{"id":"https://openalex.org/W2944127511","doi":"https://doi.org/10.3390/e21050484","title":"Numerical Simulation of Entropy Generation for Power-Law Liquid Flow over a Permeable Exponential Stretched Surface with Variable Heat Source and Heat Flux","display_name":"Numerical Simulation of Entropy Generation for Power-Law Liquid Flow over a Permeable Exponential Stretched Surface with Variable Heat Source and Heat Flux","publication_year":2019,"publication_date":"2019-05-10","ids":{"openalex":"https://openalex.org/W2944127511","doi":"https://doi.org/10.3390/e21050484","mag":"2944127511","pmid":"https://pubmed.ncbi.nlm.nih.gov/33267198"},"language":"en","primary_location":{"id":"doi:10.3390/e21050484","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21050484","pdf_url":"https://www.mdpi.com/1099-4300/21/5/484/pdf?version=1557748377","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"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":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/21/5/484/pdf?version=1557748377","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101493667","display_name":"Mohamed Abd El-Aziz","orcid":"https://orcid.org/0000-0002-2062-4801"},"institutions":[{"id":"https://openalex.org/I82952536","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30","country_code":"SA","type":"education","lineage":["https://openalex.org/I82952536"]},{"id":"https://openalex.org/I84058292","display_name":"Helwan University","ror":"https://ror.org/00h55v928","country_code":"EG","type":"education","lineage":["https://openalex.org/I84058292"]}],"countries":["EG","SA"],"is_corresponding":false,"raw_author_name":"Mohamed Abd El-Aziz","raw_affiliation_strings":["Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia","Department of Mathematics, Faculty of Science, Helwan University, Helwan-Cairo 11795, Egypt"],"raw_orcid":"https://orcid.org/0000-0002-2062-4801","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia","institution_ids":["https://openalex.org/I82952536"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Helwan University, Helwan-Cairo 11795, Egypt","institution_ids":["https://openalex.org/I84058292"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014356417","display_name":"S. Saleem","orcid":"https://orcid.org/0000-0001-6217-3626"},"institutions":[{"id":"https://openalex.org/I82952536","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30","country_code":"SA","type":"education","lineage":["https://openalex.org/I82952536"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Salman Saleem","raw_affiliation_strings":["Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia","institution_ids":["https://openalex.org/I82952536"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5014356417"],"corresponding_institution_ids":["https://openalex.org/I82952536"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.1956,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.7684953,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"21","issue":"5","first_page":"484","last_page":"484"},"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":0.9997000098228455,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9993000030517578,"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/bejan-number","display_name":"Bejan number","score":0.6225370764732361},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.6174610257148743},{"id":"https://openalex.org/keywords/heat-transfer","display_name":"Heat transfer","score":0.6110948324203491},{"id":"https://openalex.org/keywords/heat-flux","display_name":"Heat flux","score":0.5924991965293884},{"id":"https://openalex.org/keywords/second-law-of-thermodynamics","display_name":"Second law of thermodynamics","score":0.4679369330406189},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.4675551652908325},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4241897463798523},{"id":"https://openalex.org/keywords/boundary-layer","display_name":"Boundary layer","score":0.416839063167572},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.39536169171333313},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.3684494197368622},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.36439603567123413},{"id":"https://openalex.org/keywords/reynolds-number","display_name":"Reynolds number","score":0.3056793212890625},{"id":"https://openalex.org/keywords/nusselt-number","display_name":"Nusselt number","score":0.21776056289672852},{"id":"https://openalex.org/keywords/turbulence","display_name":"Turbulence","score":0.08594319224357605}],"concepts":[{"id":"https://openalex.org/C181587685","wikidata":"https://www.wikidata.org/wiki/Q3110607","display_name":"Bejan number","level":5,"score":0.6225370764732361},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.6174610257148743},{"id":"https://openalex.org/C50517652","wikidata":"https://www.wikidata.org/wiki/Q179635","display_name":"Heat transfer","level":2,"score":0.6110948324203491},{"id":"https://openalex.org/C159188206","wikidata":"https://www.wikidata.org/wiki/Q1478382","display_name":"Heat flux","level":3,"score":0.5924991965293884},{"id":"https://openalex.org/C119820323","wikidata":"https://www.wikidata.org/wiki/Q177045","display_name":"Second law of thermodynamics","level":2,"score":0.4679369330406189},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.4675551652908325},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4241897463798523},{"id":"https://openalex.org/C111603439","wikidata":"https://www.wikidata.org/wiki/Q752193","display_name":"Boundary layer","level":2,"score":0.416839063167572},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.39536169171333313},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.3684494197368622},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.36439603567123413},{"id":"https://openalex.org/C182748727","wikidata":"https://www.wikidata.org/wiki/Q178932","display_name":"Reynolds number","level":3,"score":0.3056793212890625},{"id":"https://openalex.org/C130230704","wikidata":"https://www.wikidata.org/wiki/Q898280","display_name":"Nusselt number","level":4,"score":0.21776056289672852},{"id":"https://openalex.org/C196558001","wikidata":"https://www.wikidata.org/wiki/Q190132","display_name":"Turbulence","level":2,"score":0.08594319224357605},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e21050484","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21050484","pdf_url":"https://www.mdpi.com/1099-4300/21/5/484/pdf?version=1557748377","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"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":"Entropy","raw_type":"journal-article"},{"id":"pmid:33267198","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33267198","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:fd2b506eca464ee4be57959bc8e491af","is_oa":true,"landing_page_url":"https://doaj.org/article/fd2b506eca464ee4be57959bc8e491af","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":"Entropy, Vol 21, Iss 5, p 484 (2019)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/21/5/484/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e21050484","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":"Entropy","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7514973","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7514973","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e21050484","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21050484","pdf_url":"https://www.mdpi.com/1099-4300/21/5/484/pdf?version=1557748377","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"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":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.4099999964237213,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G3964049701","display_name":null,"funder_award_id":"G.R.P-2/16/40","funder_id":"https://openalex.org/F4320324433","funder_display_name":"King Khalid University"}],"funders":[{"id":"https://openalex.org/F4320324433","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2944127511.pdf","grobid_xml":"https://content.openalex.org/works/W2944127511.grobid-xml"},"referenced_works_count":61,"referenced_works":["https://openalex.org/W964850195","https://openalex.org/W1564195631","https://openalex.org/W1976212278","https://openalex.org/W1986143726","https://openalex.org/W1989223909","https://openalex.org/W2003920229","https://openalex.org/W2014649105","https://openalex.org/W2027312055","https://openalex.org/W2060446666","https://openalex.org/W2083890211","https://openalex.org/W2103687859","https://openalex.org/W2123939989","https://openalex.org/W2134560715","https://openalex.org/W2143070725","https://openalex.org/W2218056472","https://openalex.org/W2294010957","https://openalex.org/W2343014201","https://openalex.org/W2344652846","https://openalex.org/W2375551041","https://openalex.org/W2466213629","https://openalex.org/W2514978871","https://openalex.org/W2529569242","https://openalex.org/W2533809238","https://openalex.org/W2614273431","https://openalex.org/W2744053961","https://openalex.org/W2757862847","https://openalex.org/W2762032872","https://openalex.org/W2776984336","https://openalex.org/W2786372830","https://openalex.org/W2788766711","https://openalex.org/W2794279397","https://openalex.org/W2797026897","https://openalex.org/W2799829124","https://openalex.org/W2801833873","https://openalex.org/W2805831905","https://openalex.org/W2808425278","https://openalex.org/W2808763969","https://openalex.org/W2883851468","https://openalex.org/W2885608991","https://openalex.org/W2887183711","https://openalex.org/W2888136678","https://openalex.org/W2889025531","https://openalex.org/W2894192740","https://openalex.org/W2896554150","https://openalex.org/W2896899986","https://openalex.org/W2899286234","https://openalex.org/W2899935461","https://openalex.org/W2899936364","https://openalex.org/W2902209864","https://openalex.org/W2902815782","https://openalex.org/W2903962466","https://openalex.org/W2907220473","https://openalex.org/W2913022015","https://openalex.org/W2914909524","https://openalex.org/W2920149415","https://openalex.org/W2920350101","https://openalex.org/W2922354301","https://openalex.org/W2939221416","https://openalex.org/W2942751648","https://openalex.org/W6679688048","https://openalex.org/W6755957337"],"related_works":["https://openalex.org/W4390616151","https://openalex.org/W4317619320","https://openalex.org/W4206397920","https://openalex.org/W3198467569","https://openalex.org/W4390764954","https://openalex.org/W3199714704","https://openalex.org/W2183776326","https://openalex.org/W4213123717","https://openalex.org/W2923484861","https://openalex.org/W2971445505"],"abstract_inverted_index":{"This":[0],"novel":[1],"work":[2],"explored":[3],"the":[4,19,30,33,47,51,71,76,79,89,98,105,121,126,140,150,157,163,180,189,194,207,211,215,220,231,235,239,249,258,264],"second":[5,151],"law":[6,152],"analysis":[7],"and":[8,54,75,109,116,142,155,160,169,193,218,263],"heat":[9,25,73,110,250,260],"transfer":[10,111,251],"in":[11,94,172],"a":[12],"magneto":[13],"non-Newtonian":[14],"power-law":[15,232],"fluid":[16,35,48],"model":[17],"with":[18,70,256],"presence":[20],"of":[21,32,46,78,100,153,201,214,230],"an":[22,39,198,228],"internal":[23,259],"non-uniform":[24],"source/sink.":[26],"In":[27],"this":[28,137],"investigation,":[29],"motion":[31],"studied":[34],"was":[36,167,204,225,246],"induced":[37],"by":[38,187],"exponentially":[40],"stretching":[41],"surface.":[42,81,241],"The":[43,65,175],"rheological":[44],"behavior":[45],"model,":[49],"including":[50],"shear":[52,55],"thinning":[53],"thickening":[56],"properties,":[57],"are":[58,145],"also":[59],"considered":[60],"as":[61],"special":[62],"case":[63],"studies.":[64],"physical":[66,165],"problem":[67,166],"developed":[68],"meaningfully":[69],"imposed":[72],"flux":[74],"porosity":[77],"stretched":[80,240],"Extensive":[82],"numerical":[83,138],"simulations":[84],"were":[85,132],"carried":[86],"out":[87],"for":[88],"present":[90,164],"boundary":[91,106],"layer":[92,107],"flow,":[93],"order":[95],"to":[96],"study":[97],"influence":[99],"each":[101],"control":[102],"parameter":[103],"on":[104,136],"flow":[108],"characteristics":[112],"via":[113],"various":[114],"tabular":[115],"graphical":[117],"illustrations.":[118],"By":[119,148],"employing":[120],"Shooting":[122],"Runge-Kutta-Fehlberg":[123],"Method":[124],"(SRKFM),":[125],"resulting":[127],"nonlinear":[128],"ordinary":[129],"differential":[130],"equations":[131],"solved":[133],"accurately.":[134],"Based":[135],"procedure,":[139],"velocity":[141],"temperature":[143],"fields":[144],"displayed":[146],"graphically.":[147],"applying":[149],"thermodynamics,":[154],"characterizing":[156],"entropy":[158,181,212,236],"generation":[159,182,213,237],"Bejan":[161,221],"number,":[162],"examined":[168],"discussed":[170],"thoroughly":[171],"different":[173],"situations.":[174],"attained":[176],"results":[177],"showed":[178],"that":[179,206,227,248],"can":[183,253],"be":[184,254],"improved":[185],"significantly":[186],"raising":[188],"magnetic":[190,265],"field":[191,266],"strength":[192],"group":[195],"parameter.":[196],"From":[197],"energetic":[199],"point":[200],"view,":[202],"it":[203,224,245],"found":[205],"Reynolds":[208],"number":[209],"boosts":[210],"fluidic":[216],"medium":[217],"reduces":[219],"number.":[222],"Also,":[223],"observed":[226],"amplification":[229],"index":[233],"diminished":[234],"near":[238],"As":[242],"main":[243],"results,":[244],"proven":[247],"rate":[252],"reduced":[255],"both":[257],"source":[261],"intensity":[262],"strength.":[267]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":4}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2019-05-16T00:00:00"}
