Composite Materials and Engineering

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Effect of two-temperature in an orthotropic thermoelastic media with fractional order heat transfer

  • Lata, Parveen (Department of Basic and Applied Sciences Punjabi University Patiala) ;
  • Himanshi, Himanshi (Department of Basic and Applied Sciences Punjabi University Patiala)
  • Received : 2021.07.31
  • Accepted : 2021.12.10
  • Published : 2021.08.25
⟨ Previous Next ⟩

Abstract

In this article, we studied the effect of two-temperature in a two-dimensional orthotropic thermoelastic media with fractional order heat transfer in generalized thermoelasticity with three-phase-lags due to thermomechanical sources. The boundary of the surface is subjected to linearly distributed and concentrated loads (mechanical and thermal source). The solution of the problem is obtained with the help of Laplace and Fourier transform techniques. The expressions for displacement components, stress components and conductive temperature are derived in transformed domain. Numerical inversion technique is used to obtain the results in physical domain. The effect of two-temperature on all the physical quantities has been depicted with the help graphs. Some special cases are also discussed in the present investigation.

Keywords

References

  1. Abbas, I.A., EL-Amin, M.F. and Salama, A. (2009), "Effect of thermal dispersion on free convection in a fluid saturated porous medium", Int. J. Heat Fluid Fl., 30(2), 229-236. http://doi.org/10.1016/j.ijheatfluidflow.2009.01.004.
  2. Abbas, I.A. and Kumar, R. (2014), "Deformation due to thermal source in micropolar generalized thermoelastic half-space by finite element method", J. Computat. Theor. Nanosci., 11(1), 185-190. http://doi.org/10.1166/jctn.2014.3335.
  3. Abbas, I.A. and Marin, M. (2017a), "Analytical solution of thermoelastic interaction in a half-space by pulsed laser heating", Physica E, 87, 254-260. http://doi.org/10.2016/j.physe.2016.10.048
  4. Abbas, I.A. and Marin, M. (2017b), "Analytical solution of a two-dimensional generalized thermoelastic diffusion problem due to laser pulse", Iran. J. Sci. Technol., 42(3), 57-71. http://doi.org/10.1007/s40097-017-0077-1.
  5. Abbas, I.A. (2018), "A study on fractional order theory in thermoelastic half-space under thermal loading" Phys. Mesomech., 21(2), 150-156. https://doi.org /10.1134/S102995991802008X.
  6. Abouelregal, A.E. (2018), "The effect of temperature-dependent physical properties and fractional thermoelasticity on non-local nano beams, J. Math. Theor. Phys., 1(2), 49-58. http://doi.org/10.15406/oajmtp.2018.01.00009.
  7. Alzahrani, F.S. and Abbas, I.A. (2020), "Photo-thermal interactions in a semiconducting media with a spherical cavity under hyperbolic two-temperature model", Mathematics, 8(585), 1-11. http://doi.org/10.3390/math8040585.
  8. Allam, O., Draiche, K., Bousahla, A.A., Bourada, F., Tounsi A., Benrahou, K.H., Mahmoud S.R., Adda Bedia E.A. and Tounsi A., (2020), "A generalized 4-unknown refined theory for bending and free vibration analysis of laminated composite and sandwich plates and shells", Comput. Concrete, 26(2), 185-201. http://doi.org/10.12989/cac.2020.26.2.185.
  9. Bakoura, A., Bourada, F., Bousahla, A., Tounsi A., Benrahou, K.H., Tounsi, A., Al-Zahrani, M.M. and Mahmoud, S.R., (2021), "Buckling analysis of functionally graded plates using HSDT in conjunction with the stress function method", Comput. Concrete, 27(1), 73-83. http://doi.org/10/12989/cac.2021.27.1.073. https://doi.org/10.12989/CAC.2021.27.1.073
  10. Bassiouny, E. (2021), "Mathematical model for hyperbolic two temperature fractional-order thermoelastic materials subjected to thermal loading", Appl. Math. Inform. Sci., 15(1), 23-29. http://doi.org/10.18576.amis/150104. https://doi.org/10.18576.amis/150104
  11. Bassiouny, E. and Sabry, R. (2013), "Fractional order two temperature thermoelastic behaviour of piezoelectric materials", J. Appl. Math. Phys., 1, 110-120. http://doi.org/10.4236/jamp.2013.15017.
  12. Bekkaye, T.H.L., Fahsi, B., Bousahla, A.A., Bourada, F., Tounsi A., Benrahou, K.H., Tounsi, A. and Al-Zahrani, M.M., (2021), "Porosity-dependent mechanical behaviors of FG plate using refined trigonometric shear deformation theory", Comput. Concrete, 26(5), 439-450. http://doi.org/10/12989/cac.2021.26.5.439. https://doi.org/10.12989/cac.2020.26.5.439
  13. Bendenia, N., Zidour, M., Bousahla, A.A., Bourada, F., Tounsi A., Benrahou, K.H., Adda Bedia, E.A., Mahmoud, S.R. and Tounsi, A. (2020), "Deflections, stresses and free vibration studies of FG-CNT reinforced sandwich plates resting on Pasternak elastic foundation", Comput. Concrete, 26(3), 213-226. http://doi.org/10.12989/cac.2020.26.3.213.
  14. Bhattacharya, D. and Kanoria, M. (2014), "The influence of two-temperature fractional order generalized thermoelastic diffusion inside a spherical shell", Int. J. Appl. Innov. Eng. Manag., 3(8), 96-108.
  15. Chen, P.J. and Gurtin, E.M. (1968), "On a theory of heat conduction involving two temperatures", Zeitschrift fur Angewandte Mathematik und Physik, 19(4), 614-627. https://doi.org/10.1007/BF01594969.
  16. Chen, P.J., Gurtin, M.E. and Williams, W.O. (1968), "A note on non-simple heat conduction", Zeitschrift fur Angewandte Mathematik und Physik ZAMP, 19(4), 969-970. https://doi.org/10.1007/BF01602278
  17. Chen, P.J., Gurtin, E.M. and Williams, O.W. (1969), "On the thermodynamics of non-simple elastic materials with two temperatures", Zeitschrift fur angewandte Mathematik und Physik, 20(1), 107-112. https://doi.org/10.1007/BF01591120
  18. E-L Naggar, A.M., Kishka, Z., Abd-Alla, A.M., Abbas, I.A., Abo-Dahab, S.M. and Elsagheer, M. (2013), "On the initial stress, magnetic field, voids and rotation effects on plane waves in generalized thermoelasticity", J. Computat. Theor. Nanosci., 10(6), 1408-1417. http://doi.org/10.1166/jctn.2013.2862.
  19. Ezzat, M.A., EL- Karamany, A.S. and EL-Bary, A.A. (2014), "Magneto-thermoelasticity with two fractional order heat transfer", J. Assoc. Arab Univ. Basic Appl. Sci., 19, 70-79. http://doi.org/10.1016/j.jau.bas.2014.06.009.
  20. Guellil, M., Saidi, H., Bourada, F., Bousahla, A.A., Tounsi, A., Al-Zahrani, M.M., Hussain, M. and Mahmoud, S.R. (2021), "Influences of porosity distributions and boundary conditions on mechanical bending response of functionally graded plates resting on Pasternak foundation", Steel Compos. Struct., 38(1), 1-15. http://doi.org/10.12989/scs.2021.38.1.001.
  21. Hachemi, H., Bousahla, A.A., Kaci, A., Bourada, F., Tounsi, A., Benrahou, K.H., Tounsi, A., Al-Zahrani, M.M. and Mahmoud, S.R., (2021), "Bending analysis of functionally graded plates using a new refined quasi-3D shear deformation theory and the concept of the neutral surface position", Steel Compos. Struct., 39(1), 51-64. http://doi.org/10.12989/scs.2021.39.1.051.
  22. Khamis, A.K., El-Bary, A.A., Youssef, H.M. and Bakali, A. (2020), "Generalized thermoelasticity with fractional order strain of infinite medium with a cylindrical cavity", Int. J. Adv. Appl. Sci., 7(7), 102-108. http://doi.org/10.21833/ijaas.2020.07.013.
  23. Kumar, R. and Chawla, V. (2014), "General solution and fundamental solution for two-dimensional problem in orthotropic thermoelastic media with voids", Theor. Appl. Mech., 41(4), 247-265. http://doi.org/10.2298/TAM1404247.
  24. Kumar, R., Devi, S. and Sharma, V. (2017), "Effects of hall current and rotation in modified couple stress generalized thermoelastic half space due to ramp-type heating", J. Solid Mech., 9(3), 527-542.
  25. Lata, P. and Himanshi, H. (2021a), "Orthotropic magneto-thermoelastic solid with higher order dual-phase-lag model in frequency domain", Struct. Eng. Mech., 77(3), 315-327. http://doi.org/10.12989/sem.2021.77.3.315.
  26. Lata, P. and Himanshi, H. (2021b), "Stoneley wave propagation in an orthotropic thermoelastic media with fractional order theory", Compos. Mater. Eng., 3(1), 57-70. http://doi.org/10.12989/cme.2021.3.1.057.
  27. Lata, P. and Himanshi, H. (2021c), "Orthotropic magneto-thermoelastic solid with multi-dual-phase-lag model and hall current", Coupled Syst. Mech., 10(2), 103-121. http://doi.org/10.12989/csm.2021.10.2.103.
  28. Lata, P. and Kaur, I. (2019), "Thermomechanical interactions due to time harmonic sources in a transversely isotropic magneto thermoelastic solids with rotation", Int. J. Microstruct. Mater. Properties, 14(6), 549-577. http://doi.org/10.1504/IJMMP.2019.103190.
  29. Marin, M. (1999), "An evolutionary equation in thermoelasticity of dipolar bodies", J. Math. Phys., 40(3), 1391-1399. http://doi.org/10.1063/1.532809.
  30. Marin, M., Agarwal, R.P. and Mahmoud, S.R. (2013), "Modeling a microstretch thermoelastic body with two-temperatures", Abstract Appl. Anal., 583464. http://doi.org/10.1155/2013/583464.
  31. Marin, M., Vlase, S. and Paun, M. (2015a), "Considerations on double porosity structure for micropolar bodies", AIP Adv., 5(3), 037113. http://doi.org/10.1063/1.4914912.
  32. Marin, M., Othman, M.I.A. and Abbas, I.A. (2015b), "An extension of the domain of influence theorem for generalized thermoelasticity of anisotropic material with voids", J. Computat. Theor. Nanosci., 12(8), 1594-1598. http://doi.org/10/1166/jctn.2015.3934. https://doi.org/10.1166/jctn.2015.3934
  33. Merazka, B., Bouhadra, A., Menasria, A., Selim, M. M., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K. H., Tounsi, A. and Al-Zahrani, M. M., (2021), "Hygro-thermo-mechanical bending response of FG plates resting on elastic foundations", Steel Compos. Struct., 39(5), 631-643. http://doi.org/10.12989/scs.2021.39.5.631.
  34. Molla, M.A.K., Mondal, N. and Mallik, S.H. (2019), "Effects of fractional and two-temperature parameters on stress distributions for an unbounded generalized thermoelastic medium with spherical cavity", Arab. J. Basic Appl. Sci., 26(1), 302-310. http://doi.org/10.1080/25765299.2019.1621511.
  35. Mondal, S., Maliik, S.H. and Kanoria, M. (2014), "Fractional order two-temperature dual-phase-lag thermoelasticity with variable thermal conductivity", Int. Scholar. Res. Notice., 1-13. http://doi.org/10.1155/2014/646049.
  36. Mudhaffar, M.I., Tounsi, A., Chikh, A., AL-Osta, M.A., Alzahrani, M.M. and Al-Dulaijan, S.U. (2021), "Hygro-thermo-mechanical bending behavior of advanced functionally graded ceramic metal plate resting on a viscoelastic foundation", Structures, 33, 2177-2189. https://doi.org/10.1016/j.istruc.2021.05.090.
  37. Oldham, K.B. and Spainer, J. (1974), The Fractional Calculus, Academic Press, New York, U.S.A.
  38. Palani, G. and Abbas, I. A. (2009), "Free convection MHD flow with thermal radiation from an impulsively-started vertical plate", Nonlinear Anal. Modell. Control, 14(1), 73-84. http://doi.org/10.15388/NA.2009.14.1.14531.
  39. Saeed, T., Abbas, I.A. and Marin, M. (2020), "A gl model on thermo-elastic interactions in a poroelastic material using finite element method", Symmetry, 12(3), 488. http://doi.org/10.3390/sym12030488.
  40. Sur, A. and Kanoria, M. (2012), "Fractional order two-temperature thermoelasticity with finite wave speed", Acta Mechanica, 223, 2685-2701. http://doi.org/10.1007/s00707-012-0736-7.
  41. Tahir, S.I., Chikh, A., Tounsi, A., AL-Osta, M.A., Al-Dulaijan, S.U. and Alzahrani, M.M., (2021), "Wave propagation analysis of a ceramic-metal functionally graded sandwich plate with different porosity distributions in a hygro-thermal environment", Compos. Struct., 269, 114030. https://doi.org/10.1016/j.compstruct.2021.114030.
  42. Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P. (1986), Numerical Recipes in Fortran, Cambridge University Press, New York, U.S.A.
  43. Youssef, H.M. (2006), "Theory of two temperature generalized thermoelasticity", IMA J. Appl. Math., 71(3), 383-390. https://doi.org/10.1093/imamat/hxh101.
  44. Yadav, R., Kumar, K. and Deswal, S. (2015), "Two temperature thermal viscoelasticity with fractional order strain subjected to moving heat source", J. Math., 487513. http://doi.org/10.1155/2015/487513.
  45. Zenkour, A.M. and Abouelregal, A.E. (2015), "The fractional effects of a two-temperature generalized thermoelastic semi-infinite solid induced by pulsed laser heating", Arch. Mech., 67(1), 53-73.
  46. Zenkour, A.M. (2020), "Magneto-thermal shock for a fiber-reinforced anisotropic half-space studied with a refined multi-dual-phase-lag model", J. Phys. Chem. Solids, 137, 109213. http://doi.org/10.1016/j.jpcs.2019.109213.
  47. Zerrouki, R., Karas, A., Zidour, M., Bousahla, A.A., Tounsi, A., Bourada, F., Tounsi, A., Benrahou, K.H. and Mahmoud, S.R., (2021), "Effect of nonlinear FG-CNT distribution on mechanical properties of functionally graded nano-composite beam", Struct. Eng. Mech., 78(2), 117-124. http://doi.org/10.12989/sem.2021.78.2.117.
  48. Zhang, L., Bhatti, M.M., Marin, M. and Mekheimer, M. (2020), "Entropy analysis on the blood flow through anisotropically tapered arteries filled with magnetic zinc-oxide (ZnO) nanoparticles", Entropy, 22(10), 1070. http://doi.org/10.3390/e22101070.