{"id":"https://openalex.org/W4412907449","doi":"https://doi.org/10.1080/01495739.2025.2534185","title":"Influence of internal heat source and temperature-dependent effects on thermoelasticity within Lord-Shulman framework using modified extended direct algebraic approach","display_name":"Influence of internal heat source and temperature-dependent effects on thermoelasticity within Lord-Shulman framework using modified extended direct algebraic approach","publication_year":2025,"publication_date":"2025-08-04","ids":{"openalex":"https://openalex.org/W4412907449","doi":"https://doi.org/10.1080/01495739.2025.2534185"},"language":"en","primary_location":{"id":"doi:10.1080/01495739.2025.2534185","doi":"https://doi.org/10.1080/01495739.2025.2534185","is_oa":false,"landing_page_url":"https://doi.org/10.1080/01495739.2025.2534185","pdf_url":null,"source":{"id":"https://openalex.org/S54937123","display_name":"Journal of Thermal Stresses","issn_l":"0149-5739","issn":["0149-5739","1521-074X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-1","poland-70","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Thermal Stresses","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050251039","display_name":"Karim K. Ahmed","orcid":"https://orcid.org/0000-0003-0414-4960","observed_orcids":["https://orcid.org/0000-0003-0414-4960"]},"institutions":[{"id":"https://openalex.org/I4405266782","display_name":"German International University","ror":"https://ror.org/05j3zem39","country_code":"EG","type":"education","lineage":["https://openalex.org/I4405266782"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Karim K. Ahmed","raw_affiliation_strings":["Department of Mathematics, Faculty of Engineering, German International University (GIU), New Administrative Capital","Department of Mathematics, Faculty of Engineering, German International University (GIU), New Administrative Capital, Cairo, Egypt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Engineering, German International University (GIU), New Administrative Capital","institution_ids":["https://openalex.org/I4405266782"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Engineering, German International University (GIU), New Administrative Capital, Cairo, Egypt","institution_ids":["https://openalex.org/I4405266782"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057513590","display_name":"Hamdy M. Ahmed","orcid":"https://orcid.org/0000-0001-8772-3663","observed_orcids":["https://orcid.org/0000-0001-8772-3663"]},"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":true,"raw_author_name":"Hamdy M. Ahmed","raw_affiliation_strings":["Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El Shorouk Academy","Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El Shorouk Academy, Cairo, Egypt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El Shorouk Academy","institution_ids":["https://openalex.org/I27367753","https://openalex.org/I4210120363"]},{"raw_affiliation_string":"Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El Shorouk Academy, Cairo, Egypt","institution_ids":["https://openalex.org/I27367753","https://openalex.org/I4210120363"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050225430","display_name":"Ahmed Elsayed Abouelregal","orcid":"https://orcid.org/0000-0003-3363-7924","observed_orcids":["https://orcid.org/0000-0003-3363-7924","https://orcid.org/0000-0003-4187-839X"]},"institutions":[{"id":"https://openalex.org/I159247623","display_name":"Mansoura University","ror":"https://ror.org/01k8vtd75","country_code":"EG","type":"education","lineage":["https://openalex.org/I159247623"]},{"id":"https://openalex.org/I199702508","display_name":"Jouf University","ror":"https://ror.org/02zsyt821","country_code":"SA","type":"education","lineage":["https://openalex.org/I199702508"]}],"countries":["EG","SA"],"is_corresponding":false,"raw_author_name":"Ahmed E. Abouelregal","raw_affiliation_strings":["Department of Mathematics, College of Science, Jouf University","Department of Mathematics, Faculty of Science, Mansoura University","Department of Mathematics, College of Science, Jouf University, Sakaka, Saudi Arabia","Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, Jouf University","institution_ids":["https://openalex.org/I199702508"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Mansoura University","institution_ids":["https://openalex.org/I159247623"]},{"raw_affiliation_string":"Department of Mathematics, College of Science, Jouf University, Sakaka, Saudi Arabia","institution_ids":["https://openalex.org/I199702508"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt","institution_ids":["https://openalex.org/I159247623"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076063109","display_name":"Taher A. Nofal","orcid":"https://orcid.org/0000-0002-4243-9594","observed_orcids":["https://orcid.org/0000-0002-4243-9594"]},"institutions":[{"id":"https://openalex.org/I179331831","display_name":"Taif University","ror":"https://ror.org/014g1a453","country_code":"SA","type":"education","lineage":["https://openalex.org/I179331831"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Taher A. Nofal","raw_affiliation_strings":["Department of Mathematics, College of Science, Taif University","Department of Mathematics, College of Science, Taif University, Taif, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, Taif University","institution_ids":["https://openalex.org/I179331831"]},{"raw_affiliation_string":"Department of Mathematics, College of Science, Taif University, Taif, Saudi Arabia","institution_ids":["https://openalex.org/I179331831"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004027188","display_name":"Mohamed F. Ismail","orcid":"https://orcid.org/0000-0001-8537-2222","observed_orcids":["https://orcid.org/0000-0001-8537-2222"]},"institutions":[{"id":"https://openalex.org/I4405264406","display_name":"Egyptian Chinese University","ror":"https://ror.org/01v527c20","country_code":"EG","type":"education","lineage":["https://openalex.org/I4405264406"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Mohamed F. Ismail","raw_affiliation_strings":["Faculty of Computers and Information System, Egyptian Chinese University","Faculty of Computers and Information System, Egyptian Chinese University, Cairo, Egypt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Computers and Information System, Egyptian Chinese University","institution_ids":["https://openalex.org/I4405264406"]},{"raw_affiliation_string":"Faculty of Computers and Information System, Egyptian Chinese University, Cairo, Egypt","institution_ids":["https://openalex.org/I4405264406"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5057513590"],"corresponding_institution_ids":["https://openalex.org/I27367753","https://openalex.org/I4210120363"],"apc_list":null,"apc_paid":null,"fwci":1.8427,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.82192841,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":98},"biblio":{"volume":"48","issue":"10","first_page":"1338","last_page":"1364"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11565","display_name":"Thermoelastic and Magnetoelastic Phenomena","score":0.9994999766349792,"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":0.9994999766349792,"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/T13261","display_name":"Elasticity and Wave Propagation","score":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lord-shulman-model","display_name":"Lord-Shulman theory","score":0.8820000290870667},{"id":"https://openalex.org/keywords/nonlinear-thermoelasticity","display_name":"nonlinear thermoelasticity","score":0.7870000004768372},{"id":"https://openalex.org/keywords/internal-heat-generation","display_name":"internal heat generation","score":0.9120000004768372},{"id":"https://openalex.org/keywords/temperature-dependent-material-properties","display_name":"temperature-dependent material properties","score":0.9829999804496765},{"id":"https://openalex.org/keywords/exact-solutions","display_name":"exact solutions","score":0.6669999957084656},{"id":"https://openalex.org/keywords/hyperbolic-solutions","display_name":"hyperbolic solutions","score":0.7979999780654907},{"id":"https://openalex.org/keywords/thermal-stress","display_name":"thermal stress","score":0.8399999737739563},{"id":"https://openalex.org/keywords/stress-and-displacement-fields","display_name":"stress and displacement fields","score":0.4740000069141388}],"concepts":[{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.7276873588562012},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.479672908782959},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.35515767335891724},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34524649381637573},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.3450322151184082},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.33637577295303345}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/01495739.2025.2534185","doi":"https://doi.org/10.1080/01495739.2025.2534185","is_oa":false,"landing_page_url":"https://doi.org/10.1080/01495739.2025.2534185","pdf_url":null,"source":{"id":"https://openalex.org/S54937123","display_name":"Journal of Thermal Stresses","issn_l":"0149-5739","issn":["0149-5739","1521-074X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-1","poland-70","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Thermal Stresses","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323722","display_name":"Taif University","ror":"https://ror.org/014g1a453"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W1089567646","https://openalex.org/W1970512980","https://openalex.org/W1973038067","https://openalex.org/W1983319736","https://openalex.org/W2020143254","https://openalex.org/W2022942154","https://openalex.org/W2038940027","https://openalex.org/W2045616245","https://openalex.org/W2048088339","https://openalex.org/W2050110207","https://openalex.org/W2062339590","https://openalex.org/W2068151778","https://openalex.org/W2078614534","https://openalex.org/W2081180932","https://openalex.org/W2081421425","https://openalex.org/W2144122905","https://openalex.org/W2162037624","https://openalex.org/W2473413873","https://openalex.org/W2552046600","https://openalex.org/W2803965108","https://openalex.org/W2809202834","https://openalex.org/W2890014138","https://openalex.org/W2906681440","https://openalex.org/W2979594520","https://openalex.org/W2998344313","https://openalex.org/W3035240387","https://openalex.org/W3091964289","https://openalex.org/W3124911945","https://openalex.org/W3151181456","https://openalex.org/W3197722566","https://openalex.org/W4200502483","https://openalex.org/W4220925521","https://openalex.org/W4293433619","https://openalex.org/W4308936183","https://openalex.org/W4309090779","https://openalex.org/W4322760685","https://openalex.org/W4323350955","https://openalex.org/W4385225071","https://openalex.org/W4389393318","https://openalex.org/W4390877624","https://openalex.org/W4392929669","https://openalex.org/W4393981133","https://openalex.org/W4396801030","https://openalex.org/W4399723719","https://openalex.org/W4400312982","https://openalex.org/W4400678772","https://openalex.org/W4403459522","https://openalex.org/W4404143620","https://openalex.org/W4409622302","https://openalex.org/W4410912037"],"related_works":["https://openalex.org/W4415286335","https://openalex.org/W7118766040","https://openalex.org/W4410289800","https://openalex.org/W4411770113","https://openalex.org/W4411614059","https://openalex.org/W4404318878","https://openalex.org/W4407597184","https://openalex.org/W2530898697","https://openalex.org/W7084769157","https://openalex.org/W4410912037"],"abstract_inverted_index":{"This":[0,44],"paper":[1],"introduces":[2],"the":[3,18,66,104],"modified":[4],"extended":[5],"(ME)":[6],"direct":[7],"algebraic":[8],"approach,":[9],"which":[10,29],"is":[11,47],"used":[12],"to":[13,100],"evaluate":[14],"equations":[15],"based":[16],"on":[17],"Lord-Shulman":[19],"(L-S)":[20],"theory":[21],"of":[22,40,81,109],"thermoelasticity.":[23],"Nonlinear":[24],"thermoelasticity":[25],"investigates":[26],"situations":[27],"in":[28,62],"a":[30,38,78],"material\u2019s":[31],"properties":[32],"and":[33,65,71,89,115],"shape":[34],"change":[35],"significantly":[36],"as":[37,54],"result":[39],"fluctuating":[41],"thermal":[42,60,72],"loads.":[43],"study":[45],"topic":[46],"critical":[48],"for":[49],"understanding":[50],"real-world":[51],"phenomena":[52],"such":[53],"material":[55],"behavior":[56],"at":[57],"high":[58],"temperatures,":[59],"stresses":[61],"large":[63],"structures,":[64],"complex":[67],"interplay":[68],"between":[69],"mechanical":[70],"forces.":[73],"The":[74],"proposed":[75],"approach":[76],"generates":[77],"wide":[79],"range":[80],"precise":[82],"solutions,":[83,91],"including":[84],"exponential,":[85],"polynomial,":[86],"singular":[87],"soliton,":[88],"hyperbolic":[90],"each":[92],"with":[93],"unique":[94],"free":[95],"parameters":[96],"that":[97],"have":[98],"yet":[99],"be":[101],"published.":[102],"Furthermore,":[103],"research":[105],"includes":[106],"graphical":[107],"representations":[108],"various":[110],"displacement":[111],"components,":[112],"temperature":[113],"fluctuations,":[114],"stress":[116],"tensors.":[117]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":2}],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2025-10-10T00:00:00"}