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http://dx.doi.org/10.12989/sem.2021.78.6.755

Effect of viscosity and rotation on a generalized two-temperature thermoelasticity under five theories  

Alharbi, Aamnah M. (Department of Mathematics, College of Science, Taif Univeristy)
Othman, Mohamed I.A. (Department of Mathematics, Faculty of Science, Zagazig University)
Atef, Haitham M. (Faculty of Science, Department of Mathematics, Damanhur University)
Publication Information
Structural Engineering and Mechanics / v.78, no.6, 2021 , pp. 755-764 More about this Journal
Abstract
In the current paper, an equational model for generalized thermo-visco-elasticity is set up for such an elastic medium that indicates isotropicity along with two temperatures. The angular velocity for rotating this medium is maintained uniformly. Several generalized thermoelasticity theories have been employed to fulfill the detailing purposes which include; Lord-Shulman (L-S) and Green-Lindsay (G-L) theories with one and two relaxation times respectively, coupled theory, Tzou theory consisting of dual-phase lags (DPL), and lastly Green-Naghdi (G-N II) theory in the absence of energy dissipation. The application of Normal mode examination leads to the attainment of specific articulations for the thought about factors. Some specific cases are additionally talked about with regards to the complexity. Also, Numerical as well as the graphical representation of the factors under consideration has been presented. Examinations are carried out by keeping outcome predictions in mind as anticipated by various theories (L-S, G-N II, G-L, and DPL), rotation, viscosity, and two temperatures.
Keywords
viscosity; generalized thermoelasticity; five theories; rotation; two-temperatures; normal mode analysis;
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1 Boit, M. (1954), "Theory of stress-strain relations in anisotropic viscoelasticity and relaxation phenomena", J. Appl. Phys., 25, 1385-1391.   DOI
2 Mehryan, S.A.M., Vaezi, M., Sheremet, M. and Ghalambaz, M. (2020), "Melting heat transfer of power-law non-Newtonian phase change nano-enhanced n-octadecane-mesoporous silica (MPSiO2)", Int. J. Heat Mass Transf., 151, 119385. https://doi.org/10.1016/j.ijheatmasstransfer.2020.119385.   DOI
3 Pobedria, B.E. (1984), "Coupled problems in continuum mechanics", J. Durab. Plast., 1.
4 Schoenberg, M. and Censor, D. (1973), "Elastic waves in rotating media", Quart Appl. Math., 31, 115-125.   DOI
5 Staverman, A., Schwarzl, F. and Stuart, H. (1956), Die Physik der Hochpolymeren, B and IV Springer, Berlin.
6 Sharma, J.N., Walia, V. and Gupta, S.K. (2008), "Effect of rotation and thermal relaxation on Rayleigh waves in piezothermoelastic half-space", Int. J. Mech. Sci., 50, 433-444. https://doi.org/10.1016/j.ijmecsci.2007.10.001.   DOI
7 Othman, M.I.A., Atwa, S.Y. and Farouk, R.M. (2008), "Generalized magneto-thermo-viscoelastic plane waves under the effect of rotation without energy dissipation", Int. J. Eng. Sci., 46(7), 639-653. https://doi.org/10.1016/j.ijengsci.2008.01.018.   DOI
8 Gurtin, M.E. and Sternberg, E. (1962), "On the linear theory of viscoelasticity", Arch. Rat. Mech. Anal., 11, 291-356. https://doi.org/10.1007/BF00253942.   DOI
9 Alimirzaei, S., Mohammadimehr, M. and Tounsi, A. (2019), "Nonlinear analysis of viscoelastic micro-composite beam with geometrical imperfection using FEM: MSGT electro-magneto-elastic bending, buckling and vibration solutions", Struct. Eng. Mech., 71(5), 485-502. https://doi.org/10.12989/sem.2019.71.5.485.   DOI
10 El-Bary, A.A. and Atef, H.M. (2016), "On effect of viscous fractional parameter on infinite thermo-viscoelastic medium with a spherical cavity", J Comput. Theo. Nanosci., 13(1), 1027-1037. https://doi.org/10.1166/jctn.2016.4332.   DOI
11 Othman, M.I.A., Said, S.M. and Marin, M. (2019), "A novel model of plane waves of two-temperature fiber-reinforced thermoelastic medium under the effect of gravity with threephase-lag model", Int. J. Numer. Meth. Heat Fluid Flow, 29(12), 4788-4806. https://doi.org/10.1108/HFF-04-2019-0359.   DOI
12 Sheokand, S.K., Kumar, R., Kalkal, K.K. and Deswal, S. (2019), "Propagation of plane waves in an orthotropic magneto-thermo-diffusive rotating half-space", Struct. Eng. Mech., 72(4), 455-468. https://doi.org/10.12989/sem.2019.72.4.455.   DOI
13 Fahmy, M.A. (2012), "The effect of rotation and inhomogeneity on the transient magneto-thermo-visco-elastic stresses in an anisotropic solid", ASME J. Appl. Mech., 79(5), 051015. https://doi.org/10.1115/1.4006258.   DOI
14 Ghalambaz, M., Mehryan, S.A.M., Tahmasebi, A. and Hajjar, A. (2020), "Non-Newtonian phase-change heat transfer of Nano-enhanced octadecane with meso-porous silica particles in a tilted enclosure using a deformed mesh technique", Appl. Math. Model., 85, 318-337. https://doi.org/10.1016/j.apm.2020.03.046.   DOI
15 Ilioushin, A. and Pobedria, B. (1970), "Mathematical theory of thermal visco-elasticity", Nauka, Moscow.
16 Fahmy, M.A. (2018), "Shape design sensitivity and optimization for two-temperature generalized magneto-thermoelastic problems using time-domain DRBEM", J. Therm. Stress., 41, 119-138. https://doi.org/10.1080/01495739.2017.1387880.   DOI
17 Biot, M.A. (1956), "Thermo-elasticity and irreversible thermodynamics", Appl. Phys., 27, 240-253. https://doi.org/10.1063/1.1722351.   DOI
18 Bland, D.R. (1960), The Theory of Linear Viscoelasticity, Pergamon Press, New York.
19 Fahmy, M.A. (2019b), "Design optimization for a simulation of rotating anisotropic viscoelastic porous structures using time-domain OQBEM", Math. Comput. Simul., 66, 193-205. https://doi.org/10.1016/j.matcom.2019.05.004.   DOI
20 Ferry, J.D. (1980), Vescoelastic Properties of Polymers, John Wiley & Sons.
21 Gross, B. (1953), Mathematical Structure of the Theories of Viscoelasticity, Vol. 27, Hermann, Paris.
22 Hetnaraski, R.B. and Ignaczak, J. (1996), "Solution-like waves in a low-temperature nonlinear thermoelastic solid", Int. J. Eng. Sci., 34, 1767-1787. https://doi.org/10.1016/S0020-7225(96)00046-8.   DOI
23 Ilioushin, A. (1968), "The approximation method of calculating the constructures by linear thermal viscoelastic theory", Mekhanika Polimerov Riga, 2, 168-178.
24 Koltunov, M.A. (1976), "Creeping and relaxation", Vysshaya Shkola, Moscow.
25 Fahmy, M.A. (2013b), "A three-dimensional generalized magneto-thermo-viscoelastic problem of a rotating functionally graded anisotropic solids with and without energy dissipation", Numer. Heat Transf. Part A: Appl., 63(9), 713-733. https://doi.org/10.1080/10407782.2013.751317.   DOI
26 Chen, P.J. and Gurtin, M.E. (1968), "On a theory of heat conduction involving two temperatures", ZAMP, 19, 614-627. https://doi.org/10.1007/BF01594969.   DOI
27 Chen, P.J. and Williams, W.O. (1968), "A note on non-simple heat conduction", ZAMP, 19, 614-627. https://doi.org/10.1007/BF01602278.   DOI
28 Fahmy, M.A. (2013a), "Implicit-Explicit time integration DRBEM for generalized magneto-thermoelasticity problems of rotating anisotropic viscoelastic functionally graded solids", Eng. Anal. Bound. Elem., 37(1), 107-115. https://doi.org/10.1016/j.enganabound.2012.08.002.   DOI
29 Fahmy, M.A. (2019a), "Modeling and optimization of anisotropic viscoelastic porous structures using CQBEM and moving asymptotes algorithm", Arab. J. Sci. Eng., 44, 1671-1684. https://doi.org/10.1007/s13369-018-3652-x.   DOI
30 Green, A.E. and Lindsay, K.A. (1972), "Thermoelasticity", J. Elast., 2, 1-7.   DOI
31 Green, A.E. and Naghdi, P.M. (1991), "A re-examination of the basic postulates of thermomechanics", Proc. Roy. Soc. London Ser. A: Math. Phys. Sci., 432(1885), 171-194. https://doi.org/10.1098/rspa.1991.0012   DOI
32 Othman, M.I.A. (2004), "The uniqueness and reciprocity theorems for generalized thermo-viscoelasticity with thermal relaxation times", Mech. Mech. Eng., 7, 77-87.
33 Hetnaraski, R.B. and Ignaczak, J. (1990), "Generalized thermoelasticity", J. Therm. Stress., 22, 451-476. https://doi.org/10.1080/014957399280832.   DOI
34 Kosinski, W. (1989). "Elasic waves in the presence of a new temperature scale", North-Holland Ser. Appl. Math. Mech., 35, 629-634).   DOI
35 Lata, P. and Kaur, I. (2019), "Effect of rotation and inclined load on transversely isotropic magneto-thermoelastic solid", Struct. Eng. Mech., 70(2), 245-255. https://doi.org/10.12989/sem.2019.70.2.245.   DOI
36 Othman, M.I.A. (2005), "Generalized electromagneto-thermo-elastic 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://doi.org/10.1163/157361105774538557.   DOI
37 Othman, M.I.A. (2009), "Generalized thermo-viscoelasticity under three theories", Mech. Mech. Eng., 13, 25-44.
38 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. https://doi.org/10.1007/s10765-011-1109-5.   DOI
39 Othman, M.I.A. and Song, Y.Q. (2008), "Effect of rotation on plane waves of the generalized electromagneto-thermo-viscoelasticity with two relaxation times", Appl. Math. Model., 32(5), 811-825. https://doi.org/10.1016/j.apm.2007.02.025.   DOI
40 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.   DOI
41 Abdul Gaffar, S., Ramesh Reddy, P., Ramachandra Prasad, V., Subba Rao, A. and Khan, B.M. (2020), "Viscoelastic micropolar convection flows from an inclined plane with nonlinear temperature: A numerical study", J. Appl. Comput. Mech., 6(2), 183-199. https://doi.org/10.22055/JACM.2019.28695.1498.   DOI