journal article·2023-06

Thermal Analysis of a Rotating Micropolar Medium Using a Two-Temperature Micropolar Thermoelastic Model with Higher-Order Time Derivatives

A. E. Abouelregal, R. Alanazi, A. H. Sofiyev, H. M. Sedighi

Physical Mesomechanics· Volume 26· Issue 3
Publisher page

Abstract

Abstract In this work, the propagation of planar waves in a homogeneous micropolar thermoelastic medium is studied while the entire body rotates with a uniform angular speed. The coordinate system of the rotating medium is assumed to be stationary, and therefore the kinematic equations have two additional terms, namely, the gravitational and the Coriolis accelerations. The problem is addressed based on the two-temperature thermoelastic model with higher-order time derivatives and dual-phase lag, which can explain the effect of microscopic features in nonsimple materials. With certain boundary conditions and the normal mode approach, the variations in temperature, displacement, microrotation, and thermal stresses induced by heating are derived. In the absence of rotation and two-temperature factor, comparison is made with the results of classical thermoelastic models.
Source: openalex_inverted_index · Quality: baseline

Research context

OpenAlex topics: Thermoelastic and Magnetoelastic Phenomena · Nonlocal and gradient elasticity in micro/nano structures · Numerical methods in engineering

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (61)

Show source-provided references
1. Subba Rao, V. and Nigam, S.D., Wave Propagation in Rotating Elastic Media, Mathematica, 1964, pp. 29–38. https://doi.org/10.1112/S002557930000345410.1112/S0025579300003454 ↗
2. Durukan, Y., Shevelko, M., Peregudov, A., Popkova, E., and Shevchenko, S., The Effect of a Rotating Medium on Bulk Acoustic Wave Polarization: From Theoretical Considerations to Perspective Angular Motion Sensor Design, Sensors, 2020, vol. 20(9), p. 2487. https://doi.org/10.3390/s2009248710.3390/s20092487 ↗
3. Khan, A., Islam, S., and Khan, M., Rayleigh Waves in a Rotating Orthotropic Medium, World Appl. Sci. J., 2012, vol. 16(1), pp. 73–75.
4. Jafari, S., Elastic Limit Angular Speed and Acceleration Investigation in Non-‎Uniform Rotating Disk under Time-Dependent Mechanical Loading, J. Appl. Comput. Mech., 2022, vol. 8(3), pp. 791–808. https://doi.org/10.22055/jacm.2020.32914.209910.22055/jacm.2020.32914.2099 ↗
5. Abouelregal, A.E., Atta, D., and Sedighi, H.M., Vibrational Behavior of Thermoelastic Rotating Nanobeams with Variable Thermal Properties Based on Memory-Dependent Derivative of Heat Conduction Model, Arch. Appl. Mech., 2022. https://doi.org/10.1007/s00419-022-02110-810.1007/s00419-022-02110-8 ↗
6. Sladek, J., Sladek, V., and Repka, M., The Heat Conduction in Nanosized Structures, Phys. Mesomech., 2021, vol. 24, no. 5, pp. 611–617. https://doi.org/10.1134/S102995992105012X10.1134/S102995992105012X ↗
7. Abouelregal, A.E., Sedighi, H.M., Malikan, M., and Eremeyev, V.A., Nonlocalized Thermal Behavior of Rotating Micromachined Beams under Dynamic and Thermodynamic Loads, ZAMM–J. Appl. Math. Mech., 2022, vol. 102(4), p. e202100310. https://doi.org/10.1002/zamm.20210031010.1002/zamm.202100310 ↗
8. Abouelregal, A.E. and Abo-Dahab, S.M., A Two-Dimensional Problem of a Mode-I Crack in a Rotating Fibre-Reinforced Isotropic Thermoelastic Medium under Dual-Phase-Lag Model, Sadhana, 2018, vol. 43, p. 13. https://doi.org/10.1007/s12046-017-0769-710.1007/s12046-017-0769-7 ↗
9. Abouelregal, A.E., Mohammad-Sedighi, H., Faghidian, S.A., and Shirazi, A.H., Temperature-Dependent Physical Characteristics of the Rotating Nonlocal Nanobeams Subject to a Varying Heat Source and a Dynamic Load, Facta Univ., Ser. Mech. Eng., 2021, vol. 19(4), pp. 633–656. https://doi.org/10.22190/FUME201222024A10.22190/FUME201222024A ↗
10. Abouelregal, A.E., Marin, M., and Askar, S., Thermo-Optical Mechanical Waves in a Rotating Solid Semiconductor Sphere Using the Improved Green–Naghdi III Model, Mathematics, 2021, vol. 9(22), p. 2902. https://doi.org/10.3390/math922290210.3390/math9222902 ↗
11. Biot, M., Thermoelasticity and Irreversible Thermodynamics, J. Appl. Phys., 1956, vol. 27, pp. 240–253.10.1063/1.1722351 ↗
12. Lord, H.W. and Shulman, Y.H., A Generalized Dynamical Theory of Thermoelasticity, J. Mech. Phys. Solids, 1967, vol. 15, pp. 299–309. https://doi.org/10.1063/1.172235110.1063/1.1722351 ↗
13. Green, A.E. and Naghdi, P.M., A Re-examination of the Basic Results of Thermomechanics, Proc. Math. Phys. Sci., 1991, vol. 432, pp. 171–194. https://doi.org/10.1098/rspa.1991.001210.1098/rspa.1991.0012 ↗
14. Green, A.E. and Lindsay, K.A., Thermoelasticity, J. Elasticity, 1972, vol. 2, pp. 1–7.10.1007/BF00045689 ↗
15. Green, A.E. and Naghdi, P.M., On Undamped Heat Waves in an Elastic Solid, J. Therm. Stress., 1992, vol. 15, pp. 252–264. https://doi.org/10.1007/BF0004568910.1007/BF00045689 ↗
16. Green, A.E. and Naghdi, P.M., Thermoelasticity without Energy Dissipation, J. Elasticity, 1994, vol. 31, pp. 189–208. https://doi.org/10.1007/BF0004496910.1007/BF00044969 ↗
17. Tzou, D.Y., A Unified Filed Approach for Heat Conduction from Macro to Macroscales, ASME J. Heat Transfer, 1995, vol. 117, pp. 8–16. https://doi.org/10.1115/1.282232910.1115/1.2822329 ↗
18. Tzou, D.Y., The Generalized Lagging Response in Small-Scale and High-Rate Heating, Int. J. Heat Mass Transfer, 1995, vol. 38, pp. 3231–3234. https://doi.org/10.1016/0017-9310(95)00052-B10.1016/0017-9310(95)00052-B ↗
19. Tzou, D.Y., Experimental Support for the Lagging Behavior in Heat Propagation, J. Thermophys. Heat Transfer, 1995, vol. 9, pp. 686–693. https://doi.org/10.2514/3.72510.2514/3.725 ↗
20. Abouelregal, A.E., Two-Temperature Thermoelastic Model without Energy Dissipation Including Higher Order Time-Derivatives and Two Phase-Lags, Mater. Res. Express, 2019, vol. 6, p. 116535. https://doi.org/10.1088/2053-1591/ab447f10.1088/2053-1591/ab447f ↗
21. Abouelregal, A.E., On Green and Naghdi Thermoelasticity Model without Energy Dissipation with Higher Order Time Differential and Phase-Lags, J. Appl. Comput. Mech., 2020, vol. 6(3), pp. 445–456. https://doi.org/10.22055/JACM.2019.29960.164910.22055/JACM.2019.29960.1649 ↗
22. Abouelregal, A.E., A Novel Generalized Thermoelasticity with Higher-Order Time-Derivatives and Three-Phase Lags, Multidiscipline Model. Mater. Struct., 2019, vol. 16, pp. 689–711. https://doi.org/10.1108/MMMS-07-2019-013810.1108/MMMS-07-2019-0138 ↗
23. Abouelregal, A.E., A Novel Model of Nonlocal Thermoelasticity with Time Derivatives of Higher Order, Math. Meth. Appl. Sci., 2020, vol. 43, pp. 6746–6760. https://doi.org/10.1002/mma.641610.1002/mma.6416 ↗
24. Abouelregal, A.E., Three-Phase-Lag Thermoelastic Heat Conduction Model with Higher-Order Time-Fractional Derivatives, Indian J. Phys., 2020, vol. 94, pp. 1949–1963. https://doi.org/10.1007/s12648-019-01635-z10.1007/s12648-019-01635-z ↗
25. Choudhuri, S.R., On a Thermoelastic Three-Phase-Lag Model, J. Therm. Stress., 2020, vol. 30, pp. 231–238. https://doi.org/10.1080/0149573060113091910.1080/01495730601130919 ↗
26. Chen, P.J. and Gurtin, M.E., On a Theory of Heat Conduction Involving Two Temperatures, Zeitschrift Angewandte Math. Phys., 1968, vol. 19, pp. 614–627. https://doi.org/10.1007/BF0159496910.1007/BF01594969 ↗
27. Chen, P.J. and Williams, W.O., A Note on Non-Simple Heat Conduction, Zeitschrift Angewandte Math. Phys., 1968, vol. 19, pp. 969–970. https://doi.org/10.1007/BF0160227810.1007/BF01602278 ↗
28. Chen, P.J., Gurtin, M.E., and Williams, W.O., On the Thermodynamics of Non-Simple Elastic Materials with Two Temperatures, Zeitschrift Angewandte Math. Phys., 1969, vol. 20, pp. 107–112. https://doi.org/10.1007/BF0159112010.1007/BF01591120 ↗
29. Quintanilla, R., On Existence, Structural Stability, Convergence and Spatial Behavior in Thermoelasticity with Two Temperatures, Acta Mech., 2004, vol. 168, pp. 61–73. https://doi.org/10.1007/s00707-004-0073-610.1007/s00707-004-0073-6 ↗
30. Youssef, H., Theory of Two-Temperature-Generalized Thermoelasticity, IMA J. Appl. Math., 2006, vol. 71, pp. 383–390. https://doi.org/10.1093/imamat/hxh10110.1093/imamat/hxh101 ↗
31. Ezzat, M.A. and El-Karamany, A.S., Two Temperature Theory in Generalized Magneto Thermoelasticity with Two Relaxation Times, Meccanica, 2011, vol. 46, pp. 785–794. https://doi.org/10.1007/s11012-010-9337-510.1007/s11012-010-9337-5 ↗
32. Mukhopadhyay, S., Prasad, R., and Kumar, R., On the Theory of Two-Temperature Thermoelasticity with Two Phase-Lags, J. Therm. Stress., 2011, vol. 34, pp. 352–365. https://doi.org/10.1080/01495739.2010.55081510.1080/01495739.2010.550815 ↗
33. Kumar, R., Prasad, R., and Kumar, R., Thermoelastic Interactions on Hyperbolic Two-Temperature Generalized Thermoelasticity in an Infinite Medium with a Cylindrical Cavity, Eur. J. Mech. A. Solids, 2020, vol. 82, p. 104007. https://doi.org/10.1016/j.euromechsol.2020.10400710.1016/j.euromechsol.2020.104007 ↗
34. Fernández, J.R. and Quintanilla, R., Uniqueness and Exponential Instability in a New Two-Temperature Thermoelastic Theory, AIMS Mathematics, 2021, vol. 6(6), pp. 440–5451. https://doi.org/10.3934/math.202132110.3934/math.2021321 ↗
35. Sarkar, N. and Mondal, S., Two-Dimensional Problem of Two-Temperature Generalized Thermoelasticity Using Memory-Dependent Heat Transfer: An Integral Transform Approach, Indian J. Phys., 2020, vol. 94(12), pp. 965–1974. https://doi.org/10.1007/s12648-019-01639-910.1007/s12648-019-01639-9 ↗
36. Hobiny, A., Abbas, I., and Marin, M., The Influences of the Hyperbolic Two-Temperatures Theory on Waves Propagation in a Semiconductor Material Containing Spherical Cavity, Mathematics, 2022, vol. 10(1), p. 121. https://doi.org/10.3390/math1001012110.3390/math10010121 ↗
37. Hassanpour, S. and Heppler, G.R., Micropolar Elasticity Theory: A Survey of Linear Isotropic Equations, Representative Notations, and Experimental Investigations, Math. Mech. Solids, 2017, vol. 22(2), pp. 224–242. https://doi.org/10.1177/108128651558118310.1177/1081286515581183 ↗
38. Eringen, A.C., Linear Theory of Micropolar Elasticity, J. Appl. Math. Mech., 1966, vol. 15, pp. 909–923. https://www.jstor.org/stable/24901442
39. Nowacki, W., Theory of Asymmetric Elasticity, Oxford: Pergamon, 2004.
40. Eringen, A.C., Foundations of Micropolar Thermoelasticity, International Centre for Mechanical Science, Udine Course and Lectures 23, Berlin: Springer-Verlag, 1970.10.1007/978-3-7091-2904-3 ↗
41. Tauchert, T.R., Claus, Jr.W.D., and Ariman, T., The Linear Theory of Micropolar Thermoelasticity, Int. J. Eng. Sci., 1968, vol. 6, pp. 37–47. https://doi.org/10.1016/0020-7225(68)90037-210.1016/0020-7225(68)90037-2 ↗
42. Dost, S. and Tabarrok, B., Generalized Micropolar Thermoelasticity, Int. J. Eng. Sci., 1978, vol. 16, p. 173. https://doi.org/10.1016/0020-7225(78)90046-010.1016/0020-7225(78)90046-0 ↗
43. Chandrasekhariah, D.S., Heat Flux Dependent Micropolar Elasticity, Int. J. Eng. Sci., 1986, vol. 24, pp. 1389–1395. https://doi.org/10.1016/0020-7225(86)90067-410.1016/0020-7225(86)90067-4 ↗
44. El-Karamany, A.S. and Ezzat, M.A., On the Three-Phase-Lag Linear Micropolar Thermoelasticity Theory, Eur. J. Mech. A. Solids, 2013, vol. 40, pp. 198–208. https://doi.org/10.1016/j.euromechsol.2013.01.01110.1016/j.euromechsol.2013.01.011 ↗
45. Alharbi, A.M., Said, S.M., Abd-Elaziz, E.M., and Othman, M.I.A., Mathematical Model for a Magneto-Thermoelastic Micropolar Medium with Temperature-Dependent Material Moduli under the Effect of Mechanical Strip Load, Acta Mech., 2021, vol. 232(6), pp. 2331–2346. https://doi.org/10.1007/s00707-021-02941-610.1007/s00707-021-02941-6 ↗
46. Chirilă, A., Agarwal, R.P., and Marin, M., Proving Uniqueness for the Solution of the Problem of Homogeneous and Anisotropic Micropolar Thermoelasticity, Bound. Value Probl., 2017, vol. 3, p. 2017. https://doi.org/10.1186/s13661-016-0734-010.1186/s13661-016-0734-0 ↗
47. Sharma, H., Kumari, S., and Kumar, A., Study of Micropolar Thermo-Elasticity, Adv. Appl. Math. Sci., 2020, vol. 19, pp. 929–941.
48. Hilal, M.I.M., Abd-Elaziz, E.M., and Hanoura, S.A., Reflection of Plane Waves in Magneto-Micropolar Thermoelastic Medium with Voids and One Relaxation Time due to Gravity and Two-Temperature Theory, Indian J. Phys., 2021, vol. 95, pp. 915–924. https://doi.org/10.1007/s12648-020-01772-w10.1007/s12648-020-01772-w ↗
49. Kumar, R., Prasad, R., and Kumar, R., Thermoelastic Interactions on Hyperbolic Two-Temperature Generalized Thermoelasticity in an Infinite Medium with a Cylindrical Cavity, Eur. J. Mech. A. Solids, 2020, vol. 8, p. 04007. https://doi.org/10.1016/j.euromechsol.2020.10400710.1016/j.euromechsol.2020.104007 ↗
50. Lianngenga, R. and Singh, S.S., Reflection of Coupled Dilatational and Shear Waves in the Generalized Micropolar Thermoelastic Materials, J. Vibr. Control, 2020, vol. 26, pp. 1948–1955. https://doi.org/10.1177/107754632090870510.1177/1077546320908705 ↗
51. Marin, M., Chirila, A., Öchsner, A., and Vlase, S., About Finite Energy Solutions in Thermoelasticity of Micropolar Bodies with Voids, Bound. Value Probl., 2019, vol. 89, p. 2019. https://doi.org/10.1186/s13661-019-1203-310.1186/s13661-019-1203-3 ↗
52. Abouelregal, A.E. and Zenkour, A.M., Two-Temperature Thermoelastic Surface Waves in Micropolar Thermoelastic Media Via Dual-Phase-Lag Model, Adv. Aircraft Spacecraft Sci., 2017, vol. 4, pp. 711–727. https://doi.org/10.12989/aas.2017.4.6.71110.12989/aas.2017.4.6.711 ↗
53. Guesmia, A., MuÑoz Rivera, J.E., Sepúlveda CortÉs, M.A., and Vera VillagrÁn, O., Well-Posedness and Stability of a Generalized Micropolar Thermoelastic Body with Infinite Memory, Quarterly J. Mathematics, 2021, vol. 72, pp. 1495–1515. https://doi.org/10.1093/qmath/haab01410.1093/qmath/haab014 ↗
54. Kumar, R. and Abbas, I.A., Deformation due to Thermal Source in Micropolar Thermoelastic Media with Thermal and Conductive Temperatures, J. Comput. Theor. Nanosci., 2013, vol. 10, pp. 2241–2247. https://doi.org/10.1166/jctn.2013.319310.1166/jctn.2013.3193 ↗
55. Shaw, S. and Mukhopadhyay, B., Moving Heat Source Response in Micropolar Half-Space with Two-Temperature Theory, Continuum Mech. Thermodyn., 2013, vol. 25, pp. 523–535. https://doi.org/10.1007/s00161-012-0284-310.1007/s00161-012-0284-3 ↗
56. Ezzat, M.A. and Awad, E.S., Constitutive Relations, Uniqueness of Solution and Thermal Shock Application in the Linear Theory of Micropolar Generalized Thermoelasticity Involving Two Temperatures, J. Therm. Stress., 2010, vol. 33, pp. 226–250. https://doi.org/10.1080/0149573090354282910.1080/01495730903542829 ↗
57. Quintanilla, R., Exponential Stability and Uniqueness in Thermoelasticity with Two Temperatures, Dyn. Contin. Discrete Impuls. Syst. A. Math. Anal., 2004, vol. 11, pp. 57–68.
58. Quintanilla, R., A Well Posed Problem for the Dual-Phase-Lag Heat Conduction, J. Therm. Stress., 2008, vol. 31, pp. 260–269. https://doi.org/10.1080/0149573070173827210.1080/01495730701738272 ↗
59. Chiriţă, S., On the Time Differential Dual-Phase-Lag Thermoelastic Model, Meccanica, 2017, vol. 52, pp. 349–361. https://doi.org/10.1007/s11012-016-0414-210.1007/s11012-016-0414-2 ↗
60. Chiriţă, S., Ciarletta, M., and Tibullo, V., On the Thermomechanic Consistency of the Time Differential Dual-Phase-Lag Models of Heat Conduction, Int. J. Heat Mass Transfer, 2017, vol. 114, pp. 277–285. https://doi.org/10.1016/j.ijheatmasstransfer.2017.06.07110.1016/j.ijheatmasstransfer.2017.06.071 ↗
61. Chiriţă, S., Ciarletta, M., and Tibullo, V., On the Wave Propagation in the Time Differential Dual-Phase-Lag Thermoelastic Model, Proc. R. Soc. A, 2015, vol. 471, p. 20150400. https://doi.org/10.1098/rspa.2015.04010.1098/rspa.2015.040 ↗