Loading…
On energy, uniqueness theorems and variational principle for generalized thermoelasticity with memory-dependent derivative
•The energy theorem for the generalized thermoelasticity under three-phase-lag (TPL) model with memory-dependent derivative (MDD) is stated and proved.•The uniqueness theorem for the present theory is proved from the energy theorem.•The variational principle for the present theory is constructed.•Th...
Saved in:
| Published in: | International journal of heat and mass transfer 2020-03, Vol.149, p.119112, Article 119112 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| cited_by | cdi_FETCH-LOGICAL-c370t-8c5217f4e6db4b0774271e5c68ecf6d6121f35c37dc28c399add64683d872e4d3 |
|---|---|
| cites | cdi_FETCH-LOGICAL-c370t-8c5217f4e6db4b0774271e5c68ecf6d6121f35c37dc28c399add64683d872e4d3 |
| container_end_page | |
| container_issue | |
| container_start_page | 119112 |
| container_title | International journal of heat and mass transfer |
| container_volume | 149 |
| creator | Sarkar, Indranil Mukhopadhyay, Basudeb |
| description | •The energy theorem for the generalized thermoelasticity under three-phase-lag (TPL) model with memory-dependent derivative (MDD) is stated and proved.•The uniqueness theorem for the present theory is proved from the energy theorem.•The variational principle for the present theory is constructed.•The dissipation function D extended to three-phase-lag (TPL) model is introduced.•The other renowned thermoelasticity theories, such as Lord-Shulman (L-S) model, dual-phase-lag (DPL) model with MDD and the dynamic classical theory are derived from the present model.
The research article theoretically deals with the three-phase-lag (TPL) heat conduction model of generalized thermoelasticity, reformulated in terms of the memory-dependent derivative (MDD). The energy theorem and the variational principle of this proposed model are established for an isotropic, homogeneous, thermoelastic continuum. The uniqueness theorem is derived from the energy theorem, and a few special cases are also obtained from the present model. For numerical simulation of the present model, a one-dimensional thermoelastic problem in a semi-infinite medium subjected to a time-dependent thermal shock on its bounding plane is considered. The Laplace transform together with its numerical inversion is adopted to obtain the solutions in the physical domain. The influence of the kernel function and time delay on the variation of the non-dimensional thermophysical quantities are studied graphically and finally some remarkable points are mentioned as conclusions. |
| doi_str_mv | 10.1016/j.ijheatmasstransfer.2019.119112 |
| format | article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2354303442</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S001793101934880X</els_id><sourcerecordid>2354303442</sourcerecordid><originalsourceid>FETCH-LOGICAL-c370t-8c5217f4e6db4b0774271e5c68ecf6d6121f35c37dc28c399add64683d872e4d3</originalsourceid><addsrcrecordid>eNqNkE9rGzEUxEVoIG6a7yDIpYeuoyfJ--fWEpomxZBLcxaK9DbWsiu5kuyy_vTV4t5y6ekxvJkfzBDyGdgaGNR3w9oNO9R50inlqH3qMa45g24N0AHwC7KCtukqDm33gawYg6bqBLAr8jGlYZFM1ityevYUPca3-Qs9ePf7UERKNO8wRJwS1d7So45OZxe8Huk-Om_cfkTah0jflqge3QntEolTwFGn7IzLM_3j8o5OOIU4Vxb36C36TC1Gdyy0I34il70eE978u9fk5eH7r_vHavv84-n-27YyomG5as2GQ9NLrO2rfGVNI3kDuDF1i6avbQ0cerEpXmt4a0TXaWtrWbfCtg1HacU1uT1z9zGUfimrIRxiKZMUFxspmJCSF9fXs8vEkFLEXpWqk46zAqaWxdWg3i-ulsXVefGC-HlGYGlzdOWbjENv0LqIJisb3P_D_gJMuZn_</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2354303442</pqid></control><display><type>article</type><title>On energy, uniqueness theorems and variational principle for generalized thermoelasticity with memory-dependent derivative</title><source>ScienceDirect Freedom Collection 2022-2024</source><creator>Sarkar, Indranil ; Mukhopadhyay, Basudeb</creator><creatorcontrib>Sarkar, Indranil ; Mukhopadhyay, Basudeb</creatorcontrib><description>•The energy theorem for the generalized thermoelasticity under three-phase-lag (TPL) model with memory-dependent derivative (MDD) is stated and proved.•The uniqueness theorem for the present theory is proved from the energy theorem.•The variational principle for the present theory is constructed.•The dissipation function D extended to three-phase-lag (TPL) model is introduced.•The other renowned thermoelasticity theories, such as Lord-Shulman (L-S) model, dual-phase-lag (DPL) model with MDD and the dynamic classical theory are derived from the present model.
The research article theoretically deals with the three-phase-lag (TPL) heat conduction model of generalized thermoelasticity, reformulated in terms of the memory-dependent derivative (MDD). The energy theorem and the variational principle of this proposed model are established for an isotropic, homogeneous, thermoelastic continuum. The uniqueness theorem is derived from the energy theorem, and a few special cases are also obtained from the present model. For numerical simulation of the present model, a one-dimensional thermoelastic problem in a semi-infinite medium subjected to a time-dependent thermal shock on its bounding plane is considered. The Laplace transform together with its numerical inversion is adopted to obtain the solutions in the physical domain. The influence of the kernel function and time delay on the variation of the non-dimensional thermophysical quantities are studied graphically and finally some remarkable points are mentioned as conclusions.</description><identifier>ISSN: 0017-9310</identifier><identifier>EISSN: 1879-2189</identifier><identifier>DOI: 10.1016/j.ijheatmasstransfer.2019.119112</identifier><language>eng</language><publisher>Oxford: Elsevier Ltd</publisher><subject>Computer simulation ; Conduction heating ; Conduction model ; Conductive heat transfer ; Energy ; Generalized thermoelasticity ; Kernel functions ; Laplace transforms ; Mathematical models ; Memory-dependent derivative ; Phase lag ; Response time ; Thermal shock ; Thermoelasticity ; Three-phase-lag ; Time dependence ; Time lag ; Uniqueness ; Uniqueness theorems ; Variational principle</subject><ispartof>International journal of heat and mass transfer, 2020-03, Vol.149, p.119112, Article 119112</ispartof><rights>2019 Elsevier Ltd</rights><rights>Copyright Elsevier BV Mar 2020</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c370t-8c5217f4e6db4b0774271e5c68ecf6d6121f35c37dc28c399add64683d872e4d3</citedby><cites>FETCH-LOGICAL-c370t-8c5217f4e6db4b0774271e5c68ecf6d6121f35c37dc28c399add64683d872e4d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>315,786,790,27957,27958</link.rule.ids></links><search><creatorcontrib>Sarkar, Indranil</creatorcontrib><creatorcontrib>Mukhopadhyay, Basudeb</creatorcontrib><title>On energy, uniqueness theorems and variational principle for generalized thermoelasticity with memory-dependent derivative</title><title>International journal of heat and mass transfer</title><description>•The energy theorem for the generalized thermoelasticity under three-phase-lag (TPL) model with memory-dependent derivative (MDD) is stated and proved.•The uniqueness theorem for the present theory is proved from the energy theorem.•The variational principle for the present theory is constructed.•The dissipation function D extended to three-phase-lag (TPL) model is introduced.•The other renowned thermoelasticity theories, such as Lord-Shulman (L-S) model, dual-phase-lag (DPL) model with MDD and the dynamic classical theory are derived from the present model.
The research article theoretically deals with the three-phase-lag (TPL) heat conduction model of generalized thermoelasticity, reformulated in terms of the memory-dependent derivative (MDD). The energy theorem and the variational principle of this proposed model are established for an isotropic, homogeneous, thermoelastic continuum. The uniqueness theorem is derived from the energy theorem, and a few special cases are also obtained from the present model. For numerical simulation of the present model, a one-dimensional thermoelastic problem in a semi-infinite medium subjected to a time-dependent thermal shock on its bounding plane is considered. The Laplace transform together with its numerical inversion is adopted to obtain the solutions in the physical domain. The influence of the kernel function and time delay on the variation of the non-dimensional thermophysical quantities are studied graphically and finally some remarkable points are mentioned as conclusions.</description><subject>Computer simulation</subject><subject>Conduction heating</subject><subject>Conduction model</subject><subject>Conductive heat transfer</subject><subject>Energy</subject><subject>Generalized thermoelasticity</subject><subject>Kernel functions</subject><subject>Laplace transforms</subject><subject>Mathematical models</subject><subject>Memory-dependent derivative</subject><subject>Phase lag</subject><subject>Response time</subject><subject>Thermal shock</subject><subject>Thermoelasticity</subject><subject>Three-phase-lag</subject><subject>Time dependence</subject><subject>Time lag</subject><subject>Uniqueness</subject><subject>Uniqueness theorems</subject><subject>Variational principle</subject><issn>0017-9310</issn><issn>1879-2189</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNqNkE9rGzEUxEVoIG6a7yDIpYeuoyfJ--fWEpomxZBLcxaK9DbWsiu5kuyy_vTV4t5y6ekxvJkfzBDyGdgaGNR3w9oNO9R50inlqH3qMa45g24N0AHwC7KCtukqDm33gawYg6bqBLAr8jGlYZFM1ityevYUPca3-Qs9ePf7UERKNO8wRJwS1d7So45OZxe8Huk-Om_cfkTah0jflqge3QntEolTwFGn7IzLM_3j8o5OOIU4Vxb36C36TC1Gdyy0I34il70eE978u9fk5eH7r_vHavv84-n-27YyomG5as2GQ9NLrO2rfGVNI3kDuDF1i6avbQ0cerEpXmt4a0TXaWtrWbfCtg1HacU1uT1z9zGUfimrIRxiKZMUFxspmJCSF9fXs8vEkFLEXpWqk46zAqaWxdWg3i-ulsXVefGC-HlGYGlzdOWbjENv0LqIJisb3P_D_gJMuZn_</recordid><startdate>202003</startdate><enddate>202003</enddate><creator>Sarkar, Indranil</creator><creator>Mukhopadhyay, Basudeb</creator><general>Elsevier Ltd</general><general>Elsevier BV</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>KR7</scope><scope>L7M</scope></search><sort><creationdate>202003</creationdate><title>On energy, uniqueness theorems and variational principle for generalized thermoelasticity with memory-dependent derivative</title><author>Sarkar, Indranil ; Mukhopadhyay, Basudeb</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c370t-8c5217f4e6db4b0774271e5c68ecf6d6121f35c37dc28c399add64683d872e4d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Computer simulation</topic><topic>Conduction heating</topic><topic>Conduction model</topic><topic>Conductive heat transfer</topic><topic>Energy</topic><topic>Generalized thermoelasticity</topic><topic>Kernel functions</topic><topic>Laplace transforms</topic><topic>Mathematical models</topic><topic>Memory-dependent derivative</topic><topic>Phase lag</topic><topic>Response time</topic><topic>Thermal shock</topic><topic>Thermoelasticity</topic><topic>Three-phase-lag</topic><topic>Time dependence</topic><topic>Time lag</topic><topic>Uniqueness</topic><topic>Uniqueness theorems</topic><topic>Variational principle</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Sarkar, Indranil</creatorcontrib><creatorcontrib>Mukhopadhyay, Basudeb</creatorcontrib><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>International journal of heat and mass transfer</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Sarkar, Indranil</au><au>Mukhopadhyay, Basudeb</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On energy, uniqueness theorems and variational principle for generalized thermoelasticity with memory-dependent derivative</atitle><jtitle>International journal of heat and mass transfer</jtitle><date>2020-03</date><risdate>2020</risdate><volume>149</volume><spage>119112</spage><pages>119112-</pages><artnum>119112</artnum><issn>0017-9310</issn><eissn>1879-2189</eissn><abstract>•The energy theorem for the generalized thermoelasticity under three-phase-lag (TPL) model with memory-dependent derivative (MDD) is stated and proved.•The uniqueness theorem for the present theory is proved from the energy theorem.•The variational principle for the present theory is constructed.•The dissipation function D extended to three-phase-lag (TPL) model is introduced.•The other renowned thermoelasticity theories, such as Lord-Shulman (L-S) model, dual-phase-lag (DPL) model with MDD and the dynamic classical theory are derived from the present model.
The research article theoretically deals with the three-phase-lag (TPL) heat conduction model of generalized thermoelasticity, reformulated in terms of the memory-dependent derivative (MDD). The energy theorem and the variational principle of this proposed model are established for an isotropic, homogeneous, thermoelastic continuum. The uniqueness theorem is derived from the energy theorem, and a few special cases are also obtained from the present model. For numerical simulation of the present model, a one-dimensional thermoelastic problem in a semi-infinite medium subjected to a time-dependent thermal shock on its bounding plane is considered. The Laplace transform together with its numerical inversion is adopted to obtain the solutions in the physical domain. The influence of the kernel function and time delay on the variation of the non-dimensional thermophysical quantities are studied graphically and finally some remarkable points are mentioned as conclusions.</abstract><cop>Oxford</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.ijheatmasstransfer.2019.119112</doi></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0017-9310 |
| ispartof | International journal of heat and mass transfer, 2020-03, Vol.149, p.119112, Article 119112 |
| issn | 0017-9310 1879-2189 |
| language | eng |
| recordid | cdi_proquest_journals_2354303442 |
| source | ScienceDirect Freedom Collection 2022-2024 |
| subjects | Computer simulation Conduction heating Conduction model Conductive heat transfer Energy Generalized thermoelasticity Kernel functions Laplace transforms Mathematical models Memory-dependent derivative Phase lag Response time Thermal shock Thermoelasticity Three-phase-lag Time dependence Time lag Uniqueness Uniqueness theorems Variational principle |
| title | On energy, uniqueness theorems and variational principle for generalized thermoelasticity with memory-dependent derivative |
| url | http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-09-22T09%3A35%3A33IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20energy,%20uniqueness%20theorems%20and%20variational%20principle%20for%20generalized%20thermoelasticity%20with%20memory-dependent%20derivative&rft.jtitle=International%20journal%20of%20heat%20and%20mass%20transfer&rft.au=Sarkar,%20Indranil&rft.date=2020-03&rft.volume=149&rft.spage=119112&rft.pages=119112-&rft.artnum=119112&rft.issn=0017-9310&rft.eissn=1879-2189&rft_id=info:doi/10.1016/j.ijheatmasstransfer.2019.119112&rft_dat=%3Cproquest_cross%3E2354303442%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c370t-8c5217f4e6db4b0774271e5c68ecf6d6121f35c37dc28c399add64683d872e4d3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2354303442&rft_id=info:pmid/&rfr_iscdi=true |