{"id":"https://openalex.org/W4390704417","doi":"https://doi.org/10.3390/computation12010011","title":"Analytical and Numerical Investigation of Two-Dimensional Heat Transfer with Periodic Boundary Conditions","display_name":"Analytical and Numerical Investigation of Two-Dimensional Heat Transfer with Periodic Boundary Conditions","publication_year":2024,"publication_date":"2024-01-10","ids":{"openalex":"https://openalex.org/W4390704417","doi":"https://doi.org/10.3390/computation12010011"},"language":"en","primary_location":{"id":"doi:10.3390/computation12010011","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation12010011","pdf_url":"https://www.mdpi.com/2079-3197/12/1/11/pdf?version=1704886024","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2079-3197/12/1/11/pdf?version=1704886024","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003825249","display_name":"\u0130rem Ba\u011flan","orcid":"https://orcid.org/0000-0002-1877-9791"},"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":"\u0130rem Ba\u011flan","raw_affiliation_strings":["Department of Mathematics, Kocaeli University, TR-41380 Kocaeli, T\u00fcrkiye"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Kocaeli University, TR-41380 Kocaeli, T\u00fcrkiye","institution_ids":["https://openalex.org/I51826884"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067460163","display_name":"Erman Aslan","orcid":"https://orcid.org/0000-0001-8595-6092"},"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":true,"raw_author_name":"Erman Aslan","raw_affiliation_strings":["Department of Mechanical Engineering, Kocaeli University, TR-41380 Kocaeli, T\u00fcrkiye"],"raw_orcid":"https://orcid.org/0000-0001-8595-6092","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Kocaeli University, TR-41380 Kocaeli, T\u00fcrkiye","institution_ids":["https://openalex.org/I51826884"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5067460163"],"corresponding_institution_ids":["https://openalex.org/I51826884"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01028979,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"12","issue":"1","first_page":"11","last_page":"11"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9990000128746033,"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":"Differential Equations and Numerical Methods","score":0.9990000128746033,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7165923714637756},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7055494785308838},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6100794076919556},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5673441886901855},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.49229729175567627},{"id":"https://openalex.org/keywords/heat-transfer","display_name":"Heat transfer","score":0.4858260154724121},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4839230179786682},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.47683683037757874},{"id":"https://openalex.org/keywords/periodic-boundary-conditions","display_name":"Periodic boundary conditions","score":0.46925970911979675},{"id":"https://openalex.org/keywords/heat-equation","display_name":"Heat equation","score":0.46316349506378174},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.44648435711860657},{"id":"https://openalex.org/keywords/fourier-series","display_name":"Fourier series","score":0.4303993582725525},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.41679131984710693},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15301236510276794},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.1480993926525116},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10994270443916321},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.062327057123184204}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7165923714637756},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7055494785308838},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6100794076919556},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5673441886901855},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.49229729175567627},{"id":"https://openalex.org/C50517652","wikidata":"https://www.wikidata.org/wiki/Q179635","display_name":"Heat transfer","level":2,"score":0.4858260154724121},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4839230179786682},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.47683683037757874},{"id":"https://openalex.org/C112675119","wikidata":"https://www.wikidata.org/wiki/Q2992284","display_name":"Periodic boundary conditions","level":3,"score":0.46925970911979675},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.46316349506378174},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.44648435711860657},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.4303993582725525},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.41679131984710693},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15301236510276794},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.1480993926525116},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10994270443916321},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.062327057123184204},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/computation12010011","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation12010011","pdf_url":"https://www.mdpi.com/2079-3197/12/1/11/pdf?version=1704886024","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computation","raw_type":"journal-article"},{"id":"pmh:10a40cd1-7060-4d56-9fe1-7ab9872e1de2","is_oa":true,"landing_page_url":"https://avesis.kocaeli.edu.tr/publication/details/10a40cd1-7060-4d56-9fe1-7ab9872e1de2/oai","pdf_url":"https://avesis.kocaeli.edu.tr/publication/details/10a40cd1-7060-4d56-9fe1-7ab9872e1de2/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,"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:doaj.org/article:6790b89ee8664fc38e5d19837a25d484","is_oa":true,"landing_page_url":"https://doaj.org/article/6790b89ee8664fc38e5d19837a25d484","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computation, Vol 12, Iss 1, p 11 (2024)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2079-3197/12/1/11/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/computation12010011","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computation","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/computation12010011","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation12010011","pdf_url":"https://www.mdpi.com/2079-3197/12/1/11/pdf?version=1704886024","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4390704417.pdf","grobid_xml":"https://content.openalex.org/works/W4390704417.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W1635779336","https://openalex.org/W1977776095","https://openalex.org/W1995002345","https://openalex.org/W2004191063","https://openalex.org/W2039938123","https://openalex.org/W2049334604","https://openalex.org/W2076479791","https://openalex.org/W2084893199","https://openalex.org/W2095143338","https://openalex.org/W2107839874","https://openalex.org/W2117242079","https://openalex.org/W2147092505","https://openalex.org/W2564083018","https://openalex.org/W2733391656","https://openalex.org/W2780740263","https://openalex.org/W2790213747","https://openalex.org/W2905806073","https://openalex.org/W3017881287","https://openalex.org/W3045420398","https://openalex.org/W3133900290","https://openalex.org/W3217778273","https://openalex.org/W4221102985","https://openalex.org/W4254696097","https://openalex.org/W4304585324","https://openalex.org/W4380683322","https://openalex.org/W4381665988","https://openalex.org/W4382722246","https://openalex.org/W4387217348","https://openalex.org/W4388316717","https://openalex.org/W6857097471"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W4301247218","https://openalex.org/W2129818458","https://openalex.org/W4243074410","https://openalex.org/W4289551052","https://openalex.org/W4390756076","https://openalex.org/W2340777379"],"abstract_inverted_index":{"A":[0],"two-dimensional":[1],"heat":[2,7],"diffusion":[3],"problem":[4,14,27],"with":[5],"a":[6,11],"source":[8],"that":[9],"is":[10,15,28,34,77],"quasilinear":[12],"parabolic":[13],"examined":[16],"analytically":[17],"and":[18,41,61,85],"numerically.":[19],"Periodic":[20],"boundary":[21],"conditions":[22,57],"are":[23],"employed.":[24],"As":[25],"the":[26,38,45,48,51,65,69,83],"nonlinear,":[29],"Picard\u2019s":[30],"successive":[31],"approximation":[32],"theorem":[33],"utilized.":[35],"We":[36],"demonstrate":[37],"existence,":[39],"uniqueness,":[40],"constant":[42],"dependence":[43],"of":[44,58],"solution":[46],"on":[47,64],"data":[49],"using":[50],"generalized":[52],"Fourier":[53],"method":[54],"under":[55],"specific":[56],"natural":[59],"regularity":[60],"consistency":[62],"imposed":[63],"input":[66],"data.":[67],"For":[68],"numerical":[70,86],"solution,":[71],"an":[72],"implicit":[73],"finite":[74],"difference":[75],"scheme":[76],"used.":[78],"The":[79],"results":[80],"obtained":[81],"from":[82],"analytical":[84],"solutions":[87],"closely":[88],"match":[89],"each":[90],"other.":[91]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
