{"id":"https://openalex.org/W2802655396","doi":"https://doi.org/10.1016/j.rinp.2018.04.007","title":"A new Caputo time fractional model for heat transfer enhancement of water based graphene nanofluid: An application to solar energy","display_name":"A new Caputo time fractional model for heat transfer enhancement of water based graphene nanofluid: An application to solar energy","publication_year":2018,"publication_date":"2018-04-16","ids":{"openalex":"https://openalex.org/W2802655396","doi":"https://doi.org/10.1016/j.rinp.2018.04.007","mag":"2802655396"},"language":"en","primary_location":{"id":"doi:10.1016/j.rinp.2018.04.007","doi":"https://doi.org/10.1016/j.rinp.2018.04.007","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.rinp.2018.04.007","pdf_url":"https://www.sciencedirect.com/science/article/pii/S221137971830322X/pdf","source":{"id":"https://openalex.org/S2764941219","display_name":"Results in Physics","issn_l":"2211-3797","issn":["2211-3797"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","jufo-1","norway-1","oarl","poland-70"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Results in Physics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.sciencedirect.com/science/article/pii/S221137971830322X/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078938096","display_name":"Sidra Aman","orcid":"https://orcid.org/0000-0003-3506-8737","observed_orcids":["https://orcid.org/0000-0003-3506-8737"]},"institutions":[{"id":"https://openalex.org/I102913810","display_name":"Universiti Malaysia Pahang Al-Sultan Abdullah","ror":"https://ror.org/01704wp68","country_code":"MY","type":"education","lineage":["https://openalex.org/I102913810"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Sidra Aman","raw_affiliation_strings":["Applied and Industrial Mathematics Research Group, Faculty of Industrial Sciences & Technology, Universiti Malaysia Pahang, 26300 Kuantan, Pahang, Malaysia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Applied and Industrial Mathematics Research Group, Faculty of Industrial Sciences & Technology, Universiti Malaysia Pahang, 26300 Kuantan, Pahang, Malaysia","institution_ids":["https://openalex.org/I102913810"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011875207","display_name":"Ilyas Khan","orcid":"https://orcid.org/0000-0002-2056-9371","observed_orcids":["https://orcid.org/0000-0002-2056-9371","https://orcid.org/0009-0007-3847-3849"]},"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 City, Viet Nam"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Viet Nam","institution_ids":["https://openalex.org/I141445968"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063188745","display_name":"Zulkhibri Ismail","orcid":"https://orcid.org/0000-0002-9779-4753","observed_orcids":["https://orcid.org/0000-0002-9779-4753"]},"institutions":[{"id":"https://openalex.org/I102913810","display_name":"Universiti Malaysia Pahang Al-Sultan Abdullah","ror":"https://ror.org/01704wp68","country_code":"MY","type":"education","lineage":["https://openalex.org/I102913810"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Zulkhibri Ismail","raw_affiliation_strings":["Applied and Industrial Mathematics Research Group, Faculty of Industrial Sciences & Technology, Universiti Malaysia Pahang, 26300 Kuantan, Pahang, Malaysia"],"raw_orcid":"https://orcid.org/0000-0002-9779-4753","affiliations":[{"raw_affiliation_string":"Applied and Industrial Mathematics Research Group, Faculty of Industrial Sciences & Technology, Universiti Malaysia Pahang, 26300 Kuantan, Pahang, Malaysia","institution_ids":["https://openalex.org/I102913810"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045528126","display_name":"Mohd Zuki Salleh","orcid":"https://orcid.org/0000-0001-9732-9280","observed_orcids":["https://orcid.org/0000-0001-9732-9280"]},"institutions":[{"id":"https://openalex.org/I102913810","display_name":"Universiti Malaysia Pahang Al-Sultan Abdullah","ror":"https://ror.org/01704wp68","country_code":"MY","type":"education","lineage":["https://openalex.org/I102913810"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Mohd Zuki Salleh","raw_affiliation_strings":["Applied and Industrial Mathematics Research Group, Faculty of Industrial Sciences & Technology, Universiti Malaysia Pahang, 26300 Kuantan, Pahang, Malaysia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Applied and Industrial Mathematics Research Group, Faculty of Industrial Sciences & Technology, Universiti Malaysia Pahang, 26300 Kuantan, Pahang, Malaysia","institution_ids":["https://openalex.org/I102913810"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102708546","display_name":"Iskander Tlili","orcid":"https://orcid.org/0000-0003-3521-9902","observed_orcids":["https://orcid.org/0000-0003-3521-9902"]},"institutions":[{"id":"https://openalex.org/I4391012590","display_name":"Ecole Nationale d'Ing\u00e9nieurs de Monastir","ror":"https://ror.org/045yr8682","country_code":"TN","type":"education","lineage":["https://openalex.org/I166928557","https://openalex.org/I4391012590"]}],"countries":["TN"],"is_corresponding":false,"raw_author_name":"I. Tlili","raw_affiliation_strings":["Energy and Thermal Systems Laboratory, National Engineering School of Monastir, Street Ibn El Jazzar, 5019 Monastir, Tunisia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Energy and Thermal Systems Laboratory, National Engineering School of Monastir, Street Ibn El Jazzar, 5019 Monastir, Tunisia","institution_ids":["https://openalex.org/I4391012590"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5011875207"],"corresponding_institution_ids":["https://openalex.org/I141445968"],"apc_list":{"value":1920,"currency":"USD","value_usd":1920},"apc_paid":{"value":1920,"currency":"USD","value_usd":1920},"fwci":2.8839,"has_fulltext":true,"cited_by_count":64,"citation_normalized_percentile":{"value":0.91749536,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"9","issue":null,"first_page":"1352","last_page":"1362"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10104","display_name":"Nanofluid Flow and Heat Transfer","score":0.975600004196167,"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"}},"topics":[{"id":"https://openalex.org/T10104","display_name":"Nanofluid Flow and Heat Transfer","score":0.975600004196167,"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"}},{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.023099999874830246,"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/T13116","display_name":"Heat Transfer and Numerical Methods","score":0.00019999999494757503,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/caputo-time-fractional-derivative","display_name":"Caputo time-fractional derivative","score":0.9610000252723694},{"id":"https://openalex.org/keywords/graphene-nanofluids","display_name":"graphene nanofluids","score":0.9679999947547913},{"id":"https://openalex.org/keywords/water-based-nanofluid","display_name":"water-based nanofluid","score":0.8309999704360962},{"id":"https://openalex.org/keywords/poiseuille-flow","display_name":"Poiseuille flow","score":0.996999979019165},{"id":"https://openalex.org/keywords/vertical-channel","display_name":"vertical channel","score":0.9639999866485596},{"id":"https://openalex.org/keywords/heat-transfer-enhancement","display_name":"heat transfer enhancement","score":0.921999990940094},{"id":"https://openalex.org/keywords/solar-energy","display_name":"solar energy","score":0.7760000228881836},{"id":"https://openalex.org/keywords/solar-thermal-systems","display_name":"solar thermal systems","score":0.6930000185966492},{"id":"https://openalex.org/keywords/laplace-transform-solution","display_name":"Laplace transform solution","score":0.7889999747276306},{"id":"https://openalex.org/keywords/skin-friction","display_name":"skin friction","score":0.8019999861717224},{"id":"https://openalex.org/keywords/nusselt-number","display_name":"Nusselt number","score":0.9929999709129333},{"id":"https://openalex.org/keywords/sherwood-number","display_name":"Sherwood number","score":0.9580000042915344},{"id":"https://openalex.org/keywords/thermal-grashof-number","display_name":"thermal Grashof number","score":0.7889999747276306},{"id":"https://openalex.org/keywords/nanoparticle-volume-fraction","display_name":"nanoparticle volume fraction","score":0.8859999775886536}],"concepts":[{"id":"https://openalex.org/C21946209","wikidata":"https://www.wikidata.org/wiki/Q1989679","display_name":"Nanofluid","level":3,"score":0.9368941783905029},{"id":"https://openalex.org/C13027520","wikidata":"https://www.wikidata.org/wiki/Q868719","display_name":"Grashof number","level":5,"score":0.8916112184524536},{"id":"https://openalex.org/C130230704","wikidata":"https://www.wikidata.org/wiki/Q898280","display_name":"Nusselt number","level":4,"score":0.7541066408157349},{"id":"https://openalex.org/C119103248","wikidata":"https://www.wikidata.org/wiki/Q901815","display_name":"Sherwood number","level":5,"score":0.5524573922157288},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.5501813888549805},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.5379047989845276},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.521381676197052},{"id":"https://openalex.org/C50517652","wikidata":"https://www.wikidata.org/wiki/Q179635","display_name":"Heat transfer","level":2,"score":0.4810526669025421},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.41887450218200684},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.259802907705307},{"id":"https://openalex.org/C196558001","wikidata":"https://www.wikidata.org/wiki/Q190132","display_name":"Turbulence","level":2,"score":0.2286030650138855},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.1662306785583496},{"id":"https://openalex.org/C182748727","wikidata":"https://www.wikidata.org/wiki/Q178932","display_name":"Reynolds number","level":3,"score":0.09009373188018799},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06566858291625977}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1016/j.rinp.2018.04.007","doi":"https://doi.org/10.1016/j.rinp.2018.04.007","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.rinp.2018.04.007","pdf_url":"https://www.sciencedirect.com/science/article/pii/S221137971830322X/pdf","source":{"id":"https://openalex.org/S2764941219","display_name":"Results in Physics","issn_l":"2211-3797","issn":["2211-3797"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","jufo-1","norway-1","oarl","poland-70"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Results in Physics","raw_type":"journal-article"},{"id":"pmh:oai:umpir.ump.edu.my:22997","doi":null,"is_oa":false,"landing_page_url":"http://umpir.ump.edu.my/id/eprint/22997/1/A%20new%20Caputo%20time%20fractional%20model%20for%20heat%20transfer%20enhancement%20of%20water%20based%20graphene%20nanofluid.pdf","pdf_url":"http://umpir.ump.edu.my/id/eprint/22997/1/A%20new%20Caputo%20time%20fractional%20model%20for%20heat%20transfer%20enhancement%20of%20water%20based%20graphene%20nanofluid.pdf","source":{"id":"https://openalex.org/S4377196561","display_name":"UMP Institutional Repository (Universiti Malaysia Pahang)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I102913810","host_organization_name":"Universiti Malaysia Pahang Al-Sultan Abdullah","host_organization_lineage":["https://openalex.org/I102913810"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:doaj.org/article:6d5ab06d4af04edb83ebecf0710a21af","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/6d5ab06d4af04edb83ebecf0710a21af","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,"listed_in":[],"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":"Results in Physics, Vol 9, Iss , Pp 1352-1362 (2018)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1016/j.rinp.2018.04.007","doi":"https://doi.org/10.1016/j.rinp.2018.04.007","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.rinp.2018.04.007","pdf_url":"https://www.sciencedirect.com/science/article/pii/S221137971830322X/pdf","source":{"id":"https://openalex.org/S2764941219","display_name":"Results in Physics","issn_l":"2211-3797","issn":["2211-3797"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","jufo-1","norway-1","oarl","poland-70"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Results in Physics","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.8485000133514404,"display_name":"Affordable and clean energy"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2802655396.pdf","grobid_xml":"https://content.openalex.org/works/W2802655396.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W1778311522","https://openalex.org/W1787480861","https://openalex.org/W1963643888","https://openalex.org/W1966888642","https://openalex.org/W1968546020","https://openalex.org/W2009189725","https://openalex.org/W2028969088","https://openalex.org/W2043410175","https://openalex.org/W2060364303","https://openalex.org/W2074691424","https://openalex.org/W2076978869","https://openalex.org/W2088928122","https://openalex.org/W2103233901","https://openalex.org/W2217312365","https://openalex.org/W2269679455","https://openalex.org/W2323204530","https://openalex.org/W2343863349","https://openalex.org/W2344744673","https://openalex.org/W2484844318","https://openalex.org/W2503725947","https://openalex.org/W2521237537","https://openalex.org/W2533772207","https://openalex.org/W2548483393","https://openalex.org/W2557148388","https://openalex.org/W2561947911","https://openalex.org/W2582646942","https://openalex.org/W2593743719","https://openalex.org/W2601723592","https://openalex.org/W2606904263","https://openalex.org/W2622762229","https://openalex.org/W2693271895","https://openalex.org/W2740131176","https://openalex.org/W2750661028","https://openalex.org/W2765848108","https://openalex.org/W2979562792","https://openalex.org/W3107323053"],"related_works":["https://openalex.org/W2795748653","https://openalex.org/W4401495994","https://openalex.org/W2941482539","https://openalex.org/W4280523442","https://openalex.org/W4319083707","https://openalex.org/W3195326495","https://openalex.org/W4400908313","https://openalex.org/W4327703913","https://openalex.org/W4392956809","https://openalex.org/W2777767159"],"abstract_inverted_index":{"In":[0],"this":[1],"article":[2,46],"the":[3,45,108,139],"idea":[4],"of":[5,18,29,73,99,110,138,154],"Caputo":[6,164],"time":[7,165],"fractional":[8,166],"derivatives":[9],"is":[10,42,50,69,150],"applied":[11],"to":[12,54],"MHD":[13],"mixed":[14],"convection":[15],"Poiseuille":[16],"flow":[17],"nanofluids":[19,30,49],"with":[20,75,142,158],"graphene":[21],"nanoparticles":[22,120,160],"in":[23,31,44,58,65,71,97,146],"a":[24],"vertical":[25,140],"channel.":[26],"The":[27,67,87],"applications":[28],"solar":[32,38,56,62],"energy":[33,57,63],"are":[34,95,104,130],"argued":[35,43],"for":[36,90,124],"various":[37],"thermal":[39,59,113],"systems.":[40],"It":[41,149],"that":[47,152],"using":[48],"an":[51],"alternate":[52],"source":[53],"produce":[55],"engineering":[60],"and":[61,77,80,93,119,127,135,163],"devices":[64],"industries.":[66],"problem":[68],"modelled":[70],"terms":[72,98],"PDE\u2019s":[74],"initial":[76],"boundary":[78],"conditions":[79],"solved":[81],"analytically":[82],"via":[83],"Laplace":[84],"transform":[85],"method.":[86],"obtained":[88],"solutions":[89,103],"velocity,":[91],"temperature":[92],"concentration":[94],"expressed":[96],"Wright\u2019s":[100],"function.":[101],"These":[102],"significantly":[105],"controlled":[106],"by":[107],"variations":[109],"parameters":[111],"including":[112],"Grashof":[114,117],"number,":[115],"Solutal":[116],"number":[118],"volume":[121,161],"fraction.":[122],"Expressions":[123],"skin-friction,":[125],"Nusselt":[126],"Sherwood":[128],"numbers":[129],"also":[131],"determined":[132],"on":[133],"left":[134],"right":[136],"walls":[137],"channel":[141],"important":[143],"numerical":[144],"results":[145],"tabular":[147],"form.":[148],"found":[151],"rate":[153],"heat":[155],"transfer":[156],"increases":[157],"increasing":[159],"fraction":[162],"parameters.":[167]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":14},{"year":2018,"cited_by_count":5}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2018-05-17T00:00:00"}