{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,2]],"date-time":"2026-09-02T14:12:26Z","timestamp":1788358346638,"version":"build-2803163510"},"reference-count":49,"publisher":"American Chemical Society (ACS)","issue":"48","license":[{"start":{"date-parts":[[2020,11,25]],"date-time":"2020-11-25T00:00:00Z","timestamp":1606262400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/pubs.acs.org\/page\/policy\/authorchoice_termsofuse.html"}],"funder":[{"DOI":"10.13039\/na","name":"Government of the Russian Federation","doi-asserted-by":"publisher","award":["02.A03.21.0011"],"award-info":[{"award-number":["02.A03.21.0011"]}],"id":[{"id":"10.13039\/na","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/na","name":"Ministry of Science and Higher Education of the Russian Federation","doi-asserted-by":"publisher","award":["FENU-2020-0019"],"award-info":[{"award-number":["FENU-2020-0019"]}],"id":[{"id":"10.13039\/na","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,12,8]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>This investigation is conducted to study the integration of the artificial intelligence (AI) method with computational fluid dynamics (CFD). The case study is hydrodynamic and heat-transfer analyses of water flow in a metal foam tube under a constant wall heat flux (i.e., 55 kW\/m2). The adaptive network-based fuzzy inference system (ANFIS) is an AI method. A 3D CFD model is established in ANSYS-FLUENT software. The velocity of the fluid in the x-direction (Ux) is considered as an output of the ANFIS. The x, y, and z coordinates of the node\u2019s location are added to the ANFIS step-by-step to achieve the best intelligence. The number and type of membership functions (MFs) are changed in each step. The training process is done by the CFD results on the tube cross-sections at different lengths (i.e., z = 0.1, 0.2, 0.3, 0.4, 0.6, 0.7, 0.8, and 0.9), while all data (including z = 0.5) are selected for the testing process. The results showed that the ANFIS reaches the best intelligence with all three inputs, five MFs, and \u201cgbellmf\u201d-type MF. At this condition, the regression number is close to 1.<\/jats:p>","DOI":"10.1021\/acsomega.0c04497","type":"journal-article","created":{"date-parts":[[2020,11,25]],"date-time":"2020-11-25T12:37:26Z","timestamp":1606307846000},"page":"30826-30835","source":"Crossref","is-referenced-by-count":45,"title":["Computational Modeling of Transport in Porous Media\nUsing an Adaptive Network-Based Fuzzy Inference System"],"prefix":"10.1021","volume":"5","author":[{"given":"Meisam","family":"Babanezhad","sequence":"first","affiliation":[{"name":"Duy Tan University , , ,","place":["Da Nang, Vietnam, 550000"]},{"name":"Duy Tan University , , ,","place":["Da Nang, Vietnam, 550000"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Iman","family":"Behroyan","sequence":"additional","affiliation":[{"name":"Shahid Beheshti University , , ,","place":["Tehran, Iran, 1983969411"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6244-3446","authenticated-orcid":true,"given":"Ali Taghvaie","family":"Nakhjiri","sequence":"additional","affiliation":[{"name":"Islamic Azad University , , ,","place":["Tehran, Iran, 1477893855"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1536-1960","authenticated-orcid":true,"given":"Azam","family":"Marjani","sequence":"additional","affiliation":[{"name":"Ton Duc Thang University , , ,","place":["Ho Chi Minh City, Vietnam, 758307"]},{"name":"Ton Duc Thang University , , ,","place":["Ho Chi Minh City, Vietnam"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Saeed","family":"Shirazian","sequence":"additional","affiliation":[{"name":"University of Limerick , , ,","place":["Limerick, Ireland, V94 T9PX"]},{"name":"South Ural State University , , 76 Lenin prospekt , ,","place":["Chelyabinsk, Russia, 454080"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2020,11,25]]},"reference":[{"key":"2026090209122196300_cit1","doi-asserted-by":"publisher","first-page":"4899","DOI":"10.1016\/j.ijheatmasstransfer.2010.06.002","article-title":"Numerical study\nof conjugated heat transfer in metal foam filled double-pipe","volume":"53","author":"Du","year":"2010","journal-title":"Int. J. Heat Mass Transfer"},{"key":"2026090209122196300_cit2","doi-asserted-by":"publisher","first-page":"4857","DOI":"10.1016\/s0017-9310(02)00180-1","article-title":"Analysis of microchannel\nheat sinks for electronics cooling","volume":"45","author":"Zhao","year":"2002","journal-title":"Int. J.\nHeat Mass Transfer"},{"key":"2026090209122196300_cit3","doi-asserted-by":"publisher","first-page":"698","DOI":"10.1016\/j.combustflame.2005.08.038","article-title":"Numerical and experimental\nstudy of the conversion\nof methane to hydrogen in a porous media reactor","volume":"144","author":"Dhamrat","year":"2006","journal-title":"Combust. Flame"},{"key":"2026090209122196300_cit4","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1115\/1.1287793","article-title":"Forced convection\nin high porosity metal foams","volume":"122","author":"Calmidi","year":"2000","journal-title":"J. Heat Transfer"},{"key":"2026090209122196300_cit5","doi-asserted-by":"crossref","unstructured":"Zhao, C.; Kim, T.; Lu, T.; Hodson, H.\n          Modelling on thermal transport in\ncellular metal foams.  8th AIAA\/ASME Joint\nThermophysics and Heat Transfer Conference, 2002; p 3014.","DOI":"10.2514\/6.2002-3014"},{"key":"2026090209122196300_cit6","doi-asserted-by":"publisher","first-page":"309","DOI":"10.2514\/1.11780","article-title":"Thermal transport in high porosity\ncellular metal foams","volume":"18","author":"Zhao","year":"2004","journal-title":"J. Thermophys. Heat Transfer"},{"key":"2026090209122196300_cit7","unstructured":"Kim, T.; Fuller, A.; Hodson, H.; Lu, T.\n          An experimental study on thermal\ntransport in lightweight metal foams at high Reynolds numbers.  Proceedings of Compact Heat Exchangers; A Festschrift on\nthe 60th Birthday of Ramesh K. Shah, 2002; pp 227\u2013232."},{"key":"2026090209122196300_cit8","doi-asserted-by":"publisher","first-page":"121002","DOI":"10.1115\/1.3216036","article-title":"Flow boiling heat transfer in horizontal metal-foam\ntubes","volume":"131","author":"Zhao","year":"2009","journal-title":"J. Heat Transfer"},{"key":"2026090209122196300_cit9","doi-asserted-by":"publisher","first-page":"832","DOI":"10.1002\/adem.200900139","article-title":"Numerical Modelling\nof Flow Boiling Heat Transfer in\nHorizontal Metal-Foam Tubes","volume":"11","author":"Lu","year":"2009","journal-title":"Adv. Eng. Mater."},{"key":"2026090209122196300_cit10","doi-asserted-by":"publisher","first-page":"881","DOI":"10.1016\/j.ijthermalsci.2008.06.013","article-title":"Optimal\nconfiguration of discrete\nheat sources in a vertical duct under conjugate mixed convection using\nartificial neural networks","volume":"48","author":"Sudhakar","year":"2009","journal-title":"Int. J. Therm. Sci."},{"key":"2026090209122196300_cit11","doi-asserted-by":"publisher","first-page":"443","DOI":"10.1007\/s00231-008-0445-x","article-title":"The prediction of maximum temperature\nfor single chips\u2019 cooling using artificial neural networks","volume":"45","author":"Ozsunar","year":"2009","journal-title":"Heat Mass Transfer"},{"key":"2026090209122196300_cit12","doi-asserted-by":"publisher","first-page":"1265","DOI":"10.1016\/j.cnsns.2005.12.008","article-title":"Neural\nnetworks analysis of free laminar convection\nheat transfer in a partitioned enclosure","volume":"12","author":"Mahmoud","year":"2007","journal-title":"Commun.\nNonlinear Sci. Numer. Simulat."},{"key":"2026090209122196300_cit13","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0233850","article-title":"Prediction of thermal distribution and fluid flow in\nthe domain with multi-solid structures using Cubic-Interpolated Pseudo-Particle\nmodel","volume":"15","author":"Nguyen","year":"2020","journal-title":"PLoS One"},{"key":"2026090209122196300_cit14","doi-asserted-by":"publisher","first-page":"887","DOI":"10.1016\/j.icheatmasstransfer.2007.03.004","article-title":"Prediction\nof flow\nfields and temperature distributions due to natural convection in\na triangular enclosure using Adaptive-Network-Based Fuzzy Inference\nSystem (ANFIS) and Artificial Neural Network (ANN)","volume":"34","author":"Varol","year":"2007","journal-title":"Int. Commun. Heat Mass Transfer"},{"key":"2026090209122196300_cit15","doi-asserted-by":"publisher","first-page":"1989","DOI":"10.1016\/j.eswa.2007.08.073","article-title":"Analysis of adaptive-network-based\nfuzzy inference system (ANFIS) to estimate buoyancy-induced flow field\nin partially heated triangular enclosures","volume":"35","author":"Varol","year":"2008","journal-title":"Expert\nSyst. Appl."},{"key":"2026090209122196300_cit16","doi-asserted-by":"publisher","first-page":"3571","DOI":"10.1021\/acsomega.9b03911","article-title":"Prediction\nof Nanofluid Temperature Inside the Cavity by Integration of Grid\nPartition Clustering Categorization of a Learning Structure with the\nFuzzy System","volume":"5","author":"Nabipour","year":"2020","journal-title":"ACS Omega"},{"key":"2026090209122196300_cit17","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1007\/s12650-019-00614-0","article-title":"Flow visualization\nand analysis of thermal distribution for the nanofluid by the integration\nof fuzzy c-means clustering ANFIS structure and CFD methods","volume":"23","author":"Xu","year":"2020","journal-title":"J. Visualization"},{"key":"2026090209122196300_cit18","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1007\/s40815-019-00741-8","article-title":"Simulation\nof a bubble-column reactor by three-dimensional CFD: multidimension-and\nfunction-adaptive network-based fuzzy inference system","volume":"22","author":"Tian","year":"2020","journal-title":"Int. J. Fuzzy Syst."},{"key":"2026090209122196300_cit19","doi-asserted-by":"publisher","first-page":"13313","DOI":"10.1007\/s00521-019-04677-w","article-title":"Prediction\nof fluid pattern in a shear flow on intelligent neural nodes using\nANFIS and LBM","volume":"32","author":"Cao","year":"2020","journal-title":"Neural. Comput. Appl."},{"key":"2026090209122196300_cit20","doi-asserted-by":"publisher","first-page":"1676","DOI":"10.1002\/cjce.23378","article-title":"Liquid-phase\nchemical reactors: Development of 3D hybrid model based on CFD-adaptive\nnetwork-based fuzzy inference system","volume":"97","author":"Babanezhad","year":"2019","journal-title":"Can. J.\nChem. Eng."},{"key":"2026090209122196300_cit21","doi-asserted-by":"publisher","first-page":"2049","DOI":"10.1038\/s41598-020-58472-y","article-title":"Effect of graphene oxide on modifying\npolyethersulfone\nmembrane performance and its application in wastewater treatment","volume":"10","author":"Marjani","year":"2020","journal-title":"Sci. Rep."},{"key":"2026090209122196300_cit22","doi-asserted-by":"publisher","first-page":"20558","DOI":"10.1021\/acsomega.0c02784","article-title":"Developing\nIntelligent Algorithm as a Machine Learning Overview over the Big\nData Generated by Euler\u2013Euler Method To Simulate Bubble Column\nReactor Hydrodynamics","volume":"5","author":"Babanezhad","year":"2020","journal-title":"ACS Omega"},{"key":"2026090209122196300_cit23","doi-asserted-by":"publisher","first-page":"16284","DOI":"10.1021\/acsomega.0c02117","article-title":"Changes in\nthe Number of Membership\nFunctions for Predicting the Gas Volume Fraction in Two-Phase Flow\nUsing Grid Partition Clustering of the ANFIS Method","volume":"5","author":"Babanezhad","year":"2020","journal-title":"ACS Omega"},{"key":"2026090209122196300_cit24","first-page":"199","article-title":"Modeling and simulation\nof natural convection heat\ntransfer process in porous and non-porous media","volume":"2","author":"Nakhjiri","year":"2016","journal-title":"Appl. Res. J."},{"key":"2026090209122196300_cit25","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1080\/19942060.2020.1715842","article-title":"Prediction of flow characteristics\nin the bubble column reactor by the artificial pheromone-based communication\nof biological ants","volume":"14","author":"Shamshirband","year":"2020","journal-title":"Eng. Appl. Comput. Fluid\nMech."},{"key":"2026090209122196300_cit26","doi-asserted-by":"publisher","first-page":"16284","DOI":"10.1021\/acsomega.0c02117","article-title":"Changes in\nthe Number of Membership\nFunctions for Predicting the Gas Volume Fraction in Two-Phase Flow\nUsing Grid Partition Clustering of the ANFIS Method","volume":"5","author":"Babanezhad","year":"2020","journal-title":"ACS Omega"},{"key":"2026090209122196300_cit27","doi-asserted-by":"crossref","DOI":"10.1080\/19942060.2020.1715842","article-title":"Prediction of flow characteristics\nin the bubble column reactor by the artificial pheromone-based communication\nof biological ants","author":"Shamshirband","year":"2020"},{"key":"2026090209122196300_cit28","doi-asserted-by":"publisher","first-page":"102","DOI":"10.1016\/j.ijthermalsci.2011.09.004","article-title":"Adaptive network-based\nfuzzy inference\nsystem analysis of mixed convection in a two-sided lid-driven cavity\nfilled with a nanofluid","volume":"52","author":"Aminossadati","year":"2012","journal-title":"Int. J. Therm. Sci."},{"key":"2026090209122196300_cit29","first-page":"16284","article-title":"Fluid Velocity\nPrediction Inside Bubble Column Reactor Using ANFIS Algorithm Based\non CFD Input Data","volume":"5","author":"Nguyen","year":"2020","journal-title":"Arab. J. Sci. Eng."},{"key":"2026090209122196300_cit30","doi-asserted-by":"publisher","first-page":"17658","DOI":"10.1021\/acsomega.0c02173","article-title":"Thermal and\nFlow Visualization of a Square Heat Source in a Nanofluid Material\nwith a Cubic-Interpolated Pseudo-particle","volume":"5","author":"Nguyen","year":"2020","journal-title":"ACS\nOmega"},{"key":"2026090209122196300_cit31","doi-asserted-by":"publisher","first-page":"906","DOI":"10.1080\/10407782.2013.757154","article-title":"Adaptive-network-based\nfuzzy inference system analysis to predict the temperature and flow\nfields in a lid-driven cavity","volume":"63","author":"Azwadi","year":"2013","journal-title":"Numer. Heat Transfer,\nPart A"},{"key":"2026090209122196300_cit32","doi-asserted-by":"publisher","first-page":"85652","DOI":"10.1039\/c5ra11583c","article-title":"Prediction of multiphase\nflow pattern inside a 3D bubble column reactor using a combination\nof CFD and ANFIS","volume":"5","author":"Pourtousi","year":"2015","journal-title":"RSC Adv."},{"key":"2026090209122196300_cit33","doi-asserted-by":"publisher","first-page":"466","DOI":"10.1016\/j.powtec.2015.01.038","article-title":"A combination of computational fluid dynamics (CFD)\nand adaptive neuro-fuzzy system (ANFIS) for prediction of the bubble\ncolumn hydrodynamics","volume":"274","author":"Pourtousi","year":"2015","journal-title":"Powder Technol."},{"key":"2026090209122196300_cit34","doi-asserted-by":"publisher","first-page":"383","DOI":"10.5829\/idosi.ije.2013.26.04a.07","article-title":"Nusselt number estimation\nalong a wavy wall in an inclined lid-driven cavity using adaptive\nneuro-fuzzy inference system (anfis)","volume":"26","author":"Pashaie","year":"2012","journal-title":"Int. J.\nEng. Trans. A"},{"key":"2026090209122196300_cit35","doi-asserted-by":"publisher","first-page":"7487","DOI":"10.1007\/s13369-020-04611-6","article-title":"Fluid Velocity\nPrediction Inside Bubble Column Reactor Using ANFIS Algorithm Based\non CFD Input Data","volume":"45","author":"Nguyen","year":"2020","journal-title":"Arab. J. Sci. Eng."},{"key":"2026090209122196300_cit36","doi-asserted-by":"publisher","first-page":"055010","DOI":"10.1088\/0964-1726\/25\/5\/055010","article-title":"Influence of piston and magnetic\ncoils on the field-dependent\ndamping performance of a mixed-mode magnetorheological damper","volume":"25","author":"Zeinali","year":"2016","journal-title":"Smart Mater. Struct."},{"key":"2026090209122196300_cit37","doi-asserted-by":"publisher","first-page":"575","DOI":"10.1007\/s00231-012-1104-9","article-title":"Nero-fuzzy\nmodeling of the convection heat transfer coefficient for the nanofluid","volume":"49","author":"Salehi","year":"2013","journal-title":"Heat Mass Transfer"},{"key":"2026090209122196300_cit38","doi-asserted-by":"publisher","first-page":"1512","DOI":"10.1016\/j.ijthermalsci.2011.03.003","article-title":"Numerical simulation of laminar forced\nconvection in horizontal pipe partially or completely filled with\nporous material","volume":"50","author":"Teamah","year":"2011","journal-title":"Int. J.Therm. Sci."},{"key":"2026090209122196300_cit39","doi-asserted-by":"publisher","first-page":"1512","DOI":"10.1016\/j.ijthermalsci.2011.03.003","article-title":"Numerical simulation of laminar forced\nconvection in horizontal pipe partially or completely filled with\nporous material","volume":"50","author":"Teamah","year":"2011","journal-title":"Int. J.Therm. Sci."},{"key":"2026090209122196300_cit40","doi-asserted-by":"publisher","first-page":"2956","DOI":"10.1016\/j.ijheatmasstransfer.2009.02.024","article-title":"Numerical simulation\nof turbulent fluid flow and heat\ntransfer characteristics in heat exchangers fitted with porous media","volume":"52","author":"Yang","year":"2009","journal-title":"Int. J. Heat Mass Transfer"},{"key":"2026090209122196300_cit41","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1007\/s00231-017-2149-6","article-title":"Numerical\nsimulation of heat transfer\nin metal foams","volume":"54","author":"Gangapatnam","year":"2018","journal-title":"Heat Mass Transfer"},{"key":"2026090209122196300_cit42","volume-title":"Tables on the Thermophysical\nProperties of Liquids and Gases","author":"Vargaftik","year":"1975","edition":"2"},{"key":"2026090209122196300_cit43","doi-asserted-by":"publisher","first-page":"153107","DOI":"10.1063\/1.2093936","article-title":"Empirical correlation\nfinding the role of temperature and particle size for nanofluid (Al2O3)\nthermal conductivity enhancement","volume":"87","author":"Chon","year":"2005","journal-title":"Appl. Phys.\nLett."},{"key":"2026090209122196300_cit44","doi-asserted-by":"publisher","first-page":"2747","DOI":"10.1016\/j.apt.2017.07.028","article-title":"Thermal performance of nanofluids\nin metal foam tube: Thermal dispersion model incorporating heterogeneous\ndistribution of nanoparticles","volume":"28","author":"Ameri","year":"2017","journal-title":"Adv. Powder Technol."},{"key":"2026090209122196300_cit45","doi-asserted-by":"publisher","first-page":"754","DOI":"10.1016\/j.procs.2015.04.212","article-title":"Induction motor\ncontrol using PSO-ANFIS","volume":"48","author":"Mahapatra","year":"2015","journal-title":"Procedia Comput. Sci."},{"key":"2026090209122196300_cit46","doi-asserted-by":"publisher","first-page":"82460","DOI":"10.1039\/c5ra13609a","article-title":"Synergistic\ninteractions between\nPOSS and fumed silica and their effect on the properties of crosslinked\nPDMS nanocomposite membranes","volume":"5","author":"Rezakazemi","year":"2015","journal-title":"RSC Adv."},{"key":"2026090209122196300_cit47","doi-asserted-by":"publisher","first-page":"316","DOI":"10.1080\/00986445.2013.841149","article-title":"Performance\nof PVA\/NaA mixed matrix membrane for removal of water from ethylene\nglycol solutions by pervaporation","volume":"202","author":"Baheri","year":"2015","journal-title":"Chem. Eng.\nCommun."},{"key":"2026090209122196300_cit48","doi-asserted-by":"publisher","first-page":"665","DOI":"10.1109\/21.256541","article-title":"ANFIS:\nadaptive-network-based fuzzy inference system","volume":"23","author":"Jang","year":"1993","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"2026090209122196300_cit49","doi-asserted-by":"publisher","first-page":"116","DOI":"10.1109\/tsmc.1985.6313399","article-title":"Fuzzy identification\nof systems and its applications\nto modeling and control","volume":"SMC-15","author":"Takagi","year":"1985","journal-title":"IEEE Trans. Syst. Man\nCybern."}],"container-title":["ACS Omega"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.acs.org\/doi\/pdf\/10.1021\/acsomega.0c04497","content-type":"application\/pdf","content-version":"vor","intended-application":"unspecified"},{"URL":"https:\/\/pubs.acs.org\/acsodf\/article-pdf\/5\/48\/30826\/67758346\/acsomega.0c04497.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.acs.org\/acsodf\/article-pdf\/5\/48\/30826\/67758346\/acsomega.0c04497.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,2]],"date-time":"2026-09-02T13:12:28Z","timestamp":1788354748000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.acs.org\/acsodf\/article\/5\/48\/30826\/1372460\/Computational-Modeling-of-Transport-in-Porous"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,25]]},"references-count":49,"journal-issue":{"issue":"48","published-online":{"date-parts":[[2020,11,25]]},"published-print":{"date-parts":[[2020,12,8]]}},"URL":"https:\/\/doi.org\/10.1021\/acsomega.0c04497","relation":{},"ISSN":["2470-1343"],"issn-type":[{"value":"2470-1343","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11,25]]}}}