{"id":"https://openalex.org/W2950221087","doi":"https://doi.org/10.3390/sym11060791","title":"Integral Transform Method to Solve the Problem of Porous Slider without Velocity Slip","display_name":"Integral Transform Method to Solve the Problem of Porous Slider without Velocity Slip","publication_year":2019,"publication_date":"2019-06-13","ids":{"openalex":"https://openalex.org/W2950221087","doi":"https://doi.org/10.3390/sym11060791","mag":"2950221087"},"language":"en","primary_location":{"id":"doi:10.3390/sym11060791","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11060791","pdf_url":"https://www.mdpi.com/2073-8994/11/6/791/pdf?version=1561374234","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/11/6/791/pdf?version=1561374234","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044594255","display_name":"Naeem Faraz","orcid":"https://orcid.org/0000-0003-3682-8099"},"institutions":[{"id":"https://openalex.org/I115592961","display_name":"Jiangsu University","ror":"https://ror.org/03jc41j30","country_code":"CN","type":"education","lineage":["https://openalex.org/I115592961"]},{"id":"https://openalex.org/I181326427","display_name":"Donghua University","ror":"https://ror.org/035psfh38","country_code":"CN","type":"education","lineage":["https://openalex.org/I181326427"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Naeem Faraz","raw_affiliation_strings":["Faculty of Science, Jiangsu University, Zhenjiang 212013, Jiangsu, China","International Cultural Exchange School of Donghua University, Shanghai 200051, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Science, Jiangsu University, Zhenjiang 212013, Jiangsu, China","institution_ids":["https://openalex.org/I115592961"]},{"raw_affiliation_string":"International Cultural Exchange School of Donghua University, Shanghai 200051, China","institution_ids":["https://openalex.org/I181326427"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018916879","display_name":"Yasir Khan","orcid":"https://orcid.org/0000-0002-6386-6181"},"institutions":[{"id":"https://openalex.org/I4210112337","display_name":"University of Hafr Al-Batin","ror":"https://ror.org/021jt1927","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210112337"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Yasir Khan","raw_affiliation_strings":["Department of Mathematics, University of Hafr Al-Batin, Hafr Al-Batin 1803, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Hafr Al-Batin, Hafr Al-Batin 1803, Saudi Arabia","institution_ids":["https://openalex.org/I4210112337"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100460375","display_name":"Dianchen Lu","orcid":"https://orcid.org/0000-0001-6896-172X"},"institutions":[{"id":"https://openalex.org/I115592961","display_name":"Jiangsu University","ror":"https://ror.org/03jc41j30","country_code":"CN","type":"education","lineage":["https://openalex.org/I115592961"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dian Chen Lu","raw_affiliation_strings":["Faculty of Science, Jiangsu University, Zhenjiang 212013, Jiangsu, China"],"raw_orcid":"https://orcid.org/0000-0001-6896-172X","affiliations":[{"raw_affiliation_string":"Faculty of Science, Jiangsu University, Zhenjiang 212013, Jiangsu, China","institution_ids":["https://openalex.org/I115592961"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016584984","display_name":"Marjan Goodarzi","orcid":"https://orcid.org/0000-0002-1285-0593"},"institutions":[{"id":"https://openalex.org/I141445968","display_name":"Ton Duc Thang University","ror":"https://ror.org/01drq0835","country_code":"VN","type":"education","lineage":["https://openalex.org/I141445968"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Marjan Goodarzi","raw_affiliation_strings":["Sustainable Management of Natural Resources and Environment Research Group, Faculty of Environment and Labour Safety, Ton Duc Thang University, Ho Chi Minh City, Vietnam"],"raw_orcid":"https://orcid.org/0000-0002-1285-0593","affiliations":[{"raw_affiliation_string":"Sustainable Management of Natural Resources and Environment Research Group, Faculty of Environment and Labour Safety, Ton Duc Thang University, Ho Chi Minh City, Vietnam","institution_ids":["https://openalex.org/I141445968"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5044594255"],"corresponding_institution_ids":["https://openalex.org/I115592961","https://openalex.org/I181326427"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.6301,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.81725071,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"11","issue":"6","first_page":"791","last_page":"791"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11945","display_name":"Heat Transfer Mechanisms","score":0.9958999752998352,"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/T11945","display_name":"Heat Transfer Mechanisms","score":0.9958999752998352,"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/T10998","display_name":"Heat Transfer and Optimization","score":0.9941999912261963,"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/T11379","display_name":"Rheology and Fluid Dynamics Studies","score":0.9915000200271606,"subfield":{"id":"https://openalex.org/subfields/1507","display_name":"Fluid Flow and Transfer Processes"},"field":{"id":"https://openalex.org/fields/15","display_name":"Chemical Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/adomian-decomposition-method","display_name":"Adomian decomposition method","score":0.7623879909515381},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6493938565254211},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5450518131256104},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5290989875793457},{"id":"https://openalex.org/keywords/integral-transform","display_name":"Integral transform","score":0.48012685775756836},{"id":"https://openalex.org/keywords/reynolds-number","display_name":"Reynolds number","score":0.4543154239654541},{"id":"https://openalex.org/keywords/matrix-similarity","display_name":"Matrix similarity","score":0.42993229627609253},{"id":"https://openalex.org/keywords/decomposition-method","display_name":"Decomposition method (queueing theory)","score":0.41027095913887024},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.34572476148605347},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34361422061920166},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.2281041145324707},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12973591685295105}],"concepts":[{"id":"https://openalex.org/C120317633","wikidata":"https://www.wikidata.org/wiki/Q3042796","display_name":"Adomian decomposition method","level":3,"score":0.7623879909515381},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6493938565254211},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5450518131256104},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5290989875793457},{"id":"https://openalex.org/C200052193","wikidata":"https://www.wikidata.org/wiki/Q877802","display_name":"Integral transform","level":2,"score":0.48012685775756836},{"id":"https://openalex.org/C182748727","wikidata":"https://www.wikidata.org/wiki/Q178932","display_name":"Reynolds number","level":3,"score":0.4543154239654541},{"id":"https://openalex.org/C39739852","wikidata":"https://www.wikidata.org/wiki/Q254491","display_name":"Matrix similarity","level":3,"score":0.42993229627609253},{"id":"https://openalex.org/C2778258933","wikidata":"https://www.wikidata.org/wiki/Q16918986","display_name":"Decomposition method (queueing theory)","level":2,"score":0.41027095913887024},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.34572476148605347},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34361422061920166},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.2281041145324707},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12973591685295105},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C196558001","wikidata":"https://www.wikidata.org/wiki/Q190132","display_name":"Turbulence","level":2,"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":2,"locations":[{"id":"doi:10.3390/sym11060791","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11060791","pdf_url":"https://www.mdpi.com/2073-8994/11/6/791/pdf?version=1561374234","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:63337b6812d9480c8ee5eda00ad70a42","is_oa":true,"landing_page_url":"https://doaj.org/article/63337b6812d9480c8ee5eda00ad70a42","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,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 11, Iss 6, p 791 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym11060791","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11060791","pdf_url":"https://www.mdpi.com/2073-8994/11/6/791/pdf?version=1561374234","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323710","display_name":"Donghua University","ror":"https://ror.org/035psfh38"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2950221087.pdf","grobid_xml":"https://content.openalex.org/works/W2950221087.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1582881077","https://openalex.org/W1971004981","https://openalex.org/W2007928287","https://openalex.org/W2012299572","https://openalex.org/W2026392980","https://openalex.org/W2029747087","https://openalex.org/W2035158737","https://openalex.org/W2058424173","https://openalex.org/W2065712928","https://openalex.org/W2073467701","https://openalex.org/W2118034492","https://openalex.org/W2131249117","https://openalex.org/W2407128362","https://openalex.org/W2540691828","https://openalex.org/W2905625881","https://openalex.org/W2919802663","https://openalex.org/W2944145288","https://openalex.org/W6757555784"],"related_works":["https://openalex.org/W2089904505","https://openalex.org/W2184238946","https://openalex.org/W2017928093","https://openalex.org/W2080236590","https://openalex.org/W1838417290","https://openalex.org/W1977939012","https://openalex.org/W811173482","https://openalex.org/W2027788087","https://openalex.org/W4285610872","https://openalex.org/W1566651242"],"abstract_inverted_index":{"This":[0],"study":[1],"is":[2,15,44,51,79,86],"about":[3],"the":[4,13,18,25,70,82,88],"lubrication":[5],"of":[6,118],"a":[7,38,76],"long":[8],"porous":[9,19],"slider":[10],"in":[11,65],"which":[12,34,85],"fluid":[14],"injected":[16],"into":[17],"bottom.":[20],"The":[21,41],"similarity":[22],"transformation":[23],"reduces":[24],"Navier-Stokes":[26],"equations":[27],"to":[28],"couple":[29],"nonlinear,":[30],"ordinary":[31],"differential":[32],"equations,":[33],"are":[35,73,101,110,124],"solved":[36],"by":[37],"new":[39],"algorithm.":[40],"proposed":[42,55],"technique":[43],"based":[45],"on":[46,121],"integral":[47,66],"transformation.":[48],"Apparently,":[49],"there":[50],"great":[52],"symmetry":[53],"between":[54],"method":[56,63,68],"and":[57,95,108,114],"variation":[58],"iteration":[59],"method,":[60],"Adomian":[61,92],"decomposition":[62],"but":[64],"transform":[67],"all":[69],"boundary":[71],"conditions":[72],"applied,":[74],"then":[75],"recursive":[77],"scheme":[78],"used":[80],"for":[81,103],"analytical":[83,98,113],"solutions,":[84],"unlike":[87],"Variational":[89],"Iteration":[90],"Method,":[91,94],"Decomposition":[93],"other":[96],"existing":[97],"methods.":[99,116],"Solutions":[100],"obtained":[102],"much":[104],"larger":[105],"Reynolds":[106,119],"numbers,":[107],"they":[109],"compared":[111],"with":[112],"numerical":[115],"Effects":[117],"number":[120],"velocity":[122],"components":[123],"presented.":[125]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
