{"id":"https://openalex.org/W2078490990","doi":"https://doi.org/10.1155/mpe/2006/20898","title":"A mathematical model and numerical solution of interface problems for steady state heat conduction","display_name":"A mathematical model and numerical solution of interface problems for steady state heat conduction","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2078490990","doi":"https://doi.org/10.1155/mpe/2006/20898","mag":"2078490990"},"language":"en","primary_location":{"id":"doi:10.1155/mpe/2006/20898","doi":"https://doi.org/10.1155/mpe/2006/20898","is_oa":true,"landing_page_url":"https://doi.org/10.1155/mpe/2006/20898","pdf_url":"https://downloads.hindawi.com/journals/mpe/2006/020898.pdf","source":{"id":"https://openalex.org/S178238111","display_name":"Mathematical Problems in Engineering","issn_l":"1024-123X","issn":["1024-123X","1026-7077","1563-5147"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","poland-20","vabb-shw"],"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Problems in Engineering","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://downloads.hindawi.com/journals/mpe/2006/020898.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004740463","display_name":"Zahir Seyidmamedov","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I51826884","display_name":"Kocaeli \u00dcniversitesi","ror":"https://ror.org/0411seq30","country_code":"TR","type":"education","lineage":["https://openalex.org/I51826884"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Z. Muradoglu Seyidmamedov","raw_affiliation_strings":["Applied Mathematical Sciences Research Center\nand Department of Mathematics, Kocaeli University, Umuttepe Campus"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Applied Mathematical Sciences Research Center\nand Department of Mathematics, Kocaeli University, Umuttepe Campus","institution_ids":["https://openalex.org/I51826884"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026208779","display_name":"Ebru Ozb\u0131lge","orcid":"https://orcid.org/0000-0002-2998-8134","observed_orcids":["https://orcid.org/0000-0002-2998-8134"]},"institutions":[{"id":"https://openalex.org/I15059493","display_name":"\u0130zmir University of Economics","ror":"https://ror.org/04hjr4202","country_code":"TR","type":"education","lineage":["https://openalex.org/I15059493"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Ebru Ozbilge","raw_affiliation_strings":["Department of Mathematics, Faculty of Science and Literature, Izmir University of Economics, 156 Sakarya Avenue"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science and Literature, Izmir University of Economics, 156 Sakarya Avenue","institution_ids":["https://openalex.org/I15059493"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2550,"currency":"USD","value_usd":2550},"apc_paid":{"value":2550,"currency":"USD","value_usd":2550},"fwci":0.596,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.60126805,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":95},"biblio":{"volume":"2006","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Singular Perturbation, Asymptotics and Difference Schemes","score":0.9179999828338623,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12727","display_name":"Singular Perturbation, Asymptotics and Difference Schemes","score":0.9179999828338623,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.03929999843239784,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T13116","display_name":"Heat Transfer and Numerical Methods","score":0.038100000470876694,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/interface-problems","display_name":"interface problems","score":0.8370000123977661},{"id":"https://openalex.org/keywords/transmission-problems","display_name":"transmission problems","score":0.8840000033378601},{"id":"https://openalex.org/keywords/steady-state-heat-conduction","display_name":"steady-state heat conduction","score":0.9879999756813049},{"id":"https://openalex.org/keywords/layered-media","display_name":"layered media","score":0.8429999947547913},{"id":"https://openalex.org/keywords/discontinuous-coefficients","display_name":"discontinuous coefficients","score":0.7820000052452087},{"id":"https://openalex.org/keywords/elliptic-equations","display_name":"elliptic equations","score":0.8709999918937683},{"id":"https://openalex.org/keywords/jump-conditions","display_name":"jump conditions","score":0.8259999752044678},{"id":"https://openalex.org/keywords/contact-conditions","display_name":"contact conditions","score":0.9810000061988831},{"id":"https://openalex.org/keywords/asymptotic-analysis","display_name":"asymptotic analysis","score":0.8059999942779541},{"id":"https://openalex.org/keywords/conservative-finite-difference-scheme","display_name":"conservative finite difference scheme","score":0.8519999980926514},{"id":"https://openalex.org/keywords/nonuniform-grids","display_name":"non-uniform grids","score":0.9150000214576721},{"id":"https://openalex.org/keywords/truncation-error-estimates","display_name":"truncation error estimates","score":0.8619999885559082},{"id":"https://openalex.org/keywords/fast-direct-solvers","display_name":"fast direct solvers","score":0.9200000166893005},{"id":"https://openalex.org/keywords/piecewise-constant-coefficients","display_name":"piecewise constant coefficients","score":0.9610000252723694}],"concepts":[{"id":"https://openalex.org/C172100665","wikidata":"https://www.wikidata.org/wiki/Q7465774","display_name":"Thermal conduction","level":2,"score":0.8601807355880737},{"id":"https://openalex.org/C8171440","wikidata":"https://www.wikidata.org/wiki/Q903414","display_name":"Steady state (chemistry)","level":2,"score":0.7097320556640625},{"id":"https://openalex.org/C113843644","wikidata":"https://www.wikidata.org/wiki/Q901882","display_name":"Interface (matter)","level":4,"score":0.705166757106781},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.5753316879272461},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.4084898829460144},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.3669166564941406},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3134930729866028},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.21441534161567688},{"id":"https://openalex.org/C147789679","wikidata":"https://www.wikidata.org/wiki/Q11372","display_name":"Physical chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C157915830","wikidata":"https://www.wikidata.org/wiki/Q2928001","display_name":"Bubble","level":2,"score":0.0},{"id":"https://openalex.org/C129307140","wikidata":"https://www.wikidata.org/wiki/Q6795880","display_name":"Maximum bubble pressure method","level":3,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/mpe/2006/20898","doi":"https://doi.org/10.1155/mpe/2006/20898","is_oa":true,"landing_page_url":"https://doi.org/10.1155/mpe/2006/20898","pdf_url":"https://downloads.hindawi.com/journals/mpe/2006/020898.pdf","source":{"id":"https://openalex.org/S178238111","display_name":"Mathematical Problems in Engineering","issn_l":"1024-123X","issn":["1024-123X","1026-7077","1563-5147"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","poland-20","vabb-shw"],"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Problems in Engineering","raw_type":"journal-article"},{"id":"pmh:ddea8368-136d-4366-97e7-2df0a3b040f7","doi":null,"is_oa":true,"landing_page_url":"https://avesis.kocaeli.edu.tr/publication/details/ddea8368-136d-4366-97e7-2df0a3b040f7/oai","pdf_url":"https://avesis.kocaeli.edu.tr/publication/details/ddea8368-136d-4366-97e7-2df0a3b040f7/oai/document.pdf","source":{"id":"https://openalex.org/S7407055291","display_name":"Kocaeli \u00dcniversitesi - AVES\u0130S","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:RePEc:hin:jnlmpe:020898","doi":null,"is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/MPE/2006/020898.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:03500299c812448fa6542b4f75b7e82a","doi":null,"is_oa":false,"landing_page_url":"https://doaj.org/article/03500299c812448fa6542b4f75b7e82a","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematical Problems in Engineering, Vol 2006 (2006)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/mpe/2006/20898","doi":"https://doi.org/10.1155/mpe/2006/20898","is_oa":true,"landing_page_url":"https://doi.org/10.1155/mpe/2006/20898","pdf_url":"https://downloads.hindawi.com/journals/mpe/2006/020898.pdf","source":{"id":"https://openalex.org/S178238111","display_name":"Mathematical Problems in Engineering","issn_l":"1024-123X","issn":["1024-123X","1026-7077","1563-5147"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","poland-20","vabb-shw"],"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Problems in Engineering","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2078490990.pdf","grobid_xml":"https://content.openalex.org/works/W2078490990.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1584197010","https://openalex.org/W1866311589","https://openalex.org/W1966887244","https://openalex.org/W1996432343","https://openalex.org/W2001819970","https://openalex.org/W2063458426","https://openalex.org/W2068750861","https://openalex.org/W2095548561","https://openalex.org/W2140438255","https://openalex.org/W2141613219","https://openalex.org/W2769651972","https://openalex.org/W4292360407"],"related_works":["https://openalex.org/W2461810111","https://openalex.org/W240434724","https://openalex.org/W2081357281","https://openalex.org/W4398241870","https://openalex.org/W204403906","https://openalex.org/W2323741445","https://openalex.org/W304271350","https://openalex.org/W2531172171","https://openalex.org/W1997527521","https://openalex.org/W2157970630"],"abstract_inverted_index":{"We":[0,44],"study":[1],"interface":[2,74,124],"(or":[3,50],"transmission)":[4],"problems":[5,17,125],"arising":[6],"in":[7],"the":[8,21,25,54,58,73,79,82,88,98,103,112,123,146],"steady":[9],"state":[10],"heat":[11],"conduction":[12],"for":[13,78,122],"layered":[14,59],"medium.":[15],"These":[16],"are":[18,109],"related":[19],"to":[20,93],"elliptic":[22],"equation":[23],"of":[24,48,57,72,87,102,145],"form":[26],"Au":[27],":":[28,62],"=":[29,31,42,63,133],"\u2212\u2207(k(x)\u2207u(x))":[30],"F(x),":[32],"x":[33],"\u2208":[34],"\u03a9":[35,61],"\u2282":[36],"\u211d2,":[37],"with":[38,126],"discontinuous":[39,130],"coefficient":[40,131],"k":[41,132],"k(x).":[43,134],"analyse":[45],"two":[46],"types":[47],"jump":[49],"contact)":[51],"conditions":[52],"across":[53],"interfaces":[55],"and":[56,142],"medium":[60],"\u03a91":[64],"\u222a":[65,67],"\u03a9\u03b4":[66,91],"\u03a92.":[68],"An":[69],"asymptotic":[70],"analysis":[71],"problem":[75],"is":[76],"derived":[77],"case":[80],"when":[81],"thickness":[83],"(2\u03b4":[84],">":[85],"0)":[86],"layer":[89],"(isolation)":[90],"tends":[92],"zero.":[94],"For":[95],"each":[96],"case,":[97],"local":[99],"truncation":[100],"errors":[101],"used":[104],"conservative":[105],"finite":[106],"difference":[107],"scheme":[108],"estimated":[110],"on":[111],"nonuniform":[113],"grid.":[114],"A":[115],"fast":[116],"direct":[117],"solver":[118],"has":[119],"been":[120],"applied":[121],"piecewise":[127],"constant":[128],"but":[129],"The":[135],"presented":[136],"numerical":[137],"results":[138],"illustrate":[139],"high":[140],"accuracy":[141],"show":[143],"applicability":[144],"given":[147],"approach.":[148]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}