A Study on Thermoelastic Interaction in a Poroelastic Medium with and without Energy Dissipation
Abstract
:1. Introduction
2. Mathematical Model
3. Application
4. Finite Element Scheme
5. Numerical Results and Discussions
6. Conclusions
Funding
Conflicts of Interest
References
- Biot, M.A. General solutions of the equations of elasticity and consolidation for a porous material. J. Appl. Mech. 1956, 23, 91–96. [Google Scholar]
- Biot, M.A. Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range. J. Acoust. Soc. Am. 1956, 28, 179–191. [Google Scholar] [CrossRef]
- Biot, M.A. Thermoelasticity and irreversible thermodynamics. J. Appl. Phys. 1956, 27, 240–253. [Google Scholar] [CrossRef]
- Lord, H.W.; Shulman, Y. A generalized dynamical theory of thermoelasticity. J. Mech. Phy. Solids 1967, 15, 299–309. [Google Scholar] [CrossRef]
- Green, A.E.; Naghdi, P.M. Thermoelasticity without energy dissipation. J. Elast. 1993, 31, 189–208. [Google Scholar] [CrossRef]
- Green, A.; Naghdi, P. A re-examination of the basic postulates of thermomechanics. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 1991, 432, 171–194. [Google Scholar]
- Schanz, M.; Cheng, A.-D. Transient wave propagation in a one-dimensional poroelastic column. Acta Mech. 2000, 145, 1–18. [Google Scholar] [CrossRef]
- Abbas, I. Natural frequencies of a poroelastic hollow cylinder. Acta Mech. 2006, 186, 229–237. [Google Scholar] [CrossRef]
- Youssef, H. Theory of generalized porothermoelasticity. Int. J. Rock Mech. Min. Sci. 2007, 44, 222–227. [Google Scholar] [CrossRef]
- McTigue, D. Thermoelastic response of fluid-saturated porous rock. J. Geophys. Res. Solid Earth 1986, 91, 9533–9542. [Google Scholar] [CrossRef]
- Singh, B. On propagation of plane waves in generalized porothermoelasticity. Bull. Seismol. Soc. Am. 2011, 101, 756–762. [Google Scholar] [CrossRef]
- Singh, B. Rayleigh surface wave in a porothermoelastic solid half-space. In Proceedings of the Poromechanics VI, Paris, France, 9–13 July 2017; pp. 1706–1713. [Google Scholar]
- Hussein, E.M. Effect of the porosity on a porous plate saturated with a liquid and subjected to a sudden change in temperature. Acta Mech. 2018, 229, 2431–2444. [Google Scholar] [CrossRef]
- El-Naggar, A.; Kishka, Z.; Abd-Alla, A.; Abbas, I.; Abo-Dahab, S.; Elsagheer, M. On the initial stress, magnetic field, voids and rotation effects on plane waves in generalized thermoelasticity. J. Comput. Theor. Nanosci. 2013, 10, 1408–1417. [Google Scholar] [CrossRef]
- Abbas, I.A.; El-Amin, M.; Salama, A. Effect of thermal dispersion on free convection in a fluid saturated porous medium. Int. J. Heat Fluid Flow 2009, 30, 229–236. [Google Scholar] [CrossRef]
- Marin, M.; Öchsner, A. The effect of a dipolar structure on the Hölder stability in Green-Naghdi thermoelasticity. Contin. Mech. Thermodyn. 2017, 29, 1365–1374. [Google Scholar] [CrossRef]
- Abbas, I.A. Nonlinear transient thermal stress analysis of thick-walled FGM cylinder with temperature-dependent material properties. Meccanica 2014, 49, 1697–1708. [Google Scholar] [CrossRef]
- Abbas, I.A.; Abo-Dahab, S. On the numerical solution of thermal shock problem for generalized magneto-thermoelasticity for an infinitely long annular cylinder with variable thermal conductivity. J. Comput. Theor. Nanosci. 2014, 11, 607–618. [Google Scholar] [CrossRef]
- Kumar, R.; Abbas, I.A. Deformation due to thermal source in micropolar thermoelastic media with thermal and conductive temperatures. J. Comput. Theor. Nanosci. 2013, 10, 2241–2247. [Google Scholar] [CrossRef]
- Abbas, I.A.; Zenkour, A.M. LS model on electro-magneto-thermoelastic response of an infinite functionally graded cylinder. Compos. Struct. 2013, 96, 89–96. [Google Scholar] [CrossRef]
- Abbas, I.A.; Youssef, H.M. A nonlinear generalized thermoelasticity model of temperature-dependent materials using finite element method. Int. J. Thermophys. 2012, 33, 1302–1313. [Google Scholar] [CrossRef]
- Abbas, I.A.; Othman, M.I. Generalized thermoelastic interaction in a fiber-reinforced anisotropic half-space under hydrostatic initial stress. J. Vib. Control 2012, 18, 175–182. [Google Scholar] [CrossRef]
- Riaz, A.; Ellahi, R.; Bhatti, M.M.; Marin, M. Study of heat and mass transfer in the Eyring-Powell model of fluid propagating peristaltically through a rectangular compliant channel. Heat Transfer Res. 2019, 50, 1539–1560. [Google Scholar] [CrossRef]
- Sur, A.; Kanoria, M. Memory response on thermal wave propagation in an elastic solid with voids. Mech. Based Des. Struct. Mach. 2020, 48, 326–347. [Google Scholar] [CrossRef]
- Abbas, I.A. Three-phase lag model on thermoelastic interaction in an unbounded fiber-reinforced anisotropic medium with a cylindrical cavity. J. Comput. Theor. Nanosci. 2014, 11, 987–992. [Google Scholar] [CrossRef]
- Sarkar, N.; Mondal, S. Transient responses in a two-temperature thermoelastic infinite medium having cylindrical cavity due to moving heat source with memory-dependent derivative. ZAMM-J. Appl. Math. Mech./Zeitschrift für Angewandte Mathematik und Mechanik 2019, 99, e201800343. [Google Scholar] [CrossRef]
- Othman, M.I.; Mondal, S. Memory-dependent derivative effect on wave propagation of micropolar thermoelastic medium under pulsed laser heating with three theories. Int. J. Numer. Methods Heat Fluid Flow 2019, 30, 1025–1046. [Google Scholar] [CrossRef]
- Abbas, I.A.; Youssef, H.M. Finite element analysis of two-temperature generalized magneto-thermoelasticity. Arch. Appl. Mech. 2009, 79, 917–925. [Google Scholar] [CrossRef]
- Othman, M.I.; Abbas, I.A. Effect of rotation on plane waves at the free surface of a fibre-reinforced thermoelastic half-space using the finite element method. Meccanica 2011, 46, 413–421. [Google Scholar] [CrossRef]
- Sharma, N.; Kumar, R.; Lata, P. Disturbance due to inclined load in transversely isotropic thermoelastic medium with two temperatures and without energy dissipation. Mater. Phys. Mech. 2015, 22, 107–117. [Google Scholar]
- Sur, A.; Kanoria, M. Thermoelastic interaction in a viscoelastic functionally graded half-space under three-phase-lag model. Eur. J. Comput. Mech. 2014, 23, 179–198. [Google Scholar] [CrossRef]
- Zeeshan, A.; Ellahi, R.; Mabood, F.; Hussain, F. Numerical study on bi-phase coupled stress fluid in the presence of Hafnium and metallic nanoparticles over an inclined plane. Int. J. Numer. Methods Heat Fluid Flow 2019, 29, 2854–2869. [Google Scholar] [CrossRef]
- Sheikholeslami, M.; Ellahi, R.; Shafee, A.; Li, Z. Numerical investigation for second law analysis of ferrofluid inside a porous semi annulus: An application of entropy generation and exergy loss. Int. J. Numer. Methods Heat Fluid Flow 2019, 29, 1079–1102. [Google Scholar] [CrossRef]
- Ellahi, R.; Sait, S.M.; Shehzad, N.; Ayaz, Z. A hybrid investigation on numerical and analytical solutions of electro-magnetohydrodynamics flow of nanofluid through porous media with entropy generation. Int. J. Numer. Methods Heat Fluid Flow 2019, 30, 834–854. [Google Scholar] [CrossRef]
- Milani Shirvan, K.; Mamourian, M.; Mirzakhanlari, S.; Rahimi, A.; Ellahi, R. Numerical study of surface radiation and combined natural convection heat transfer in a solar cavity receiver. Int. J. Numer. Methods Heat Fluid Flow 2017, 27, 2385–2399. [Google Scholar] [CrossRef]
- Milani Shirvan, K.; Mamourian, M.; Ellahi, R. Numerical investigation and optimization of mixed convection in ventilated square cavity filled with nanofluid of different inlet and outlet port. Int. J. Numer. Methods Heat Fluid Flow 2017, 27, 2053–2069. [Google Scholar] [CrossRef]
- Marin, M.; Vlase, S.; Ellahi, R.; Bhatti, M. On the partition of energies for the backward in time problem of thermoelastic materials with a dipolar structure. Symmetry 2019, 11, 863. [Google Scholar] [CrossRef] [Green Version]
- Marin, M.; Ellahi, R.; Chirilă, A. On solutions of Saint-Venant’s problem for elastic dipolar bodies with voids. Carpathian J. Math. 2017, 33, 219–232. [Google Scholar]
- Abbas, I.A.; Marin, M. Analytical solution of thermoelastic interaction in a half-space by pulsed laser heating. Phys. E Low-Dimens. Syst. Nanostruct. 2017, 87, 254–260. [Google Scholar] [CrossRef]
- Marin, M.; Nicaise, S. Existence and stability results for thermoelastic dipolar bodies with double porosity. Contin. Mech. Thermodyn. 2016, 28, 1645–1657. [Google Scholar] [CrossRef]
- Marin, M.; Craciun, E.-M.; Pop, N. Considerations on mixed initial-boundary value problems for micropolar porous bodies. Dyn. Syst. Appl. 2016, 25, 175–196. [Google Scholar]
- Ezzat, M.; Ezzat, S. Fractional thermoelasticity applications for porous asphaltic materials. Pet. Sci. 2016, 13, 550–560. [Google Scholar] [CrossRef] [Green Version]
- Abbas, I.A.; Kumar, R. Deformation due to thermal source in micropolar generalized thermoelastic half-space by finite element method. J. Comput. Theor. Nanosci. 2014, 11, 185–190. [Google Scholar] [CrossRef]
- Mohamed, R.; Abbas, I.A.; Abo-Dahab, S. Finite element analysis of hydromagnetic flow and heat transfer of a heat generation fluid over a surface embedded in a non-Darcian porous medium in the presence of chemical reaction. Commun. Nonlinear Sci. Numer. Simul. 2009, 14, 1385–1395. [Google Scholar] [CrossRef]
- Singh, B. Reflection of plane waves from a free surface of a porothermoelastic solid half-space. J. Porous Media 2013, 16, 945–957. [Google Scholar] [CrossRef]
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Saeed, T. A Study on Thermoelastic Interaction in a Poroelastic Medium with and without Energy Dissipation. Mathematics 2020, 8, 1286. https://doi.org/10.3390/math8081286
Saeed T. A Study on Thermoelastic Interaction in a Poroelastic Medium with and without Energy Dissipation. Mathematics. 2020; 8(8):1286. https://doi.org/10.3390/math8081286
Chicago/Turabian StyleSaeed, Tareq. 2020. "A Study on Thermoelastic Interaction in a Poroelastic Medium with and without Energy Dissipation" Mathematics 8, no. 8: 1286. https://doi.org/10.3390/math8081286