{"id":"https://openalex.org/W3004022331","doi":"https://doi.org/10.1155/2020/1890972","title":"Heat and Mass Transfer in Unsteady Boundary Layer Flow of Williamson Nanofluids","display_name":"Heat and Mass Transfer in Unsteady Boundary Layer Flow of Williamson Nanofluids","publication_year":2020,"publication_date":"2020-02-01","ids":{"openalex":"https://openalex.org/W3004022331","doi":"https://doi.org/10.1155/2020/1890972","mag":"3004022331"},"language":"en","primary_location":{"id":"doi:10.1155/2020/1890972","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/1890972","pdf_url":"https://downloads.hindawi.com/journals/jam/2020/1890972.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2020/1890972.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102742869","display_name":"Tesfaye Kebede","orcid":null},"institutions":[{"id":"https://openalex.org/I57092466","display_name":"Bahir Dar University","ror":"https://ror.org/01670bg46","country_code":"ET","type":"education","lineage":["https://openalex.org/I57092466"]}],"countries":["ET"],"is_corresponding":false,"raw_author_name":"Tesfaye Kebede","raw_affiliation_strings":["Department of Mathematics, Bahir Dar University, P.O. Box 79, Bahir Dar, Ethiopia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Bahir Dar University, P.O. Box 79, Bahir Dar, Ethiopia","institution_ids":["https://openalex.org/I57092466"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108740856","display_name":"Eshetu Haile","orcid":null},"institutions":[{"id":"https://openalex.org/I57092466","display_name":"Bahir Dar University","ror":"https://ror.org/01670bg46","country_code":"ET","type":"education","lineage":["https://openalex.org/I57092466"]}],"countries":["ET"],"is_corresponding":false,"raw_author_name":"Eshetu Haile","raw_affiliation_strings":["Department of Mathematics, Bahir Dar University, P.O. Box 79, Bahir Dar, Ethiopia"],"raw_orcid":"https://orcid.org/0000-0002-2428-1842","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Bahir Dar University, P.O. Box 79, Bahir Dar, Ethiopia","institution_ids":["https://openalex.org/I57092466"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062566819","display_name":"Gurju Awgichew","orcid":"https://orcid.org/0000-0002-4274-8450"},"institutions":[{"id":"https://openalex.org/I57092466","display_name":"Bahir Dar University","ror":"https://ror.org/01670bg46","country_code":"ET","type":"education","lineage":["https://openalex.org/I57092466"]}],"countries":["ET"],"is_corresponding":false,"raw_author_name":"Gurju Awgichew","raw_affiliation_strings":["Department of Mathematics, Bahir Dar University, P.O. Box 79, Bahir Dar, Ethiopia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Bahir Dar University, P.O. Box 79, Bahir Dar, Ethiopia","institution_ids":["https://openalex.org/I57092466"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002684228","display_name":"Tadesse Walelign","orcid":"https://orcid.org/0000-0001-7524-7567"},"institutions":[{"id":"https://openalex.org/I57092466","display_name":"Bahir Dar University","ror":"https://ror.org/01670bg46","country_code":"ET","type":"education","lineage":["https://openalex.org/I57092466"]}],"countries":["ET"],"is_corresponding":true,"raw_author_name":"Tadesse Walelign","raw_affiliation_strings":["Department of Mathematics, Bahir Dar University, P.O. Box 79, Bahir Dar, Ethiopia"],"raw_orcid":"https://orcid.org/0000-0001-7524-7567","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Bahir Dar University, P.O. Box 79, Bahir Dar, Ethiopia","institution_ids":["https://openalex.org/I57092466"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5002684228"],"corresponding_institution_ids":["https://openalex.org/I57092466"],"apc_list":{"value":1050,"currency":"USD","value_usd":1050},"apc_paid":{"value":1050,"currency":"USD","value_usd":1050},"fwci":3.3156,"has_fulltext":true,"cited_by_count":89,"citation_normalized_percentile":{"value":0.93059812,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"2020","issue":null,"first_page":"1","last_page":"13"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10104","display_name":"Nanofluid Flow and Heat Transfer","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T10104","display_name":"Nanofluid Flow and Heat Transfer","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T11945","display_name":"Heat Transfer Mechanisms","score":0.998199999332428,"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":0.9952999949455261,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/boundary-layer","display_name":"Boundary layer","score":0.7419707775115967},{"id":"https://openalex.org/keywords/mass-transfer","display_name":"Mass transfer","score":0.6847968101501465},{"id":"https://openalex.org/keywords/nanofluid","display_name":"Nanofluid","score":0.6648890972137451},{"id":"https://openalex.org/keywords/homotopy-analysis-method","display_name":"Homotopy analysis method","score":0.6420505046844482},{"id":"https://openalex.org/keywords/dimensionless-quantity","display_name":"Dimensionless quantity","score":0.5800173282623291},{"id":"https://openalex.org/keywords/heat-transfer","display_name":"Heat transfer","score":0.5619511604309082},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.5480849146842957},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5342162251472473},{"id":"https://openalex.org/keywords/schmidt-number","display_name":"Schmidt number","score":0.5186304450035095},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.5050936341285706},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5027563571929932},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.4795674681663513},{"id":"https://openalex.org/keywords/boundary-layer-thickness","display_name":"Boundary layer thickness","score":0.4777373671531677},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.4625733494758606},{"id":"https://openalex.org/keywords/matrix-similarity","display_name":"Matrix similarity","score":0.45953086018562317},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4537626802921295},{"id":"https://openalex.org/keywords/thermal-radiation","display_name":"Thermal radiation","score":0.4256271421909332},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.30765920877456665},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.26384401321411133},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.23759698867797852},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1756344735622406},{"id":"https://openalex.org/keywords/homotopy","display_name":"Homotopy","score":0.1651138961315155},{"id":"https://openalex.org/keywords/prandtl-number","display_name":"Prandtl number","score":0.11877742409706116}],"concepts":[{"id":"https://openalex.org/C111603439","wikidata":"https://www.wikidata.org/wiki/Q752193","display_name":"Boundary layer","level":2,"score":0.7419707775115967},{"id":"https://openalex.org/C51038369","wikidata":"https://www.wikidata.org/wiki/Q909534","display_name":"Mass transfer","level":2,"score":0.6847968101501465},{"id":"https://openalex.org/C21946209","wikidata":"https://www.wikidata.org/wiki/Q1989679","display_name":"Nanofluid","level":3,"score":0.6648890972137451},{"id":"https://openalex.org/C173636693","wikidata":"https://www.wikidata.org/wiki/Q17030668","display_name":"Homotopy analysis method","level":3,"score":0.6420505046844482},{"id":"https://openalex.org/C24872484","wikidata":"https://www.wikidata.org/wiki/Q126818","display_name":"Dimensionless quantity","level":2,"score":0.5800173282623291},{"id":"https://openalex.org/C50517652","wikidata":"https://www.wikidata.org/wiki/Q179635","display_name":"Heat transfer","level":2,"score":0.5619511604309082},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.5480849146842957},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5342162251472473},{"id":"https://openalex.org/C155231867","wikidata":"https://www.wikidata.org/wiki/Q581997","display_name":"Schmidt number","level":4,"score":0.5186304450035095},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.5050936341285706},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5027563571929932},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.4795674681663513},{"id":"https://openalex.org/C151890184","wikidata":"https://www.wikidata.org/wiki/Q1660471","display_name":"Boundary layer thickness","level":3,"score":0.4777373671531677},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.4625733494758606},{"id":"https://openalex.org/C39739852","wikidata":"https://www.wikidata.org/wiki/Q254491","display_name":"Matrix similarity","level":3,"score":0.45953086018562317},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4537626802921295},{"id":"https://openalex.org/C89394759","wikidata":"https://www.wikidata.org/wiki/Q192593","display_name":"Thermal radiation","level":2,"score":0.4256271421909332},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.30765920877456665},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.26384401321411133},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.23759698867797852},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1756344735622406},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.1651138961315155},{"id":"https://openalex.org/C72687893","wikidata":"https://www.wikidata.org/wiki/Q815306","display_name":"Prandtl number","level":3,"score":0.11877742409706116},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2020/1890972","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/1890972","pdf_url":"https://downloads.hindawi.com/journals/jam/2020/1890972.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1589421626","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1589421626","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:1890972","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2020/1890972.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,"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:1fb024c1b4ab496db550bdc0e2b7c4fc","is_oa":true,"landing_page_url":"https://doaj.org/article/1fb024c1b4ab496db550bdc0e2b7c4fc","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":"Journal of Applied Mathematics, Vol 2020 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2020/1890972","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/1890972","pdf_url":"https://downloads.hindawi.com/journals/jam/2020/1890972.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3004022331.pdf","grobid_xml":"https://content.openalex.org/works/W3004022331.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W345975803","https://openalex.org/W1073553325","https://openalex.org/W1997184249","https://openalex.org/W2020876389","https://openalex.org/W2021285882","https://openalex.org/W2040487665","https://openalex.org/W2049973561","https://openalex.org/W2082195985","https://openalex.org/W2082727206","https://openalex.org/W2085748554","https://openalex.org/W2089279505","https://openalex.org/W2112901718","https://openalex.org/W2116021594","https://openalex.org/W2142418682","https://openalex.org/W2142880762","https://openalex.org/W2291202721","https://openalex.org/W2322506099","https://openalex.org/W2444443601","https://openalex.org/W2533772207","https://openalex.org/W2557355663","https://openalex.org/W2566795113","https://openalex.org/W2605120803","https://openalex.org/W2757853460","https://openalex.org/W2789550710","https://openalex.org/W2789738781","https://openalex.org/W2801871209","https://openalex.org/W2805663072","https://openalex.org/W2907105334","https://openalex.org/W2921552289","https://openalex.org/W2970910834","https://openalex.org/W3141380901"],"related_works":["https://openalex.org/W2083189133","https://openalex.org/W2064014453","https://openalex.org/W2046976628","https://openalex.org/W2337185740","https://openalex.org/W4212892837","https://openalex.org/W4387268984","https://openalex.org/W4288347615","https://openalex.org/W2896441896","https://openalex.org/W2001880666","https://openalex.org/W2997846528"],"abstract_inverted_index":{"In":[0],"this":[1,167],"paper,":[2],"analytic":[3],"approximation":[4],"to":[5,57,117],"the":[6,35,52,73,80,87,105,108,112,119,124,130,150,156,161],"heat":[7,157],"and":[8,42,93,111,126,179],"mass":[9,151],"transfer":[10,152,158],"characteristics":[11],"of":[12,17,37,68,86,107,145,166],"a":[13,21,27],"two-dimensional":[14],"time-dependent":[15],"flow":[16],"Williamson":[18,113],"nanofluids":[19],"over":[20],"permeable":[22],"stretching":[23,109],"sheet":[24,110],"embedded":[25],"in":[26,160,183],"porous":[28],"medium":[29],"has":[30],"been":[31],"presented":[32],"by":[33,60],"considering":[34],"effects":[36],"magnetic":[38,138],"field,":[39],"thermal":[40,141],"radiation,":[41,142],"chemical":[43,146],"reaction.":[44],"The":[45,65,84,164],"governing":[46],"partial":[47],"differential":[48,70],"equations":[49,71],"along":[50],"with":[51,72,171],"boundary":[53,75,95,162],"conditions":[54,76],"were":[55,169],"reduced":[56],"dimensionless":[58],"forms":[59],"using":[61],"suitable":[62],"similarity":[63],"transformation.":[64],"resulting":[66],"system":[67],"ordinary":[69],"corresponding":[74],"was":[77,115,133],"solved":[78],"via":[79],"homotopy":[81],"analysis":[82],"method.":[83],"results":[85,165],"study":[88,168],"show":[89],"that":[90,136],"velocity,":[91],"temperature,":[92],"concentration":[94,127],"layer":[96],"thicknesses":[97],"generally":[98],"decrease":[99],"as":[100],"we":[101],"move":[102],"away":[103],"from":[104],"surface":[106],"parameter":[114],"found":[116,135,182],"retard":[118],"velocity":[120],"but":[121,153],"it":[122],"enhances":[123],"temperature":[125],"profiles":[128],"near":[129],"surface.":[131],"It":[132],"also":[134],"increasing":[137],"field":[139],"strength,":[140],"or":[143],"rate":[144],"reaction":[147],"speeds":[148],"up":[149],"slows":[154],"down":[155],"rates":[159],"layer.":[163],"compared":[170],"some":[172,177],"previously":[173],"published":[174],"works":[175],"under":[176],"restrictions,":[178],"they":[180],"are":[181],"excellent":[184],"agreement.":[185]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":20},{"year":2024,"cited_by_count":22},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":18},{"year":2021,"cited_by_count":14},{"year":2020,"cited_by_count":3}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}