{"id":"https://openalex.org/W7225595674","doi":"https://doi.org/10.1038/s41598-026-72189-4","title":"Thermoelastic response to an internal heat source and an electromagnetic field in solids using a refined Lord\u2013Shulman framework with reference temperature","display_name":"Thermoelastic response to an internal heat source and an electromagnetic field in solids using a refined Lord\u2013Shulman framework with reference temperature","publication_year":2026,"publication_date":"2026-11-09","ids":{"openalex":"https://openalex.org/W7225595674","doi":"https://doi.org/10.1038/s41598-026-72189-4"},"language":"en","primary_location":{"id":"doi:10.1038/s41598-026-72189-4","doi":"https://doi.org/10.1038/s41598-026-72189-4","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41598-026-72189-4","pdf_url":"https://www.nature.com/articles/s41598-026-72189-4.pdf","source":{"id":"https://openalex.org/S196734849","display_name":"Scientific Reports","issn_l":"2045-2322","issn":["2045-2322"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","doyens","jufo-1","ki-jl-1","medline","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Reports","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.nature.com/articles/s41598-026-72189-4.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044539251","display_name":"Samia M. S. Said","orcid":"https://orcid.org/0000-0001-6878-7530","observed_orcids":["https://orcid.org/0000-0001-6878-7530"]},"institutions":[{"id":"https://openalex.org/I192398990","display_name":"Zagazig University","ror":"https://ror.org/053g6we49","country_code":"EG","type":"education","lineage":["https://openalex.org/I192398990"]}],"countries":["EG"],"is_corresponding":true,"raw_author_name":"Samia M. Said","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Zagazig University, P.O. Box 44519, Zagazig, Egypt"],"raw_orcid":"https://orcid.org/0000-0001-6878-7530","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Zagazig University, P.O. Box 44519, Zagazig, Egypt","institution_ids":["https://openalex.org/I192398990"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010116490","display_name":"Emad K. Jaradat","orcid":"https://orcid.org/0000-0001-5335-7060","observed_orcids":["https://orcid.org/0000-0001-5335-7060","https://orcid.org/0009-0008-5225-2206"]},"institutions":[{"id":"https://openalex.org/I240666556","display_name":"Imam Mohammad ibn Saud Islamic University","ror":"https://ror.org/05gxjyb39","country_code":"SA","type":"education","lineage":["https://openalex.org/I240666556"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Emad K. Jaradat","raw_affiliation_strings":["Department of Physics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), 11623, Riyadh, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), 11623, Riyadh, Saudi Arabia","institution_ids":["https://openalex.org/I240666556"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080797734","display_name":"Sayed Mohamed Abo-Dahab","orcid":"https://orcid.org/0000-0002-7088-9912","observed_orcids":["https://orcid.org/0000-0002-7088-9912"]},"institutions":[{"id":"https://openalex.org/I189575948","display_name":"South Valley University","ror":"https://ror.org/00jxshx33","country_code":"EG","type":"education","lineage":["https://openalex.org/I189575948"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"S. M. Abo-Dahab","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt","institution_ids":["https://openalex.org/I189575948"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021465015","display_name":"Sarhan Y. Atwa","orcid":"https://orcid.org/0000-0001-9964-0320","observed_orcids":["https://orcid.org/0000-0001-9964-0320"]},"institutions":[{"id":"https://openalex.org/I27367753","display_name":"El Shorouk Academy","ror":"https://ror.org/025xjs150","country_code":"EG","type":"education","lineage":["https://openalex.org/I27367753"]},{"id":"https://openalex.org/I4210120363","display_name":"Higher Institute of Engineering","ror":"https://ror.org/02pyw9g57","country_code":"EG","type":"education","lineage":["https://openalex.org/I4210120363"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Sarhan Y. Atwa","raw_affiliation_strings":["Department of Physics and Engineering Mathematics, Higher Institute of Engineering El-Shorouk Academy, El-Shorouk, Egypt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics and Engineering Mathematics, Higher Institute of Engineering El-Shorouk Academy, El-Shorouk, Egypt","institution_ids":["https://openalex.org/I27367753","https://openalex.org/I4210120363"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5044539251"],"corresponding_institution_ids":["https://openalex.org/I192398990"],"apc_list":{"value":2690,"currency":"USD","value_usd":2690},"apc_paid":{"value":2690,"currency":"USD","value_usd":2690},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"16","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11565","display_name":"Thermoelastic and Magnetoelastic Phenomena","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11565","display_name":"Thermoelastic and Magnetoelastic Phenomena","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11856","display_name":"Thermography and Photoacoustic Techniques","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10662","display_name":"Ultrasonics and Acoustic Wave Propagation","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/magneto-thermoelasticity","display_name":"magneto-thermoelasticity","score":0.9470000267028809},{"id":"https://openalex.org/keywords/lord-shulman-model","display_name":"Lord-Shulman theory","score":0.9539999961853027},{"id":"https://openalex.org/keywords/internal-heat-generation","display_name":"internal heat generation","score":0.7440000176429749},{"id":"https://openalex.org/keywords/reference-temperature","display_name":"reference temperature","score":0.7329999804496765},{"id":"https://openalex.org/keywords/magnetic-field","display_name":"magnetic field","score":0.5809999704360962},{"id":"https://openalex.org/keywords/thermomechanical-coupling","display_name":"thermo-mechanical coupling","score":0.699999988079071},{"id":"https://openalex.org/keywords/magnetoelastic-coupling","display_name":"magnetoelastic coupling","score":0.906000018119812},{"id":"https://openalex.org/keywords/normal-mode-analysis","display_name":"normal mode analysis","score":0.7540000081062317},{"id":"https://openalex.org/keywords/induced-magnetic-field","display_name":"induced magnetic field","score":0.7910000085830688},{"id":"https://openalex.org/keywords/coupled-wave-propagation","display_name":"coupled wave propagation","score":0.6579999923706055}],"concepts":[{"id":"https://openalex.org/C92458943","wikidata":"https://www.wikidata.org/wiki/Q7783171","display_name":"Thermoelastic damping","level":3,"score":0.9215999841690063},{"id":"https://openalex.org/C129716092","wikidata":"https://www.wikidata.org/wiki/Q912130","display_name":"Internal heating","level":2,"score":0.7365000247955322},{"id":"https://openalex.org/C28843909","wikidata":"https://www.wikidata.org/wiki/Q177625","display_name":"Electromagnetic field","level":2,"score":0.6256999969482422},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5461000204086304},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.4693000018596649},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.4041999876499176},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4016000032424927},{"id":"https://openalex.org/C172100665","wikidata":"https://www.wikidata.org/wiki/Q7465774","display_name":"Thermal conduction","level":2,"score":0.367000013589859},{"id":"https://openalex.org/C72293138","wikidata":"https://www.wikidata.org/wiki/Q909741","display_name":"Temperature measurement","level":2,"score":0.321399986743927},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.296999990940094},{"id":"https://openalex.org/C149773537","wikidata":"https://www.wikidata.org/wiki/Q12969754","display_name":"Electromagnetic radiation","level":2,"score":0.28839999437332153},{"id":"https://openalex.org/C50517652","wikidata":"https://www.wikidata.org/wiki/Q179635","display_name":"Heat transfer","level":2,"score":0.26989999413490295},{"id":"https://openalex.org/C2983309280","wikidata":"https://www.wikidata.org/wiki/Q751960","display_name":"Electromagnetic heating","level":3,"score":0.26190000772476196},{"id":"https://openalex.org/C14589660","wikidata":"https://www.wikidata.org/wiki/Q64122","display_name":"Electromagnetic pulse","level":2,"score":0.2581999897956848},{"id":"https://openalex.org/C89394759","wikidata":"https://www.wikidata.org/wiki/Q192593","display_name":"Thermal radiation","level":2,"score":0.2563000023365021}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1038/s41598-026-72189-4","doi":"https://doi.org/10.1038/s41598-026-72189-4","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41598-026-72189-4","pdf_url":"https://www.nature.com/articles/s41598-026-72189-4.pdf","source":{"id":"https://openalex.org/S196734849","display_name":"Scientific Reports","issn_l":"2045-2322","issn":["2045-2322"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","doyens","jufo-1","ki-jl-1","medline","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Reports","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1038/s41598-026-72189-4","doi":"https://doi.org/10.1038/s41598-026-72189-4","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41598-026-72189-4","pdf_url":"https://www.nature.com/articles/s41598-026-72189-4.pdf","source":{"id":"https://openalex.org/S196734849","display_name":"Scientific Reports","issn_l":"2045-2322","issn":["2045-2322"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","doyens","jufo-1","ki-jl-1","medline","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Reports","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7225595674.pdf","grobid_xml":"https://content.openalex.org/works/W7225595674.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W1963821052","https://openalex.org/W1970512980","https://openalex.org/W1970577138","https://openalex.org/W1973038067","https://openalex.org/W1984619633","https://openalex.org/W2000761434","https://openalex.org/W2002116400","https://openalex.org/W2026296128","https://openalex.org/W2046353658","https://openalex.org/W2055282150","https://openalex.org/W2062073793","https://openalex.org/W2130893425","https://openalex.org/W2165112292","https://openalex.org/W2611524066","https://openalex.org/W2611750127","https://openalex.org/W2968583679","https://openalex.org/W2979594520","https://openalex.org/W3026696382","https://openalex.org/W3104429189","https://openalex.org/W3126607005","https://openalex.org/W4233354664","https://openalex.org/W4295213545","https://openalex.org/W4384009210","https://openalex.org/W4385746598","https://openalex.org/W4388654567","https://openalex.org/W4391437644","https://openalex.org/W4392656875","https://openalex.org/W4400007835","https://openalex.org/W4406626471","https://openalex.org/W4409574980","https://openalex.org/W7129047111","https://openalex.org/W7152746345","https://openalex.org/W7160151614","https://openalex.org/W7161112674","https://openalex.org/W7161476495"],"related_works":["https://openalex.org/W2156422062","https://openalex.org/W2328275938","https://openalex.org/W4230827342","https://openalex.org/W2581452714","https://openalex.org/W4405394486","https://openalex.org/W3016850979","https://openalex.org/W4256010696","https://openalex.org/W2185028277","https://openalex.org/W2027193569","https://openalex.org/W2008190430"],"abstract_inverted_index":{"An":[0],"extended":[1],"Lord\u2013Shulman":[2,198],"thermoelastic":[3,131],"formulation":[4,55,242],"has":[5],"been":[6],"developed":[7,201],"to":[8,65,72,76,205,228],"investigate":[9],"the":[10,26,34,48,57,60,73,93,99,108,117,130,135,140,144,150,155,162,177,195,240],"coupled":[11,74,151,211,249],"effects":[12,58],"of":[13,28,59,149,194],"an":[14,186,244],"external":[15],"magnetic":[16,43,95,167],"field,":[17],"internal":[18,109],"heat":[19,110],"source,":[20],"and":[21,41,69,81,101,119,122,147,165,181,207,214,222,231,234,252,262],"non-zero":[22],"reference":[23,126],"temperature":[24,35,118,127,163],"on":[25],"behavior":[27],"magneto-thermoelastic":[29,256],"materials.":[30],"Analytical":[31],"expressions":[32],"for":[33,247],"variation,":[36],"displacement,":[37],"dilatation,":[38],"stress":[39,121],"components,":[40,219],"induced":[42,166],"field":[44,96,168,253],"are":[45,84],"obtained":[46],"using":[47,86],"normal":[49],"mode":[50],"analysis":[51],"method.":[52],"The":[53,89,125,200],"resulting":[54],"enables":[56],"newly":[61],"introduced":[62],"physical":[63],"parameters":[64],"be":[66,77],"identified":[67],"separately":[68],"their":[70],"contributions":[71],"response":[75,132],"quantified.":[78],"Numerical":[79],"computations":[80],"graphical":[82],"simulations":[83],"performed":[85],"MATLAB":[87],"R2013a.":[88],"results":[90,157],"demonstrate":[91],"that":[92],"applied":[94],"significantly":[97],"modifies":[98],"mechanical":[100,263],"thermal":[102,180,232],"responses":[103],"through":[104],"magnetoelastic":[105,218],"coupling,":[106],"while":[107],"source":[111],"produces":[112],"a":[113,174],"pronounced":[114],"alteration":[115],"in":[116,161,176,255],"associated":[120],"displacement":[123],"fields.":[124,152],"also":[128],"affects":[129],"by":[133],"modifying":[134],"thermal\u2013mechanical":[136],"coupling":[137],"terms,":[138],"whereas":[139],"vertical":[141],"distance":[142],"governs":[143],"spatial":[145],"attenuation":[146],"propagation":[148,251],"In":[153],"particular,":[154],"numerical":[156],"reveal":[158],"sign":[159],"changes":[160],"variation":[164],"under":[169,258],"certain":[170],"parameter":[171],"combinations,":[172],"indicating":[173],"reversal":[175],"corresponding":[178],"local":[179],"electromagnetic":[182,215,220,237],"perturbations":[183],"rather":[184],"than":[185],"unphysical":[187],"behavior.":[188],"These":[189],"findings":[190],"constitute":[191],"clear":[192],"outcomes":[193],"present":[196],"refined":[197],"framework.":[199],"model":[202],"is":[203],"relevant":[204],"engineering":[206],"applied-science":[208],"problems":[209],"involving":[210],"thermal,":[212,261],"mechanical,":[213],"effects,":[216],"including":[217],"heating":[221],"sensing":[223],"systems,":[224],"geophysical":[225],"materials":[226],"subjected":[227],"geomagnetic":[229],"fields":[230],"disturbances,":[233],"thermally":[235],"affected":[236],"devices.":[238],"Thus,":[239],"proposed":[241],"provides":[243],"analytical":[245],"framework":[246],"predicting":[248],"wave":[250],"distributions":[254],"media":[257],"simultaneous":[259],"magnetic,":[260],"influences.":[264]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-09T00:00:00"}