Dual phase lag two temperature fractional thermoelasticity in the context of Green Naghdi type II
The linear thermoelasticity theory without energy dissipation developed by Green Naghdi has been reconstructed using two-phase lags and two temperature theory in the framework of the fractional time derivative. In half space, the mathematical model for one dimensional wave propagation subject to th...
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Western Libraries
2024-12-01
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| Series: | Mathematics in Applied Sciences and Engineering |
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| Online Access: | https://ojs.lib.uwo.ca/index.php/mase/article/view/20987 |
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| author | Sagar Sankeshwari Vinayak Kulkarni |
| author_facet | Sagar Sankeshwari Vinayak Kulkarni |
| author_sort | Sagar Sankeshwari |
| collection | DOAJ |
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The linear thermoelasticity theory without energy dissipation developed by Green Naghdi has been reconstructed using two-phase lags and two temperature theory in the framework of the fractional time derivative. In half space, the mathematical model for one dimensional wave propagation subject to thermal shock on the bounding surface is discussed. Assume that the bounding surface is traction free. The analytical solutions have been obtained in the Laplace domain. The Gaver-Stehfest technique is simple, efficient, and robust. It has been numerically used to perform an inversion of the Laplace transform, satisfying Kuznetsov’s convergence condition in the time domain. The significance of the fractional order parameter on variations of various fields inside the medium is addressed graphically. The utilization of delay time translations in heat flux vector and thermal displacement gradient causes the finite speed of wave propagation and depicts microscopic responses more precisely.
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| format | Article |
| id | doaj-art-3de159c8d49e42eaaa985dca2787b6bc |
| institution | DOAJ |
| issn | 2563-1926 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Western Libraries |
| record_format | Article |
| series | Mathematics in Applied Sciences and Engineering |
| spelling | doaj-art-3de159c8d49e42eaaa985dca2787b6bc2025-08-20T03:16:42ZengWestern LibrariesMathematics in Applied Sciences and Engineering2563-19262024-12-016110.5206/mase/20987Dual phase lag two temperature fractional thermoelasticity in the context of Green Naghdi type IISagar Sankeshwari0Vinayak Kulkarni1SVKM's NMIMS Deemed to be University, Navi Mumbai, IndiaDepartment of Mathematics, University of Mumbai, Mumbai The linear thermoelasticity theory without energy dissipation developed by Green Naghdi has been reconstructed using two-phase lags and two temperature theory in the framework of the fractional time derivative. In half space, the mathematical model for one dimensional wave propagation subject to thermal shock on the bounding surface is discussed. Assume that the bounding surface is traction free. The analytical solutions have been obtained in the Laplace domain. The Gaver-Stehfest technique is simple, efficient, and robust. It has been numerically used to perform an inversion of the Laplace transform, satisfying Kuznetsov’s convergence condition in the time domain. The significance of the fractional order parameter on variations of various fields inside the medium is addressed graphically. The utilization of delay time translations in heat flux vector and thermal displacement gradient causes the finite speed of wave propagation and depicts microscopic responses more precisely. https://ojs.lib.uwo.ca/index.php/mase/article/view/20987Fractional thermoelasticity, Green-Naghdi II theory, half space problem, thermal shock, two temperature thermoelasticity, dual phase lag. |
| spellingShingle | Sagar Sankeshwari Vinayak Kulkarni Dual phase lag two temperature fractional thermoelasticity in the context of Green Naghdi type II Mathematics in Applied Sciences and Engineering Fractional thermoelasticity, Green-Naghdi II theory, half space problem, thermal shock, two temperature thermoelasticity, dual phase lag. |
| title | Dual phase lag two temperature fractional thermoelasticity in the context of Green Naghdi type II |
| title_full | Dual phase lag two temperature fractional thermoelasticity in the context of Green Naghdi type II |
| title_fullStr | Dual phase lag two temperature fractional thermoelasticity in the context of Green Naghdi type II |
| title_full_unstemmed | Dual phase lag two temperature fractional thermoelasticity in the context of Green Naghdi type II |
| title_short | Dual phase lag two temperature fractional thermoelasticity in the context of Green Naghdi type II |
| title_sort | dual phase lag two temperature fractional thermoelasticity in the context of green naghdi type ii |
| topic | Fractional thermoelasticity, Green-Naghdi II theory, half space problem, thermal shock, two temperature thermoelasticity, dual phase lag. |
| url | https://ojs.lib.uwo.ca/index.php/mase/article/view/20987 |
| work_keys_str_mv | AT sagarsankeshwari dualphaselagtwotemperaturefractionalthermoelasticityinthecontextofgreennaghditypeii AT vinayakkulkarni dualphaselagtwotemperaturefractionalthermoelasticityinthecontextofgreennaghditypeii |