Refined multi-phase-lags theory and Thomson effect on a micropolar thermoelastic medium with voids

Journal title

Archives of Thermodynamics


Alharbi, Amnah M. : Taif University, Department of Mathematics, College of Science, P.O. Box 11099, Taif, 21944, Saudi Arabia ; Abd-Elaziz, Elsayed M. : Ministry of Higher Education, Zagazig Higher Institute of Engineering & Technology, Zagazig, Egypt ; Othman, Mohamed I.A. : Zagazig University, Department of Mathematics, Faculty of Science, P.O. Box 44519, Zagazig, Egypt



Micropolar ; Voids ; Refined-phase-lags theory ; Thomson effect ; Normal mode analysis

Divisions of PAS

Nauki Techniczne




The Committee of Thermodynamics and Combustion of the Polish Academy of Sciences and The Institute of Fluid-Flow Machinery Polish Academy of Sciences


[1] Biot M.A.: Thermoelasticity and irreversible thermodynamics. J. Appl. Phys. 7(1956), 3, 240–253.
[2] Lord H.W., Shulman Y.: A generalized dynamical theory of thermoelasticity. J. Mech. Phys. Sol. 15(1967), 5, 299–309.
[3] Green A.E., Lindsay K.A.: Thermoelasticity. J. Elast. 2(1972), 1, 1–7.
[4] Green A.E., Naghdi P.M.: A re-examination of the basic postulates of thermosmechanics. Proc. R. Soc. Lond. A 432(1991), 1885, 171–194.
[5] Green A.E., Naghdi P.M.: On undamped heat wave in elastic solids. J. Therm. Stress. 15(1992), 2, 253–264.
[6] Green A.E., Naghdi P.M.: Thermoelasticity without energy dissipation. J. Elast. 31(1993), 189–209.
[7] Tzou D.Y.: The generalized lagging response in small-scale and high-rate heating. Int. J. Heat Mass Trans. 38(1995), 17, 3231–3240.
[8] Tzou D.Y.: A unified field approach for heat conduction from macro- to microscales. J. Heat Trans. 117(1995), 1, 8–16.
[9] Roy Choudhuri S.K.: On a thermoelastic three-phase-lag model. J. Therm. Stress. 30(2007), 3, 231–238.
[10] Eringen A.C.: Linear theory of micropolar elasticity. ONR Techn. Rep. 29 (School of Aeronautics, Aeronautics and Engineering Science), Purdue Univ., West Lafayett 1965.
[11] Eringen A.C.: A unified theory of thermomechanical materials. Int. J. Eng. Sci. 4(1966), 2, 179–202.
[12] Eringen A.C.: Linear theory of micropolar elasticity. J. Math. Mech. 15(1966), 6, 909–924.
[13] Nowacki W.: Couple stresses in the theory of thermoelasticity III. Bull. Acad. Pol. Sci. Tech. Ser. Sci. Tech. 14(1966), 8, 801–809.
[14] Tauchert T.R., Claus Jr. W.D., Ariman T.: The linear theory of micropolar thermo- elasticity. Int. J. Eng. Sci. 6(1968), 1, 36–47.
[15] Nowacki W., Olszak W. (Eds.): Micropolar Thermoelasticity. CISM Courses and Lectures 151, Springer-Verlag, Vienna 1974.
[16] Dhaliwal R.S., Singh A.: Micropolar thermoelasticity. In: Thermal Stresses II (R.B. Hetnarski, Ed.), Elsevier, Amsterdam 1987.
[17] Marin M., Nicaise S.: Existence and stability results for thermoelastic dipolar bodies with double porosity. Continuum Mech. Thermodyn. 28(2016), 6, 1645–1657.
[18] Marin M., Ellahi R., Chirila A.: On solutions of Saint–Venant’S problem for elastic dipolar bodies with voids. Carpathian J. Math. 33(2017), 2, 219–232.
[19] Othman M.I.A., Hasona W.M., Abed-Elaziz E.M.: Effect of rotation on micropolar generalized thermoelasticity with two temperatures using a dual-phase lag model. Can. J. Phys. 92(2014), 2, 148–159.
[20] Othman M.I.A., Hasona W.M., Abed-Elaziz E.M.: The influence of thermal loading due to laser pulse on generalized micropolar thermoelastic solid with comparison of different theories. Multi. Model. Mater. Struct. 10(2014), 3, 328–345.
[21] Chandrasekharaiah D.S.: Heat flux dependent micropolar thermoelasticity. Int. J. Eng. Sci. 24(1986), 8, 1389–1395.
[22] Othman M.I.A., Hasona W.M., Abed-Elaziz E.M.: Effect of rotation and initial stresses on generalized micropolar thermoelastic medium with three-phase-lag. J. Comput. Theor. Nanosci. 12(2015), 9, 2030–2040.
[23] Othman M.I.A., Abed-Elaziz E.M.: Effect of rotation and gravitational on a micropolar magneto-thermoelastic medium with dual-phase-lag model. Microsyst. Tech. 23(2017), 10, 4979–4987.
[24] Othman M.I.A., Abd-alla A.N., Abed-Elaziz E.M.: Effect of heat laser pulse on wave propagation of generalized thermoelastic micropolar medium with energy dissipation. Ind. J. Phys. 94(2020), 3, 309–317.
[25] Cowin S.C., Nunziato J.W.: Linear elastic materials with voids. J. Elast. 13(1983), 2, 125–147.
[26] Othman M.I.A., Abed–Elaziz E.M.: The effect of thermal loading due to laser pulse in generalized thermoelastic medium with voids in dual-phase-lag model. J. Therm. Stress. 38(2015), 9, 1068–1082.
[27] Abd-Elaziz E.M., Othman M.I.A.: Effect of Thomson and thermal loading due to laser pulse in a magneto-thermoelastic porous medium with energy dissipation. ZAMM-Z. Angew. Math. Me. 99(2019), 8, 201900079.
[28] Abd-Elaziz E.M., Marin M., Othman M.I.A.: On the effect of Thomson and initial stress in a thermos-porous elastic solid under G-N electromagnetic theory. Symmetry. 11(2019), 3, 413–430.
[29] Othman M.I.A., Marin M.: Effect of thermal loading due to laser pulse on thermoelastic porous media under G-N theory. Results Phys. 7(2017), 3863–3872.
[30] Othman M.I.A, Abd-Elaziz E.M.: Plane waves in a magneto-thermoelastic solids with voids and microtemperatures due to hall current and rotation. Results Phys. 7(2017), 4253–4263.
[31] Othman M.I.A., Tantawi R.S., Eraki E.E.M.: Effect of rotation on a semi conducting medium with two-temperature under L–S theory. Arch. Thermodyn. 38(2017), 2, 101–122.
[32] Chirita S., Ciarletta M., Tibullo V.: On the thermomechanical consistency of the time differential dual-phase-lag models of heat conduction. Int. J. Heat Mass Tran. 114(2017), 277–285.
[33] (accessed 17 Feb. 2021)






DOI: 10.24425/ather.2021.138120

Editorial Board

International Advisory Board

J. Bataille, Ecole Central de Lyon, Ecully, France
A. Bejan, Duke University,  Durham, USA
W. Blasiak, Royal Institute of Technology,  Stockholm, Sweden
G. P. Celata, ENEA,  Rome, Italy
M. W. Collins, South Bank University,  London, UK
J. M. Delhaye, CEA, Grenoble, France
M. Giot, Université Catholique de Louvain, Belgium
D. Jackson, University of Manchester, UK
S. Michaelides, University of North Texas, Denton, USA
M. Moran, Ohio State University,  Columbus, USA
W. Muschik, Technische Universität, Berlin, Germany
I. Müller, Technische Universität, Berlin, Germany
V. E. Nakoryakov, Institute of Thermophysics, Novosibirsk, Russia
M. Podowski, Rensselaer Polytechnic Institute, Troy, USA
M.R. von Spakovsky, Virginia Polytechnic Institute and State University, Blacksburg, USA

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