{"id":"https://openalex.org/W3019372673","doi":"https://doi.org/10.3390/sym12040663","title":"Symmetric MHD Channel Flow of Nonlocal Fractional Model of BTF Containing Hybrid Nanoparticles","display_name":"Symmetric MHD Channel Flow of Nonlocal Fractional Model of BTF Containing Hybrid Nanoparticles","publication_year":2020,"publication_date":"2020-04-22","ids":{"openalex":"https://openalex.org/W3019372673","doi":"https://doi.org/10.3390/sym12040663","mag":"3019372673"},"language":"en","primary_location":{"id":"doi:10.3390/sym12040663","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12040663","pdf_url":"https://www.mdpi.com/2073-8994/12/4/663/pdf?version=1587912154","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/2073-8994/12/4/663/pdf?version=1587912154","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075336738","display_name":"Muhammad Saqib","orcid":"https://orcid.org/0000-0003-2248-9903"},"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":"Muhammad Saqib","raw_affiliation_strings":["Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia JB, Johor Bahru 81310, Johor, Malaysia"],"raw_orcid":"https://orcid.org/0000-0003-2248-9903","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia JB, Johor Bahru 81310, Johor, Malaysia","institution_ids":["https://openalex.org/I4576418"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051905793","display_name":"Sharidan Shafie","orcid":"https://orcid.org/0000-0001-7795-2278"},"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":"Sharidan Shafie","raw_affiliation_strings":["Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia JB, Johor Bahru 81310, Johor, Malaysia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia JB, Johor Bahru 81310, Johor, Malaysia","institution_ids":["https://openalex.org/I4576418"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011875207","display_name":"Ilyas Khan","orcid":"https://orcid.org/0000-0002-2056-9371"},"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":true,"raw_author_name":"Ilyas Khan","raw_affiliation_strings":["Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh 72915, Vietnam"],"raw_orcid":"https://orcid.org/0000-0002-2056-9371","affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh 72915, Vietnam","institution_ids":["https://openalex.org/I141445968"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046314241","display_name":"Yu\u2010Ming Chu","orcid":"https://orcid.org/0000-0002-0944-2134"},"institutions":[{"id":"https://openalex.org/I3018263800","display_name":"Huzhou University","ror":"https://ror.org/04mvpxy20","country_code":"CN","type":"education","lineage":["https://openalex.org/I3018263800"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yu-Ming Chu","raw_affiliation_strings":["Department of Mathematics, Huzhou University, Huzhou 313000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Huzhou University, Huzhou 313000, China","institution_ids":["https://openalex.org/I3018263800"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057525661","display_name":"Kottakkaran Sooppy Nisar","orcid":"https://orcid.org/0000-0001-5769-4320"},"institutions":[{"id":"https://openalex.org/I142608572","display_name":"Prince Sattam Bin Abdulaziz University","ror":"https://ror.org/04jt46d36","country_code":"SA","type":"education","lineage":["https://openalex.org/I142608572"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Kottakkaran Sooppy Nisar","raw_affiliation_strings":["Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-5769-4320","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia","institution_ids":["https://openalex.org/I142608572"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5011875207"],"corresponding_institution_ids":["https://openalex.org/I141445968"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":3.2402,"has_fulltext":false,"cited_by_count":52,"citation_normalized_percentile":{"value":0.9287345,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":100},"biblio":{"volume":"12","issue":"4","first_page":"663","last_page":"663"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10104","display_name":"Nanofluid Flow and Heat Transfer","score":0.9998000264167786,"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":0.9998000264167786,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11945","display_name":"Heat Transfer Mechanisms","score":0.9860000014305115,"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/nanofluid","display_name":"Nanofluid","score":0.889417827129364},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5869268178939819},{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.5610116720199585},{"id":"https://openalex.org/keywords/magnetohydrodynamics","display_name":"Magnetohydrodynamics","score":0.5214178562164307},{"id":"https://openalex.org/keywords/magnetohydrodynamic-drive","display_name":"Magnetohydrodynamic drive","score":0.5039250254631042},{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.4883265197277069},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.4660447835922241},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.447654128074646},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4137882590293884},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3742380142211914},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.36231324076652527},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.350449800491333},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34744757413864136},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3347892761230469},{"id":"https://openalex.org/keywords/heat-transfer","display_name":"Heat transfer","score":0.18739333748817444},{"id":"https://openalex.org/keywords/magnetic-field","display_name":"Magnetic field","score":0.10692167282104492}],"concepts":[{"id":"https://openalex.org/C21946209","wikidata":"https://www.wikidata.org/wiki/Q1989679","display_name":"Nanofluid","level":3,"score":0.889417827129364},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5869268178939819},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.5610116720199585},{"id":"https://openalex.org/C31532427","wikidata":"https://www.wikidata.org/wiki/Q2549249","display_name":"Magnetohydrodynamics","level":3,"score":0.5214178562164307},{"id":"https://openalex.org/C42471609","wikidata":"https://www.wikidata.org/wiki/Q1779048","display_name":"Magnetohydrodynamic drive","level":4,"score":0.5039250254631042},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.4883265197277069},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.4660447835922241},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.447654128074646},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4137882590293884},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3742380142211914},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.36231324076652527},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.350449800491333},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34744757413864136},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3347892761230469},{"id":"https://openalex.org/C50517652","wikidata":"https://www.wikidata.org/wiki/Q179635","display_name":"Heat transfer","level":2,"score":0.18739333748817444},{"id":"https://openalex.org/C115260700","wikidata":"https://www.wikidata.org/wiki/Q11408","display_name":"Magnetic field","level":2,"score":0.10692167282104492},{"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:10.3390/sym12040663","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12040663","pdf_url":"https://www.mdpi.com/2073-8994/12/4/663/pdf?version=1587912154","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:af1c5f16f6df4c16b66296338bdb8eca","is_oa":true,"landing_page_url":"https://doaj.org/article/af1c5f16f6df4c16b66296338bdb8eca","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 12, Iss 4, p 663 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/12/4/663/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym12040663","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":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym12040663","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12040663","pdf_url":"https://www.mdpi.com/2073-8994/12/4/663/pdf?version=1587912154","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":[{"score":0.800000011920929,"display_name":"Clean water and sanitation","id":"https://metadata.un.org/sdg/6"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3019372673.pdf"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W1981816363","https://openalex.org/W1987609780","https://openalex.org/W2010364254","https://openalex.org/W2016213857","https://openalex.org/W2037437319","https://openalex.org/W2088328305","https://openalex.org/W2093717036","https://openalex.org/W2111271983","https://openalex.org/W2134837756","https://openalex.org/W2467491119","https://openalex.org/W2480455111","https://openalex.org/W2533772207","https://openalex.org/W2551589055","https://openalex.org/W2556784265","https://openalex.org/W2562074243","https://openalex.org/W2566390775","https://openalex.org/W2595719915","https://openalex.org/W2602194826","https://openalex.org/W2616507152","https://openalex.org/W2733185460","https://openalex.org/W2740131176","https://openalex.org/W2744892576","https://openalex.org/W2759824122","https://openalex.org/W2782888113","https://openalex.org/W2791757467","https://openalex.org/W2793781800","https://openalex.org/W2808479388","https://openalex.org/W2843070407","https://openalex.org/W2883208441","https://openalex.org/W2891670432","https://openalex.org/W2899089014","https://openalex.org/W2899742671","https://openalex.org/W2901210206","https://openalex.org/W2903004649","https://openalex.org/W2903991298","https://openalex.org/W2905272168","https://openalex.org/W2911383909","https://openalex.org/W2911924211","https://openalex.org/W2921552289","https://openalex.org/W2944583214","https://openalex.org/W2949800347","https://openalex.org/W2963641381","https://openalex.org/W2979723159","https://openalex.org/W2999857370","https://openalex.org/W3000256349","https://openalex.org/W4233449160","https://openalex.org/W6730176618","https://openalex.org/W6749452370"],"related_works":["https://openalex.org/W2912591334","https://openalex.org/W2929715323","https://openalex.org/W4317627639","https://openalex.org/W4313396013","https://openalex.org/W3024206168","https://openalex.org/W3005643231","https://openalex.org/W2806181810","https://openalex.org/W2064964639","https://openalex.org/W2087038011","https://openalex.org/W4386003862"],"abstract_inverted_index":{"A":[0],"nonlocal":[1,76,111],"fractional":[2,27,78,112,122,127,182,203],"model":[3,71,97,113],"of":[4,19,55,85,95,145,162,201],"Brinkman":[5],"type":[6],"fluid":[7,42],"(BTF)":[8],"containing":[9],"a":[10,47,62,66,75,82,115,190,194],"hybrid":[11,21,48],"nanostructure":[12],"was":[13,23,59,72,165,169],"examined.":[14],"The":[15,50,69,92,106,126],"magnetohydrodynamic":[16],"(MHD)":[17],"flow":[18,54],"the":[20,26,56,96,110,121,142,146,148,160,172,181,184,199,202,208],"nanofluid":[22,57],"studied":[24],"using":[25,74],"calculus":[28],"approach.":[29],"Hybridized":[30],"silver":[31],"(Ag)":[32],"and":[33,103,154,178,186,210],"Titanium":[34],"dioxide":[35],"(TiO2)":[36],"nanoparticles":[37],"were":[38,98,118,129,151,174],"dissolved":[39],"in":[40,61],"base":[41],"water":[43],"(H2O)":[44],"to":[45,100,131],"form":[46],"nanofluid.":[49],"MHD":[51],"free":[52],"convection":[53],"(Ag-TiO2-H2O)":[58],"considered":[60],"microchannel":[63],"(flow":[64],"with":[65,88],"bounded":[67],"domain).":[68],"BTF":[70],"generalized":[73],"Caputo-Fabrizio":[77],"operator":[79],"(CFFO)":[80],"without":[81,114],"singular":[83,116],"kernel":[84,117],"order":[86],"\u03b1":[87,136],"effective":[89],"thermophysical":[90],"properties.":[91],"governing":[93],"equations":[94],"subjected":[99],"physical":[101],"initial":[102],"boundary":[104],"conditions.":[105],"exact":[107],"solutions":[108,128,133,150,173],"for":[109,193],"developed":[119],"via":[120],"Laplace":[123],"transform":[124],"technique.":[125],"reduced":[130],"local":[132],"by":[134],"limiting":[135],"\u2192":[137],"1":[138],".":[139],"To":[140],"understand":[141],"rheological":[143],"behavior":[144],"fluid,":[147],"obtained":[149],"numerically":[152],"computed":[153],"plotted":[155],"on":[156],"various":[157],"graphs.":[158],"Finally,":[159],"influence":[161],"pertinent":[163],"parameters":[164],"physically":[166],"studied.":[167],"It":[168],"found":[170],"that":[171],"general,":[175],"reliable,":[176],"realistic":[177],"fixable.":[179],"For":[180],"parameter,":[183,204],"velocity":[185],"temperature":[187],"profiles":[188],"showed":[189],"decreasing":[191],"trend":[192],"constant":[195],"time.":[196],"By":[197],"setting":[198],"values":[200],"excellent":[205],"agreement":[206],"between":[207],"theoretical":[209],"experimental":[211],"results":[212],"could":[213],"be":[214],"attained.":[215]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":21},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":3}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}