarkar, N. and Atwa, S.Y. (2013), "Effect of fractional parameter on plane waves of generalized thermo- magneto-elastic diffusion with reference temperature dependent elastic medium", Comput. Math. with Appl., 65(7), 1103-1118. doi:10.1016/j.camwa.2013.01.047.
  26. Othman, M.I.A. and Said, S.M. (2014), "2-D problem of magneto-hermoelasticity fiber-reinforced medium under temperature-dependent properties with three-phase-lag theory", Meccanica, 49(5), 1225-1243. DOI 10.1007/s11012-014-9879-z.
  27. Othman, M.I.A. and Abd-Elaziz, E.M. (2017), "Effect of rotation on a micropolar magneto-thermoelastic medium with dual- phase-lag model under gravitational field", Microsystem Tech., 23(10), 4979-4987. DOI 10.1007/s00542-017-3295-y.
  28. Othman, M.I.A., Abouelregal, A.E. and S.M. Said, (2019), "The effect of variable thermal conductivity on an infinite fiber-reinforced thick plate under initial stress", J. Mech. Mater. Struct., 14(2), 277-293. dx.doi.org/10.2140/jomms.2019.14.277.
  29. Othman, M.I.A. and Mondal, S. (2020), "Memory dependent-derivative effect on wave propagation of micropolar thermo-elastic medium under pulsed laser heating with three theories", Int. J. Numer. Method. Heat Fluid Fl., 30(3), 1025-1046. DOI 10.1108/HFF-05-2019-0402.
  30. Povstenko, Y.Z. (2004), "Fractional heat conduction equation and associated thermal stress", J. Therm. Stress., 28, 83-102. DOI: 10.1093/qjmam/hbn016.
  31. Quintanilla, R. and Racke, R. (2008), "A note on stability in three- phase-lag heat conduction", Int. J. Heat Mass Transfer, 51, 24-29. https://doi.org/10.1080/014957390523741.
  32. Riaz, A., Ellahi, R., Bhatti, M.M. and Marin, M. (2019), "Study of heat and mass transfer in the Eyring-Powell model of fluid propagating peristaltically through a rectangular compliant channel", Heat Transf Res, 50(16), 1539-1560. DOI: 10.1615/HeatTransRes.2019025622
  33. Rostami, A.K., Hosseinzadeh, Kh. and Ganji, D.D. (2020), "Hydrothermal analysis of ethylene glycol nanofluid in a porous enclosure with complex snowflake shaped inner wall", Waves in Random and Complex Media, 1-18. DOI 10.1080/17455030.2020.1758358
  34. Roy Chaudhuri, S.K. and Debnath, L. (1983), "Magneto-thermo- elastic plane waves in rotating media", Int. J. Eng. Sci., 21(2), 155-163. https://doi.org/10.1016/0020-7225(83)90007-1.
  35. Roy Choudhuri, S.K. (2007), "On a thermoelastic three-phase-lag model", J. Therm. Stress., 30, 231-238. DOI: 10.1080/01495730601130919.
  36. Sarkar, N. and Mondal, S. (2020), "Two-dimensional problem of two-temperature generalized thermoelasticity using memory-dependent heat transfer: an integral transform approach", Ind. J. Phys., in press. https://doi.org/10.1007/s12648-019-01639-9.
  37. Said, S.M. and Othman, M.I.A. (2020), "The effect of gravity andhydrostatic initial stress with variable thermal conductivity on a magneto-fiber-reinforced", Struct. Eng. Mech., 74(3), 425-434. https://doi.org/10.12989/sem.2020.74.3.425.
  38. Salehi, S., Nori, A., Hosseinzadeh, Kh. and Ganji, D.D. (2020), "Hydrothermal analysis of MHD squeezing mixture fluid suspended by hybrid nanoparticles between two parallel plates", Case Studies in Therm. Eng., 21, 100650, https://doi.org/10.1016/j.csite.2020.100650.
  39. Schoenberg, M. and Censor, D. (1973), "Elastic waves in rotating Media", Quart. Appl. Math., 31(1), 115-125. https://www.jstor.org/stable/43636594. https://doi.org/10.1090/qam/99708
  40. Singh, S., Kumar, D. and Rai, K.N. (2014), "Convective-radiative fin with temperature dependent thermal conductivity, heat transfer coefficient and wavelength dependent surface emissivity", Propul. Power Res., 3(4), 207-221. https://doi.org/10.1016/j.jppr.2014.11.003.
  41. Thomas, L. (1980), "Fundamentals of heat transfer", Prentice-Hall Inc, Englewood Cliffs.
  42. Wang, J.L. and Li, H.F. (2011), "Surpassing the fractional derivative: Concept of the memory-dependent derivative", Comput. Math. Appl., 62, 1562-1567. https://doi.org/10.1016/j.camwa.2011.04.028.
  43. Yu, Y.J., Hu, W. and Tian, X.G. (2014), "A novel generalized thermoelasticity model based on memory-dependent derivative", Int. J. Eng. Sci., 81, 123-134. DOI 10.1016/j.ijengsci.2014.04.014.
  44. Zarga, D., Tounsi, A., Bousahla, A.A., Bourada, F. and Mahmoud, S.R. (2019), "Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory", Steel Compos. Struct., 32(3), 389-410. https://doi.org/10.12989/scs.2019.32.3.389

Cited by

  1. The effect of multi-phase-lag and Coriolis acceleration on a fiber-reinforced isotropic thermoelastic medium vol.39, pp.2, 2021, https://doi.org/10.12989/scs.2021.39.2.125
  2. Effect of gravity on a magneto-thermoelastic porous medium with the frame of a memory-dependent derivative in the context of the 3PHL model vol.40, pp.6, 2020, https://doi.org/10.12989/scs.2021.40.6.881