{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T14:42:06Z","timestamp":1787064126098,"version":"3.56.0"},"reference-count":34,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2018,8,29]],"date-time":"2018-08-29T00:00:00Z","timestamp":1535500800000},"content-version":"vor","delay-in-days":240,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Science Education Project in Tianjin City","award":["HE1017"],"award-info":[{"award-number":["HE1017"]}]},{"name":"Science Education Project in Tianjin City","award":["2013YQ470767"],"award-info":[{"award-number":["2013YQ470767"]}]},{"name":"National Key Foundation for Exploring Scientific Instrument of China","award":["HE1017"],"award-info":[{"award-number":["HE1017"]}]},{"name":"National Key Foundation for Exploring Scientific Instrument of China","award":["2013YQ470767"],"award-info":[{"award-number":["2013YQ470767"]}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>The boundary element method (BEM) and sequential function specification method (SFSM) are used to research the inverse problem of boundary heat flux identification in the two\u2010dimensional heat conduction system. The future time step in the SFSM is optimized by introducing the residual error principles to get the more accurate inversion results. For the forward problems, the BEM is used to calculate the required temperature value of discrete point; for the inverse problems, the impacts of different future time steps, measuring point position, and measuring error on the inversion results are discussed. Furthermore, the comparison is made for the optimal future time step obtained by introducing the residual error principle and the inherent future time step. The example analysis shows that the method proposed still has higher accuracy when the measuring error exists or the measuring point position is far away from the boundary heat flux.<\/jats:p>","DOI":"10.1155\/2018\/6741632","type":"journal-article","created":{"date-parts":[[2018,8,29]],"date-time":"2018-08-29T19:53:04Z","timestamp":1535572384000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Solving of Two\u2010Dimensional Unsteady Inverse Heat Conduction Problems Based on Boundary Element Method and Sequential Function Specification Method"],"prefix":"10.1155","volume":"2018","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2608-4946","authenticated-orcid":false,"given":"Shoubin","family":"Wang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuanzheng","family":"Deng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8909-9857","authenticated-orcid":false,"given":"Xiaogang","family":"Sun","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2018,8,29]]},"reference":[{"key":"e_1_2_10_1_2","doi-asserted-by":"publisher","DOI":"10.1155\/2018\/8783946"},{"key":"e_1_2_10_2_2","doi-asserted-by":"publisher","DOI":"10.1155\/2017\/2861342"},{"key":"e_1_2_10_3_2","volume-title":"Direct and Inverse Heat Conduction Problems Solving by the Boundary Element Method","author":"Sheng C.","year":"2007"},{"key":"e_1_2_10_4_2","doi-asserted-by":"publisher","DOI":"10.1155\/2017\/2461498"},{"key":"e_1_2_10_5_2","doi-asserted-by":"publisher","DOI":"10.2514\/1.T5209"},{"key":"e_1_2_10_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijheatmasstransfer.2015.01.082"},{"key":"e_1_2_10_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.expthermflusci.2017.09.006"},{"key":"e_1_2_10_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijheatmasstransfer.2007.10.029"},{"key":"e_1_2_10_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijheatmasstransfer.2013.12.073"},{"key":"e_1_2_10_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ast.2016.01.015"},{"key":"e_1_2_10_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijheatmasstransfer.2015.09.029"},{"key":"e_1_2_10_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2013.07.019"},{"key":"e_1_2_10_13_2","volume-title":"Further Studies on Fuzzy Inference Method for Inverse Heat Transfer Problems","author":"Zhaoming L.","year":"2014"},{"key":"e_1_2_10_14_2","first-page":"145","article-title":"Estimation of surface heat flux for nonlinear inverse heat conduction problem","volume":"30","author":"Qian W. 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