Browse > Article
http://dx.doi.org/10.12989/csm.2021.10.2.103

Orthotropic magneto-thermoelastic solid with multi-dual-phase-lag model and hall current  

Lata, Parveen (Department of Basic and Applied Sciences, Punjabi University Patiala)
Himanshi, Himanshi (Department of Basic and Applied Sciences, Punjabi University Patiala)
Publication Information
Coupled systems mechanics / v.10, no.2, 2021 , pp. 103-121 More about this Journal
Abstract
The present research deals with the investigation of the effect of hall current in an orthotropic magneto-thermoelastic medium with two temperature in the context of multi-phase-lag heat transfer due to thermomechanical sources. The bounding surface is subjected to linearly distributed and concentrated loads(mechanical and thermal source).Laplace and Fourier transform techniques are used to solve the problem. The expressions for displacement components,stress components and conductive temperature are derived in transformed domain and furtherin physical domain with the help of numerical inversion techniques. The effect ofrotation and hall parameter hasshown with the help of graphs.
Keywords
orthotropic; hall current; rotation; multi-dual-phase-lag; two temperature; laplace transform; fourier transform; concentrated and linearly distributed loads;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Chikr, S.C., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Adda Bedia, E.A., Mahmoud, S.R., Benrahou, S.R. and Tounsi, A. (2020), "A novel four-unknown integral model for buckling response of FG sandwich plates resting on elastic foundations under various boundary conditions using Galerkin's approach", Geomech. Eng., 21(5), 471-487. https://doi.org/10.12989/gae.2020.21.5.471.   DOI
2 Das, B. and Lahiri, A. (2015), "Generalized Magneto-thermoelasticity for isotropic media", J. Therm. Stress., 38(2), 210-228. http://doi.org/10.1080/01495739.2014.985564.   DOI
3 Draiche, K., Bousahla, A.A., Tounsi, A., Alwabli, A.S., Tounsi, A. and Mahmoud, S.R. (2019), "Static analysis of laminated reinforced composite plates using a simple first order shear deformation theory", Comput. Concrete, 24(4), 369-378. https://doi.org/10.12989/cac.2019.24.4.369.   DOI
4 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.   DOI
5 Honig, G. and Hirdes, U. (1984), "A method for numerical inversion of Laplace transforms", J. Comput. Appl. Math., 10(1), 113-132. http://doi.org/10.1016/0377-0427(84)90075-x.   DOI
6 Kaddari, M., Kaci, A., Bousahla, A.A., Tounsi, A., Bourada, F., Tounsi, A., Adda Bedia, E.A. and Al-Osta, M.A. (2020), "A study on the structural behaviour of functionally graded porous plates on elastic foundation using a new quasi-3D model: Bending and Free vibration analysis", Comput. Concrete, 25(1), 37-57. https://doi.org/10.12989/cac.2020.25.1.037.   DOI
7 Refrafi, S., Bousahla, A.A., Bouhadra, A., Menasria, A., Bourada, F., Tounsi, A., Adda Bedia, E.A., Mahmoud, S.R., Benrahou, K.H. and Tounsi, A. (2020), "Effects of hygro-thermo-mechanical conditions on the buckling of FG sandwich plates resting on elastic foundations", Comput. Concrete, 25(4), 311-325. https://doi.org/10.12989/cac.2020.25.4.311.   DOI
8 Kumar, R. and Abbas, I.A. (2013), "Deformation due to thermal source in micropolar thermoelastic media with thermal and conductive temperatures", J. Comput. Theor. Nanosci., 10(9), 2241-2247. http://doi.org/10.1166/jctn.2013.3193.   DOI
9 Kumar, R. and Chawla, V. (2014), "General solution and fundamental solution for two-dimensional problem in orthotropic thermoelastic media with voids", J. Adv. Math. Appl., 3(1), 47-54. http://doi.org/10.2298/TAM1404247.   DOI
10 Biot, M.A. (1956), "Thermoelasticity and irreversible thermodynamics", J. Appl. Phys., 27(3), 240-253. http://doi.org/10.1063/1.1722351.   DOI
11 Biswas, S. and Abo-Dahab, S.M. (2018), "Effect of phase lags on Rayleigh wave propagation in initially stressed magneto-thermoelastic orthotropic medium", Appl. Math. Model., 59, 713-727. http://doi.org/10.1016/j.apm.2018.02.025.   DOI
12 Biswas, S., Mukhopadhyay, B. and Shaw, S. (2017a), "Thermal shock response in magneto-thermoelastic orthotropic medium with three-phase-lag model", J. Electromagnet. Wave. Appl., 31(9), 879-897. http://doi.org/10.1080/09205071.2017.1326851.   DOI
13 Biswas, S., Mukhopadhyay, B. and Shaw, S. (2017b), "Rayleigh surface wave propagation in orthotropic thermoelastic solid under three phase lag model", J. Therm. Stress., 40(4), 403-419. http://doi.org/10.1080/01495739.2017.1283971.   DOI
14 Bousahla, A.A., Bourada, F., Mahmoud, S.R., Tounsi, A., Algarni, A., Adda Bedia, E.A. and Tounsi, A. (2020), "Buckling and dynamic behavior of the simply supported CNT-RC beams using an integral-first shear deformation theory", Comput. Concrete, 25(2), 155-166. https://doi.org/10.12989/cac.2020.25.2.155.   DOI
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.   DOI
16 Marin, M. (1995), "On existence and uniqueness in thermoelasticity of micropolar bodies", Comptes Rendus De Lacademie Des Sciences Serie II Fascicule B-Mecanique Physique Astronomie, 321(12), 475-480
17 Chen, P.J., Gurtin, M.E. 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.   DOI
18 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.   DOI
19 Abbas, I.A. (2018b), "Free vibrations of nanoscale beam under two-temperature Green and Naghdi Model", Int. J. Acoust. Vib., 23(3), 289-293. http://doi.org/10.20855/ijav.2018.23.31051.   DOI
20 Marin, M. (2010), "Some estimates on vibrations in thermoelasticity of dipolar bodies", J. Vib. Control, 16(1), 33-47. http://doi.org//10.1177/1077546309103419.   DOI
21 Marin, M. (1997), "An uniqueness result for body with voids in linear thermoelasticity", Rendiconti di Mathematica, 17(7), 103-113.
22 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.
23 Matouk, H., Bousahla, A.A., Heireche, H., Bourada, F., Adda Bedia, E.A., Tounsi, A., Mahmoud, S.R., Tounsi, A. and Benrahou, K.H. (2020), "Investigation on hygro-thermal vibration of P-FG and symmetric S-FG nanobeam using integral Timoshenko beam theory", Adv. Nano Res., 8(4), 293-305. https://doi.org/10.12989/anr.2020.8.4.293.   DOI
24 Kumar, R., Sharma, N. and Lata, P. (2017a)," Effects of hall current and two temperature transversely isotropic magneto-thermoelastic with and without energy dissipation due to ramp type heat", Mech. Adv. Mater Struct., 24(8), 625-635. http://doi.org/10.1080/15376494.2016.1196769.   DOI
25 Othman, M.I.A. and Abbas, I.A. (2011), "Effect of rotation on plane waves at the free surface of a fiber reinforced thermoelastic half-space using the finite element method", Meccanica, 46(2), 413-421. http://doi.org/10.1007/s11012-010-9322-z.   DOI
26 Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P. (1986), FORTRAN Numerical Recipes, Cambridge University Press Cambridge.
27 Rahmani, M.C., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Adda Bedia, E.A., Mahmoud, S.R., Benrahou K.H. and Tounsi A. (2020), "Influence of boundary conditions on the bending and free vibration behavior of FGM sandwich plates using a four-unknown refined integral plate theory", Comput. Concrete, 25(3), 225-244. https://doi.org/10.12989/cac.2020.25.3.225.   DOI
28 Kumar, R., Sharma, N. and Lata, P. (2016), "Thermomechanical interactions in transversely isotropic magneto-thermoelastic medium with vacuum and with and without energy dissipation with combined effects of rotation, vacuum and two temperatures", Appl. Math. Model., 40(13-14), 6560-6575. http://doi.org/10.1016/j.apm.2016.01.061.   DOI
29 Kumar, R., Sharma, N. and Lata, P. (2016), "Thermomechanical interactions due to hall current in transversely isotropic thermoelastic with and without energy dissipation with two temperatures and rotation", J. Solid Mech., 8(4), 840-858.
30 Kumar, R., Sharma, N., Lata, P. and Abo-Dahab, S.M. (2017b), "Rayleigh waves in anisotropic magneto thermoelastic medium", Coupl. Syst. Mech., 6(3), 317-333. http://doi.org/10.12989/csm.2017.6.3.317.   DOI
31 Lata, P. and Kaur, I. (2018), "Effect of hall current in transversely isotropic magneto-thermoelastic rotating medium with fractional order heat transfer due to normal force", Adv. Mater. Res., 7(3), 203-220. http://doi.org/10.12989/amr.2018.7.3.203.   DOI
32 Lata, P. and Zakhmi, H. (2019), "Fractional order generalized thermoelastic study in orthotropic medium of type GN-III", Geomech. Eng., 19(4), 295-305. http://doi.org/10.12989/gae.2019.19.4.295.   DOI
33 Lata, P. and Kaur, I. (2019a), "Transversely isotropic magneto thermoelastic solid with two temperature and without energy dissipation in generalized thermoelasticity due to inclined load", SN Appl. Sci., 1(5), 1-13. http://doi.org/10.1007/s42452-019-0438-z.   DOI
34 Lata, P. and Kaur, I. (2019c), "Effect of rotation and inclined load on transversely isotropic magneto thermoelastic solid", Struct. Eng. Mech., 70(2), 245-255. http://doi.org/10.12289/sem.2019.70.2.245.   DOI
35 Lata, P. and Kaur, I. (2020), "Thermomechanical interactions in transversely isotropic magneto-thermoelastic medium with fractional order generalized heat transfer and hall current", Arab J. Basic Appl. Sci., 27(1), 13-26. https://doi.org/10.1080/25765299.2019.1703494.   DOI
36 Lata, P. and Zakhmi, H. (2020), "Time harmonic interactions in an orthotropic media in the context of fractional order theory of thermoelasticity", Struct. Eng. Mech., 73(6), 725-735. http://doi.org/10.12989/sem.2020.73.6.725.   DOI
37 Lord, H.W. and Shulman, Y. (1967), "A generalized dynamical theory of thermoelasticity", J. Mech. Phys. Solid., 15, 299-309. http://doi.org/10.1016/0022-5096(67)90024-5.   DOI
38 Lata, P. and Kaur, I. (2019b), "Effect of hall current on a propagation of plane wave in transversely isotropic thermoelastic medium with two temperature and fractional order heat transfer", SN Appl. Sci., 1(8), 1-16. http://doi.org/10.1007/s42452-019-0942-1.   DOI
39 Marin, M. (1994), "The Lagrange identity method in thermoelasticity of bodies with microstructure", Int. J. Eng. Sci., 32(8), 1229-1240. http://doi.org/10.1016/0020-7225(94)90034-5.   DOI
40 Lata, P. (2018), "Effect of energy dissipation on plane waves in sandwiched layered thermoelastic medium", Steel Compos. Struct., 27(4), 439-451. http://doi.org/10.12989/scs.2018.27.4.439.   DOI
41 Schoenberg, M. and Censor, D. (1973), "Elastic waves in rotating media", Quart. Appl. Math., 31, 115-125. http://doi.org/10.1090/QAM/99708.   DOI
42 Sharma, K. and Marin, M. (2014), "Reflection and transmission of waves from imperfect boundary between two heat conducting micropolar thermoelastic solids", Analele Universitatii "Ovidius" Constanta-Seria Mathematica, 22(2), 151-175. http://doi.org/10.2478/auom-2014-0040.   DOI
43 Youssef, H.M. (2006), "Theory of two temperature generalized thermoelasticity", IMA J. Appl. Math., 71(3), 383-390. http://doi.org/10.1093/imamat/hxh101.   DOI
44 Sharma, N., Kumar, R. and Lata, P. (2015), "Disturbance due to inclined load in transversely isotropic thermoelastic medium with two temperatures and without energy dissipation", Mater. Phys. Mech., 22(2), 107-117.
45 Tounsi, A., Al-Dulaijan, S.U., Al-Osta, M.A., Chikh, A., Al-Zahrani, M.M., Sharif, A. and Tounsi, A. (2020), "A four variable trigonometric integral plate theory for hygro-thermo-mechanical bending analysis of AFG ceramic-metal plates resting on a two-parameter elastic foundation", Steel Compos. Struct., 34(4), 511-524. https://doi.org/10.12989/scs.2020.34.4.51.   DOI
46 Tzou, D.Y. (1995), "A unified field approach for heat conduction from macro to micro scales", ASME J. Heat Transf., 117(1), 8-16. https://doi.org/10.1115/1.2822329.   DOI
47 Zakaria, M. (2012). "Effects of hall current and rotation on magneto-micropolar generalized thermoelasticity due to ramp-type heating", Int. J. Electromagnet Appl., 2(3), 24-32. http://doi.org/10.5923/j.ijea.20120203.02.   DOI
48 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. Solid., 137, https://doi.org/10.1016/j.jpcs.2019.109213.   DOI
49 Abbas, I.A. (2014), "Nonlinear transient thermal stress analysis of thick-walled FGM cylinder with temperature-dependent material properties", Meccanica, 49(7), 1697-1708. http://doi.org/10.1007/s11012-014-9948-3.   DOI
50 Alzahrani, F.S. and Abbas, I.A. (2020), "Photo-thermal interactions in a semiconducting media with a spherical cavity under hyperbolic two-temperature model", Math., 8(585), 1-11. http://doi.org/10.3390/math8040585.   DOI
51 Abbas, I.A. (2018a), "A study on fractional order theory in thermoelastic half-space under thermal loading", Phys. Mesomech., 21(2), 150-156. http://doi.org/10.1134/S102995991802008X.   DOI
52 Abbas, I.A. and Youssef, H.M. (2009), "Finite element analysis of two-temperature generalized magneto thermoelasticity", Arch. Appl. Mech., 79(10), 917-925. http://doi.org/10.1007/s00419-008-0259-9.   DOI
53 Abbas, I.A., Abd-alla, A.N. and Othman, M.I.A. (2011), "Generalized magneto-thermoelasticity in a fiberreinforced anisotropic half-space", Int. J. Thermophys., 32(5), 1071-1085. http://doi.org/10.1007/s10765-011-0957-3.   DOI
54 Abd-alla, A.N. and Abbas, I.A. (2002), "A problem of generalized magneto thermoelasticity for an infinitely long, perfectly conducting cylinder", J. Therm. Stress., 25(11), 1009-1025. http://doi.org/10.1080/01495730290074612.   DOI
55 Abualnour, M., Chikh, A., Hebali, H., Kaci, A., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2019), "Thermomechanical analysis of antisymmetric laminated reinforced composite plates using a new four variable trigonometric refined plate theory", Comput. Concrete, 24(6), 489-498. https://doi.org/10.12989/cac.2019.24.6.489.   DOI
56 Belbachir, N., Draich, K., Bousahla, A.A., Bourada, M., Tounsi, A. and Mohammadimehr, M. (2019), "Bending analysis of anti-symmetric cross-ply laminated plates under nonlinear thermal and mechanical loadings", Steel Compos. Struct., 33(1), 81-92. https://doi.org/10.12989/scs.2019.33.1.081.   DOI
57 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. http://doi.org/10.1615/HeattransRes.2019025622.   DOI
58 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. http://doi.org/10.1142/S0217984919504396.   DOI