Structural Engineering and Mechanics

  • 제76권5호
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  • Pages.579-590
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  • 2020
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Effect of gravity on a micropolar thermoelastic medium with voids under three-phase-lag model

  • Alharbi, Amnah M. (Department of Mathematics, Faculty of Science, Taif University) ;
  • Othman, Mohamed I.A. (Department of Mathematics, Faculty of Science, Zagazig University) ;
  • Al-Autabi, Al-Anoud M.Kh. (Department of Mathematics, Faculty of Science, Taif University)
  • 투고 : 2020.04.06
  • 심사 : 2020.07.30
  • 발행 : 2020.12.10
⟨ 이전 논문 다음 논문 ⟩

초록

This paper's objective is to investigate the effect of gravity on a micropolar thermoelastic medium with voids. The problem is assessed according to the three-phase-lag model. An analysis of the resulting non-dimensional displacement, temperature variation, and internal stress of the study material is carried out and presented graphically. The non-dimensional displacement, temperature, micro-rotation, the change in the volume fraction field and stress of the material are obtained and illustrated graphically. Comparisons are made with the results predicted by different theories for different values of gravity, the phase-lag of the heat flux and the phase-lag of the temperature gradient. The numerical results reveal that gravity and relaxation times have a significant influence on the distribution of the field quantities. Some notable insights of interest are deduced from the investigation.

키워드

과제정보

The authors thank Taif University Researchers Supporting Project Number (TURSP-2020/230), Taif University, Taif, Saudi Arabia.

참고문헌

  1. Abd-Elaziz, E.M., Marin, M. and Othman, M.I.A. (2019), "On the effect of Thomson and initial stress in a thermo-porous elastic solid under G-N electromagnetic theory", Symmetry, Basel, 11(3), 413-430. https://doi.org/10.3390/sym11030413
  2. Banik, S. and Kanoria, M. (2012), "Effects of three-phase-lag on two-temperature generalized thermoelasticity for infinite medium with spherical Cavity", Appl. Math. Mech. Eng. Ed., 33, 483-498. https://doi.org/10.1007/s10483-012-1565-8
  3. Bhatti, M.M., Shahid, A., Abbas, T., Alamri, S.Z. and Ellahi, R. (2020), "Study of activation energy on the movement of gyrotactic microorganism in a magnetized nano-fluids past a porous plate". Processes, 8(3), 328. https://doi.org/10.3390/pr8030328
  4. 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", Modern Phys. Lett. B, 33(35).1950439 https://doi.org/10.1142/S0217984919504396
  5. Chandrasekharaiah, D.S. (1986), "Heat flux dependent micropolar thermoelasticity", Int. J. Eng. Sci., 24, 1389-1395. https://doi.org/10.1016/0020-7225(86)90067-4
  6. Choudhuri, S.R. (2007), "On thermoelastic three-phase-lag model", J. Therm. Stress, 30, 231-238. https://doi.org/10.1080/01495730601130919
  7. Cowin, S.C. and Nunziato, J.W. (1983), "Linear elastic materials with voids", J. Elast., 13, 125-147. https://doi.org/10.1007/BF00041230
  8. Dhaliwal, R.S. and Singh, A. (1987), "Micropolar thermoelasticity", Thermal Stresses II, Mechanical and Mathematical Methods, Series 2, Noth-Holland, the Netherlands.
  9. El-Karamany, A.S. and Ezzat, M.A. (2013), "On the three-phaselag linear micropolar thermoelasticity theory", Eur. J. Mech. Sol., 40, 198-208. https://doi.org/10.1016/j.euromechsol.2013.01.011
  10. Eringen, A.C. (1965), "Linear theory of micropolar elasticity", ONR Technical Report No. 29; School of Aeronautics, Aeronautics and Engineering Science, Purdue University, USA.
  11. Eringen, A.C. (1966a), "A unified theory of thermo-mechanical materials", Int. J. Eng. Sci., 4, 179-202. https://doi.org/10.1016/0020-7225(66)90022-X
  12. Eringen, A.C. (1966b), "Linear theory of micropolar elasticity", J. Math. Mech., 15, 909-924.
  13. Hosseini, S.M. (2020), "A GN-based modified model for size-dependent coupled thermoelasticity analysis in nano scale, considering nonlocality in heat conduction and elasticity: An analytical solution for a nano beam with energy dissipation", Struct. Eng. Mech., 73(3), 287-302. https://doi.org/10.12989/sem.2020.73.3.287
  14. Marin, M., Ellahi, R., Vlase, S. and Bhatti, M.M. (2020), "On the decay of exponwential type for the solutions in a dipolar elastic body", J. Taibah University Sci., 14(1), 534-540. https://doi.org/10.1080/16583655.2020.1751963
  15. Mondal, S., Sarkar, N. and Sarkar, N. (2019), "Waves in dual-phase-lag thermoelastic materials with voids based on Eringen's nonlocal elasticity", J. Therm. Stress, 42(8), 1035-1050. https://doi.org/10.1080/01495739.2019.1591249
  16. Nowacki, W. (1966), "Couple stresses in the theory of thermoelasticity III", Bull. Acad. Polon. Sci., Ser. Sci Tech., 14(8), 801-809.
  17. Nowacki, W. and Olszak, W. (1974), "Micropolar thermoelasticity", CISM Courses and Lectures. No 151, Udine, Springer-Verlag, Vienna.
  18. Othman, M.I.A., Hasona, W.M. and Abd-Elaziz, E.M. (2015), "Effect of rotation and initial stresses on generalized micropolar thermoelastic medium with three-phase-lag", J. Comput. and Theor. Nanosci., 12, 2030-2040. https://doi.org/10.1166/jctn.2015.3983
  19. Othman, M.I.A. and Abd-Elaziz, E.M. (2015), "The effect of thermal loading due to laser pulse in generalized thermoelastic medium with voids in dual-phase-lag model", J. Therm. Stress., 38(9), 1068-1082. https://doi.org/10.1080/01495739.2015.1073492
  20. Othman, M.I.A., and Ahmed, E.A.A. (2015), "The effect ofrotation on piezo-thermoelastic medium using different theories", Struct. Eng. Mech., 56(4), 649-665. http://dx.doi.org/10.12989/sem.2015.56.4.649
  21. Othman, M.I.A. and Abd-Elaziz, E.M. (2017), "Effect of rotation and gravitational on a micropolar magneto-thermoelastic medium with dual-phase-lag model", Microsys. Techno., 23, 4979-4987. https://doi.org/10.1007/s00542-017-3295-y
  22. Othman, M.I.A., Fekry, M. and Marin, M. (2020), "Plane waves in generalized magneto-thermo-viscoelastic medium with voids under the effect of initial stress and laser pulse heating", Struct. Eng. Mech., 73(6), 621-629. https://doi.org/10.12989/sem.2020.73.6.621
  23. 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/10.1016/j.ijheatmasstransfer.2007.04.045
  24. Quintanilla, R. (2009), "Spatial behavior of solutions of the three-phase-lag heat equation", Appl. Math. Comput.. 213, 153-162. https://doi.org/10.1016/j.amc.2009.03.005
  25. Riaz, A., Ellahi, R., 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. https://doi.org/10.1615/heattransres.2019025622
  26. Said, S.M. and Othman, M.I.A. (2016), "Wave propagation in a two-temperature fiber-reinforced magneto-thermoelastic medium with three-phase-lag model", Struct. Eng. Mech., 57(2), 201-220. http://doi.org/10.12989/sem.2016.57.2.201
  27. Sarkar, N. and Tomar, S.K. (2019), "Plane waves in non-local thermoelastic solid with voids", J. Therm. Stress., 42(5), 580-606. https://doi.org/10.1080/01495739.2018.1554395
  28. Scarpetta, E. (1990), "On the fundamental solutions in micropolar elasticity with voids", Acta. Mechanica, 82, 151-158. https://doi.org/10.1007/BF01173624
  29. Shanker, M. and Dhaliwal, R. (1975), "Dynamic coupled thermoelastic problems in micropolar theory I", Int. J. Eng. Sci., 13, 121-148. https://doi.org/10.1016/0020-7225(75)90024-5
  30. Shahid, A., Huang, H. Bhatti, M.M., Zhang, L. and Ellahi, R. (2020), "Numerical investigation on the swimming of gyrotactic microorganisms in nano-fluids through porous medium over a stretched surface", Mathematics, 8(3), 380. https://doi.org/10.3390/math8030380
  31. Tauchert, T.R., Claus Jr, W.D. and Ariman, T. (1968), "The linear theory of micro- polar thermoelasticity", Int. J. Eng. Sci., 6, 36-47.
  32. Xiong, Q.L. and Tian, X.G. (2016), "Transient magneto-thermoelasto-diffusive responses of rotating porous media without energy dissipation under thermal shock", Meccanica, 51, 2435-2447. DOI.10.1007/s11012-016-0377-3

피인용 문헌

  1. Wave propagation in porous thermoelasticity with two delay times vol.45, pp.3, 2020, https://doi.org/10.1002/mma.7869