{"id":"https://openalex.org/W2026184283","doi":"https://doi.org/10.1155/2011/408132","title":"New Exact Solutions for an Oldroyd\u2010B Fluid in a Porous Medium","display_name":"New Exact Solutions for an Oldroyd\u2010B Fluid in a Porous Medium","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2026184283","doi":"https://doi.org/10.1155/2011/408132","mag":"2026184283"},"language":"en","primary_location":{"id":"doi:10.1155/2011/408132","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/408132","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2011/408132.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"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":"International Journal of Mathematics and Mathematical Sciences","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/ijmms/2011/408132.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"I. Khan","orcid":null},"institutions":[{"id":"https://openalex.org/I4576418","display_name":"University of Technology Malaysia","ror":"https://ror.org/026w31v75","country_code":"MY","type":"education","lineage":["https://openalex.org/I4576418"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"I. Khan","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Technological University of Malaysia (UTM), 81310 Skudai, Malaysia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Technological University of Malaysia (UTM), 81310 Skudai, Malaysia","institution_ids":["https://openalex.org/I4576418"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018885296","display_name":"Muhammad Imran","orcid":"https://orcid.org/0000-0002-2363-5039"},"institutions":[{"id":"https://openalex.org/I4576418","display_name":"University of Technology Malaysia","ror":"https://ror.org/026w31v75","country_code":"MY","type":"education","lineage":["https://openalex.org/I4576418"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"M. Imran","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Technological University of Malaysia (UTM), 81310 Skudai, Malaysia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Technological University of Malaysia (UTM), 81310 Skudai, Malaysia","institution_ids":["https://openalex.org/I4576418"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058170294","display_name":"K. Fakhar","orcid":null},"institutions":[{"id":"https://openalex.org/I4576418","display_name":"University of Technology Malaysia","ror":"https://ror.org/026w31v75","country_code":"MY","type":"education","lineage":["https://openalex.org/I4576418"]}],"countries":["MY"],"is_corresponding":true,"raw_author_name":"K. Fakhar","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Technological University of Malaysia (UTM), 81310 Skudai, Malaysia","Ibnu Sina Institute for Fundamental Science Studies, Technological University of Malaysia (UTM), 81310 Skudai, Malaysia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Technological University of Malaysia (UTM), 81310 Skudai, Malaysia","institution_ids":["https://openalex.org/I4576418"]},{"raw_affiliation_string":"Ibnu Sina Institute for Fundamental Science Studies, Technological University of Malaysia (UTM), 81310 Skudai, Malaysia","institution_ids":["https://openalex.org/I4576418"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5058170294"],"corresponding_institution_ids":["https://openalex.org/I4576418"],"apc_list":{"value":1050,"currency":"USD","value_usd":1050},"apc_paid":{"value":1050,"currency":"USD","value_usd":1050},"fwci":0.626,"has_fulltext":true,"cited_by_count":21,"citation_normalized_percentile":{"value":0.69586383,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"2011","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10104","display_name":"Nanofluid Flow and Heat Transfer","score":0.9994999766349792,"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/T11379","display_name":"Rheology and Fluid Dynamics Studies","score":0.9983999729156494,"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/magnetohydrodynamic-drive","display_name":"Magnetohydrodynamic drive","score":0.7661033868789673},{"id":"https://openalex.org/keywords/magnetohydrodynamics","display_name":"Magnetohydrodynamics","score":0.7476351857185364},{"id":"https://openalex.org/keywords/porous-medium","display_name":"Porous medium","score":0.6750315427780151},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.6343225836753845},{"id":"https://openalex.org/keywords/newtonian-fluid","display_name":"Newtonian fluid","score":0.6236389875411987},{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.5909391641616821},{"id":"https://openalex.org/keywords/shear-stress","display_name":"Shear stress","score":0.5535118579864502},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.525734543800354},{"id":"https://openalex.org/keywords/non-newtonian-fluid","display_name":"Non-Newtonian fluid","score":0.48196884989738464},{"id":"https://openalex.org/keywords/porosity","display_name":"Porosity","score":0.4578183889389038},{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.4467525780200958},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4384470582008362},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.43312638998031616},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27961426973342896},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.27920258045196533},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2405591905117035},{"id":"https://openalex.org/keywords/magnetic-field","display_name":"Magnetic field","score":0.1709500551223755},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07528185844421387}],"concepts":[{"id":"https://openalex.org/C42471609","wikidata":"https://www.wikidata.org/wiki/Q1779048","display_name":"Magnetohydrodynamic drive","level":4,"score":0.7661033868789673},{"id":"https://openalex.org/C31532427","wikidata":"https://www.wikidata.org/wiki/Q2549249","display_name":"Magnetohydrodynamics","level":3,"score":0.7476351857185364},{"id":"https://openalex.org/C105569014","wikidata":"https://www.wikidata.org/wiki/Q3271208","display_name":"Porous medium","level":3,"score":0.6750315427780151},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.6343225836753845},{"id":"https://openalex.org/C294558","wikidata":"https://www.wikidata.org/wiki/Q366968","display_name":"Newtonian fluid","level":2,"score":0.6236389875411987},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.5909391641616821},{"id":"https://openalex.org/C21141959","wikidata":"https://www.wikidata.org/wiki/Q657936","display_name":"Shear stress","level":2,"score":0.5535118579864502},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.525734543800354},{"id":"https://openalex.org/C84403224","wikidata":"https://www.wikidata.org/wiki/Q860589","display_name":"Non-Newtonian fluid","level":2,"score":0.48196884989738464},{"id":"https://openalex.org/C6648577","wikidata":"https://www.wikidata.org/wiki/Q622669","display_name":"Porosity","level":2,"score":0.4578183889389038},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.4467525780200958},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4384470582008362},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.43312638998031616},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27961426973342896},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.27920258045196533},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2405591905117035},{"id":"https://openalex.org/C115260700","wikidata":"https://www.wikidata.org/wiki/Q11408","display_name":"Magnetic field","level":2,"score":0.1709500551223755},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07528185844421387},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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":3,"locations":[{"id":"doi:10.1155/2011/408132","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/408132","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2011/408132.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"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":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jijmms:408132","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/IJMMS/2011/408132.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:9dbee36b0f094f80840d9ffd5db2f58f","is_oa":true,"landing_page_url":"https://doaj.org/article/9dbee36b0f094f80840d9ffd5db2f58f","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":"International Journal of Mathematics and Mathematical Sciences, Vol 2011 (2011)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2011/408132","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/408132","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2011/408132.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"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":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2026184283.pdf","grobid_xml":"https://content.openalex.org/works/W2026184283.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1967376630","https://openalex.org/W1980015599","https://openalex.org/W1983539776","https://openalex.org/W1987189221","https://openalex.org/W1995844854","https://openalex.org/W2004497270","https://openalex.org/W2008716366","https://openalex.org/W2018252138","https://openalex.org/W2018294014","https://openalex.org/W2025325892","https://openalex.org/W2032718257","https://openalex.org/W2035282134","https://openalex.org/W2048186379","https://openalex.org/W2055006381","https://openalex.org/W2066796067","https://openalex.org/W2069473991","https://openalex.org/W2069861426","https://openalex.org/W2070093857","https://openalex.org/W2072442552","https://openalex.org/W2073171977","https://openalex.org/W2082384340","https://openalex.org/W2088702114","https://openalex.org/W2094744802","https://openalex.org/W2094823119","https://openalex.org/W2095105230","https://openalex.org/W2115779355","https://openalex.org/W2264437926","https://openalex.org/W6998884446"],"related_works":["https://openalex.org/W2055293444","https://openalex.org/W4377038149","https://openalex.org/W2950491349","https://openalex.org/W2267170039","https://openalex.org/W2119517210","https://openalex.org/W3180443531","https://openalex.org/W2412209297","https://openalex.org/W2051136817","https://openalex.org/W2315658369","https://openalex.org/W134010077"],"abstract_inverted_index":{"New":[0],"exact":[1],"solutions":[2,48,67],"for":[3,32,49,68,83],"unsteady":[4],"magnetohydrodynamic":[5],"(MHD)":[6],"flows":[7],"of":[8,62],"an":[9],"Oldroyd\u2010B":[10,16,51],"fluid":[11,17,52,71],"have":[12,26,38,96],"been":[13,27,39],"derived.":[14],"The":[15,29,46],"saturates":[18],"the":[19,59,63,84,91],"porous":[20,75],"space.":[21],"Two":[22],"different":[23],"flow":[24],"cases":[25,61],"considered.":[28],"analytical":[30],"expressions":[31],"velocity":[33,100],"and":[34,93,101],"shear":[35,102],"stress":[36,103],"fields":[37],"obtained":[40,64],"by":[41],"using":[42],"Laplace":[43],"transform":[44],"technique.":[45],"corresponding":[47],"hydrodynamic":[50],"in":[53],"a":[54,74],"nonporous":[55],"space":[56,76],"appeared":[57],"as":[58],"limiting":[60],"solutions.":[65],"Similar":[66],"MHD":[69,92],"Newtonian":[70],"passing":[72],"through":[73],"are":[77,81],"also":[78],"recovered.":[79],"Graphs":[80],"sketched":[82],"pertinent":[85],"parameters.":[86],"It":[87],"is":[88],"found":[89],"that":[90],"porosity":[94],"parameters":[95],"strong":[97],"influence":[98],"on":[99],"fields.":[104]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}