{"id":"https://openalex.org/W4306362305","doi":"https://doi.org/10.3390/axioms11100556","title":"A Shortcut Method to Solve for a 1D Heat Conduction Model under Complicated Boundary Conditions","display_name":"A Shortcut Method to Solve for a 1D Heat Conduction Model under Complicated Boundary Conditions","publication_year":2022,"publication_date":"2022-10-14","ids":{"openalex":"https://openalex.org/W4306362305","doi":"https://doi.org/10.3390/axioms11100556"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11100556","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11100556","pdf_url":"https://www.mdpi.com/2075-1680/11/10/556/pdf?version=1666687329","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/11/10/556/pdf?version=1666687329","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059925090","display_name":"Ting Wei","orcid":"https://orcid.org/0000-0002-2210-4877"},"institutions":[{"id":"https://openalex.org/I16365422","display_name":"Hefei University of Technology","ror":"https://ror.org/02czkny70","country_code":"CN","type":"education","lineage":["https://openalex.org/I16365422"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ting Wei","raw_affiliation_strings":["School of Civil Engineering, Hefei University of Technology, Hefei 230009, China"],"affiliations":[{"raw_affiliation_string":"School of Civil Engineering, Hefei University of Technology, Hefei 230009, China","institution_ids":["https://openalex.org/I16365422"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059054165","display_name":"Yuezan Tao","orcid":null},"institutions":[{"id":"https://openalex.org/I16365422","display_name":"Hefei University of Technology","ror":"https://ror.org/02czkny70","country_code":"CN","type":"education","lineage":["https://openalex.org/I16365422"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yuezan Tao","raw_affiliation_strings":["School of Civil Engineering, Hefei University of Technology, Hefei 230009, China"],"affiliations":[{"raw_affiliation_string":"School of Civil Engineering, Hefei University of Technology, Hefei 230009, China","institution_ids":["https://openalex.org/I16365422"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080766858","display_name":"Honglei Ren","orcid":null},"institutions":[{"id":"https://openalex.org/I16365422","display_name":"Hefei University of Technology","ror":"https://ror.org/02czkny70","country_code":"CN","type":"education","lineage":["https://openalex.org/I16365422"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Honglei Ren","raw_affiliation_strings":["School of Civil Engineering, Hefei University of Technology, Hefei 230009, China"],"affiliations":[{"raw_affiliation_string":"School of Civil Engineering, Hefei University of Technology, Hefei 230009, China","institution_ids":["https://openalex.org/I16365422"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039912568","display_name":"Fei Lin","orcid":"https://orcid.org/0000-0002-5832-1128"},"institutions":[{"id":"https://openalex.org/I16365422","display_name":"Hefei University of Technology","ror":"https://ror.org/02czkny70","country_code":"CN","type":"education","lineage":["https://openalex.org/I16365422"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fei Lin","raw_affiliation_strings":["School of Civil Engineering, Hefei University of Technology, Hefei 230009, China"],"affiliations":[{"raw_affiliation_string":"School of Civil Engineering, Hefei University of Technology, Hefei 230009, China","institution_ids":["https://openalex.org/I16365422"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5059054165"],"corresponding_institution_ids":["https://openalex.org/I16365422"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.5948,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.61568816,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"11","issue":"10","first_page":"556","last_page":"556"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10998","display_name":"Heat Transfer and Optimization","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"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/T10998","display_name":"Heat Transfer and Optimization","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9965999722480774,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.994700014591217,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/inflection-point","display_name":"Inflection point","score":0.7727482318878174},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7164523005485535},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6020613312721252},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5584391355514526},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5461647510528564},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.4850982427597046},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4747655391693115},{"id":"https://openalex.org/keywords/thermal-diffusivity","display_name":"Thermal diffusivity","score":0.433931827545166},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.4272539019584656},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.421619713306427},{"id":"https://openalex.org/keywords/linear-interpolation","display_name":"Linear interpolation","score":0.4120672941207886},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20545604825019836},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.2034783959388733},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15099328756332397}],"concepts":[{"id":"https://openalex.org/C74545648","wikidata":"https://www.wikidata.org/wiki/Q212794","display_name":"Inflection point","level":2,"score":0.7727482318878174},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7164523005485535},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6020613312721252},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5584391355514526},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5461647510528564},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.4850982427597046},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4747655391693115},{"id":"https://openalex.org/C37668627","wikidata":"https://www.wikidata.org/wiki/Q3381809","display_name":"Thermal diffusivity","level":2,"score":0.433931827545166},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.4272539019584656},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.421619713306427},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.4120672941207886},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20545604825019836},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.2034783959388733},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15099328756332397},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms11100556","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11100556","pdf_url":"https://www.mdpi.com/2075-1680/11/10/556/pdf?version=1666687329","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:f114053d69b74026b67873dcd1e10eed","is_oa":true,"landing_page_url":"https://doaj.org/article/f114053d69b74026b67873dcd1e10eed","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":"Axioms, Vol 11, Iss 10, p 556 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/10/556/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11100556","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":"Axioms; Volume 11; Issue 10; Pages: 556","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11100556","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11100556","pdf_url":"https://www.mdpi.com/2075-1680/11/10/556/pdf?version=1666687329","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G166188413","display_name":null,"funder_award_id":"sklhse-2020-D-06","funder_id":"https://openalex.org/F4320322392","funder_display_name":"Tsinghua University"}],"funders":[{"id":"https://openalex.org/F4320322392","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549"},{"id":"https://openalex.org/F4320327033","display_name":"State Key Laboratory of Hydroscience and Engineering","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4306362305.pdf","grobid_xml":"https://content.openalex.org/works/W4306362305.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W2038660707","https://openalex.org/W2040355178","https://openalex.org/W2290122632","https://openalex.org/W2334324548","https://openalex.org/W2348826992","https://openalex.org/W2353927698","https://openalex.org/W2363077502","https://openalex.org/W2539340507","https://openalex.org/W2575870713","https://openalex.org/W2755345807","https://openalex.org/W2789274122","https://openalex.org/W2794433085","https://openalex.org/W2804856463","https://openalex.org/W2900511345","https://openalex.org/W2908073661","https://openalex.org/W2912913403","https://openalex.org/W2960245980","https://openalex.org/W2961370220","https://openalex.org/W3038845102","https://openalex.org/W3040879030","https://openalex.org/W3047101332","https://openalex.org/W3083557647","https://openalex.org/W3162749987","https://openalex.org/W3178017980","https://openalex.org/W3210506648","https://openalex.org/W4210470571","https://openalex.org/W4293125295"],"related_works":["https://openalex.org/W3183609115","https://openalex.org/W2985206855","https://openalex.org/W2387056800","https://openalex.org/W2389908107","https://openalex.org/W2108850688","https://openalex.org/W2354295809","https://openalex.org/W2532653122","https://openalex.org/W2359833404","https://openalex.org/W1994390986","https://openalex.org/W2378343395"],"abstract_inverted_index":{"The":[0,73,93,167],"function":[1,133],"of":[2,35,47,76,79,86,91,98,105,157,161,174,196,201],"boundary":[3,36,134,207],"temperature":[4,199,208],"variation":[5,155,200],"with":[6,192],"time,":[7],"f(t)":[8,64],"is":[9],"generally":[10],"defined":[11],"according":[12],"to":[13],"measured":[14,103],"data.":[15],"For":[16],"f(t),":[17,99],"which":[18],"has":[19],"a":[20,23,41,52,120],"complicated":[21],"expression,":[22],"corresponding":[24,121],"one-dimensional":[25],"heat":[26],"conduction":[27],"model":[28,117],"was":[29,55,107],"constructed":[30],"under":[31,60,129],"the":[32,48,58,61,70,77,84,89,102,110,116,126,130,136,146,154,158,162,172,179,187,193,197,202,204,211,214],"first":[33],"type":[34],"conditions":[37],"(Dirichlet":[38],"conditions)":[39],"in":[40,69,206],"semi-infinite":[42],"domain.":[43],"By":[44],"taking":[45],"advantage":[46],"Fourier":[49],"transform":[50],"properties,":[51],"theoretical":[53,111],"solution":[54,74,128],"given":[56],"for":[57,144],"model,":[59],"condition":[62],"that":[63,171,186],"does":[65],"not":[66],"directly":[67],"participate":[68],"transformation":[71],"process.":[72],"consists":[75],"product":[78],"erfc(t)":[80,87],"and":[81,83,88,118,140,151,153,185,210],"f(0)":[82],"convolution":[85],"derivative":[90],"f(t).":[92],"piecewise":[94],"linear":[95,131],"interpolation":[96],"equation":[97],"based":[100],"on":[101,125],"data":[104],"temperature,":[106],"substituted":[108],"into":[109],"solution,":[112],"thus":[113],"quickly":[114],"solving":[115],"deriving":[119],"analytical":[122,127],"solution.":[123],"Based":[124],"decay":[132],"condition,":[135],"inflection":[137,163,188],"point":[138,164,189],"method":[139,143],"curve":[141],"fitting":[142],"calculating":[145],"thermal":[147,175],"diffusivity":[148,176],"were":[149,165],"introduced":[150],"exemplified,":[152],"laws":[156],"appearance":[159],"moment":[160],"discussed.":[166],"obtained":[168],"results":[169],"show":[170],"values":[173,190,195],"calculated":[177],"by":[178],"two":[180],"methods":[181],"are":[182],"basically":[183],"consistent,":[184],"rise":[191],"increasing":[194],"initial":[198],"boundary,":[203,215],"decrease":[205],"velocity,":[209],"distance":[212],"from":[213],"respectively.":[216]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4}],"updated_date":"2026-03-14T08:43:22.919905","created_date":"2022-10-17T00:00:00"}