{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T01:59:13Z","timestamp":1775267953839,"version":"3.50.1"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"9","license":[{"start":{"date-parts":[[2018,11,12]],"date-time":"2018-11-12T00:00:00Z","timestamp":1541980800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"Ioan Pop","award":["the grant PN-III-P4-ID-PCE-2016-0036"],"award-info":[{"award-number":["the grant PN-III-P4-ID-PCE-2016-0036"]}]},{"name":"Ioan Pop","award":["UEFISCDI of Romanian Ministry of Sciences."],"award-info":[{"award-number":["UEFISCDI of Romanian Ministry of Sciences."]}]},{"name":"Romanian Ministry of Sciences","award":["grant PN-III-P4-ID-PCE-2016-0036"],"award-info":[{"award-number":["grant PN-III-P4-ID-PCE-2016-0036"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput & Applic"],"published-print":{"date-parts":[[2020,5]]},"DOI":"10.1007\/s00521-018-3770-0","type":"journal-article","created":{"date-parts":[[2018,11,12]],"date-time":"2018-11-12T05:51:09Z","timestamp":1542001869000},"page":"4575-4582","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Flow and heat transfer over a permeable biaxial stretching\/shrinking sheet in a nanofluid"],"prefix":"10.1007","volume":"32","author":[{"given":"Teodor","family":"Gro\u015fan","sequence":"first","affiliation":[]},{"given":"Ioan","family":"Pop","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,11,12]]},"reference":[{"key":"3770_CR1","volume-title":"Extrusion of plastics","author":"EG Fisher","year":"1967","unstructured":"Fisher EG (1967) Extrusion of plastics. Wiley, New York"},{"key":"3770_CR2","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1007\/s00245-013-9216-2","volume":"62","author":"M Sofonea","year":"2014","unstructured":"Sofonea M, P\u0103trulescu F, Farca\u015f A (2014) A viscoplastic contact problem with normal compliance, unilateral constraint and memory term. Appl Math Opt 62:175\u2013198","journal-title":"Appl Math Opt"},{"key":"3770_CR3","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1177\/1081286512440004","volume":"18","author":"M Sofonea","year":"2013","unstructured":"Sofonea M, P\u0103trulescu F (2013) Analysis of a history-dependent frictionless contact problem. Math Mech Solids 18:409\u2013430","journal-title":"Math Mech Solids"},{"key":"3770_CR4","doi-asserted-by":"publisher","first-page":"645","DOI":"10.1007\/BF01587695","volume":"21","author":"LJ Crane","year":"1970","unstructured":"Crane LJ (1970) Flow past a stretching plate. J Appl Math Phys (ZAMP) 21:645\u2013647","journal-title":"J Appl Math Phys (ZAMP)"},{"key":"3770_CR5","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1146\/annurev.fl.23.010191.001111","volume":"23","author":"CY Wang","year":"1991","unstructured":"Wang CY (1991) Exact solutions of the steady state Navier\u2013Stokes equations. Annu Rev Fluid Mech 23:159\u2013177","journal-title":"Annu Rev Fluid Mech"},{"key":"3770_CR6","doi-asserted-by":"publisher","first-page":"1915","DOI":"10.1063\/1.864868","volume":"27","author":"CY Wang","year":"1984","unstructured":"Wang CY (1984) The three-dimensional flow due to a stretching flat surface. Phys Fluids 27:1915\u20131917","journal-title":"Phys Fluids"},{"key":"3770_CR7","first-page":"084502-1","volume":"137","author":"CY Wang","year":"2015","unstructured":"Wang CY (2015) Uniform flow over a bi-axial stretching surface. J Fluids Eng 137:084502-1\u2013084502-3","journal-title":"J Fluids Eng"},{"key":"3770_CR8","doi-asserted-by":"publisher","first-page":"1996","DOI":"10.1016\/0017-9310(86)90020-7","volume":"29","author":"CDS Devi","year":"1986","unstructured":"Devi CDS, Takhar HS, Nath G (1986) Unsteady three-dimensional boundary layer flow due to a stretching surface. Int J Heat Mass Transf 29:1996\u20131999","journal-title":"Int J Heat Mass Transf"},{"key":"3770_CR9","doi-asserted-by":"publisher","first-page":"1165","DOI":"10.1115\/1.2723820","volume":"74","author":"T Hayat","year":"2007","unstructured":"Hayat T, Abbas Z, Sajid M (2007) On the analytic solution of magnetohydrodynamic flow of a second grade fluid over a shrinking sheet. ASME J Appl Mech 74:1165\u20131171","journal-title":"ASME J Appl Mech"},{"key":"3770_CR10","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1016\/j.rinp.2016.12.011","volume":"7","author":"G Kumaran","year":"2017","unstructured":"Kumaran G, Sandeep N, Ali ME (2017) Computational analysis of magnetohydrodynamic Casson and Maxwell flows over a stretching sheet with cross diffusion. Results Phys 7:147\u2013155","journal-title":"Results Phys"},{"key":"3770_CR11","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1090\/S0033-569X-06-01002-5","volume":"64","author":"M Miklav\u010di\u010d","year":"2006","unstructured":"Miklav\u010di\u010d M, Wang CY (2006) Viscous flow due to a shrinking sheet. Q Appl Math 64:283\u2013290","journal-title":"Q Appl Math"},{"key":"3770_CR12","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1016\/j.ijnonlinmec.2007.12.021","volume":"43","author":"CY Wang","year":"2008","unstructured":"Wang CY (2008) Stagnation flow towards a shrinking sheet. Int J Nonlinear Mech 43:377\u2013382","journal-title":"Int J Nonlinear Mech"},{"key":"3770_CR13","first-page":"0147031","volume":"26","author":"TG Fang","year":"2009","unstructured":"Fang TG, Zhang J, Yaho SS (2009) Viscous flow over an unsteady shrinking sheet with mass transfer. Chin Phys Lett 26:0147031\u20130147034","journal-title":"Chin Phys Lett"},{"key":"3770_CR14","doi-asserted-by":"publisher","first-page":"1440","DOI":"10.1016\/j.icheatmasstransfer.2010.08.002","volume":"37","author":"T Fan","year":"2010","unstructured":"Fan T, Xu H, Pop I (2010) Unsteady stagnation flow and heat transfer towards a shrinking sheet. Int Commun Heat Mass Transf 37:1440\u20131446","journal-title":"Int Commun Heat Mass Transf"},{"key":"3770_CR15","doi-asserted-by":"publisher","first-page":"308","DOI":"10.1016\/j.ijheatmasstransfer.2010.09.041","volume":"54","author":"K Bhattacharyya","year":"2011","unstructured":"Bhattacharyya K, Mukhopadhyay S, Layek GC (2011) Slip effects on boundary layer stagnation-point flow and heat transfer towards a shrinking sheet. Int J Heat Mass Transfer 54:308\u2013313","journal-title":"Int J Heat Mass Transfer"},{"key":"3770_CR16","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1016\/j.ijthermalsci.2013.08.005","volume":"75","author":"AM Rohni","year":"2014","unstructured":"Rohni AM, Ahmad S, Pop I (2014) Flow and heat transfer at a stagnation-point over an exponentially shrinking vertical sheet with suction. Int J Therm Sci 75:164\u2013170","journal-title":"Int J Therm Sci"},{"key":"3770_CR17","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1017\/S0022112065000034","volume":"21","author":"J Goldstein","year":"1965","unstructured":"Goldstein J (1965) On backward boundary layers and flow in converging passages. J Fluid Mech 21:33\u201345","journal-title":"J Fluid Mech"},{"key":"3770_CR18","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-10559-3","volume-title":"Nanoscience: the science of the small in physics, engineering, chemistry, biology and medicine","author":"H-E Shaefer","year":"2010","unstructured":"Shaefer H-E (2010) Nanoscience: the science of the small in physics, engineering, chemistry, biology and medicine. Springer, New York"},{"key":"3770_CR19","doi-asserted-by":"crossref","unstructured":"Manca, O, Jaluria, Y, Poulikakos D (2010) Heat transfer in nanofluids. Adv Mech Eng 2010. Article ID 380826","DOI":"10.1155\/2010\/380826"},{"key":"3770_CR20","doi-asserted-by":"crossref","unstructured":"Choi SUS (1995) Enhancing thermal conductivity of fluids with nanoparticles. In: Proceedings of the 1995 ASME international mechanical engineering congress and exposition, FED 231\/MD, vol 66, pp 99\u2013105","DOI":"10.1115\/IMECE1995-0926"},{"key":"3770_CR21","volume-title":"Nanofluids: science and technology","author":"SK Das","year":"2008","unstructured":"Das SK, Choi SUS, Yu W, Pradeep Y (2008) Nanofluids: science and technology. Wiley, New Jersey"},{"key":"3770_CR22","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-5541-7","volume-title":"Convection in porous media","author":"DA Nield","year":"2013","unstructured":"Nield DA, Bejan A (2013) Convection in porous media, 4th edn. Springer, New York","edition":"4"},{"key":"3770_CR23","doi-asserted-by":"publisher","DOI":"10.1201\/9781315367637","volume-title":"Convective flow and heat transfer from wavy surfaces: viscous fluids, porous media and nanofluids","author":"AM Shenoy","year":"2016","unstructured":"Shenoy AM, Sheremet M, Pop I (2016) Convective flow and heat transfer from wavy surfaces: viscous fluids, porous media and nanofluids. CRC Press, Taylor & Francis Group, New York"},{"key":"3770_CR24","doi-asserted-by":"publisher","first-page":"3187","DOI":"10.1016\/j.ijheatmasstransfer.2009.02.006","volume":"52","author":"S Kaka\u00e7","year":"2009","unstructured":"Kaka\u00e7 S, Pramuanjaroenkij A (2009) Review of convective heat transfer enhancement with nanofluids. Int J Heat Mass Transf 52:3187\u20133196","journal-title":"Int J Heat Mass Transf"},{"key":"3770_CR25","first-page":"1","volume":"2010","author":"KFV Wong","year":"2010","unstructured":"Wong KFV, Leon OD (2010) Applications of nanofluids: current and future. Adv Mech Eng 2010:1\u201311","journal-title":"Adv Mech Eng"},{"key":"3770_CR26","doi-asserted-by":"publisher","first-page":"582","DOI":"10.1016\/j.ijheatmasstransfer.2012.10.037","volume":"57","author":"O Mahian","year":"2013","unstructured":"Mahian O, Kianifar A, Kalogirou SA, Pop I, Wongwises S (2013) A review of the applications of nanofluids in solar energy. Int J Heat Mass Transf 57:582\u2013594","journal-title":"Int J Heat Mass Transf"},{"key":"3770_CR27","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1016\/j.jtice.2016.05.014","volume":"65","author":"M Sheikholeslami","year":"2016","unstructured":"Sheikholeslami M, Ganji DD (2016) Nanofluid convective heat transfer using semi analytical and numerical approaches: a review. J Taiwan Inst Chem Eng 65:43\u201377","journal-title":"J Taiwan Inst Chem Eng"},{"key":"3770_CR28","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1016\/j.ijheatmasstransfer.2017.03.118","volume":"111","author":"TG Myers","year":"2017","unstructured":"Myers TG, Ribera H, Cregan V (2017) Does mathematics contribute to the nanofluid debate? Int J Heat Mass Transfer 111:279\u2013288","journal-title":"Int J Heat Mass Transfer"},{"key":"3770_CR29","doi-asserted-by":"publisher","first-page":"240","DOI":"10.1115\/1.2150834","volume":"128","author":"J Buongiorno","year":"2006","unstructured":"Buongiorno J (2006) Convective transport in nanofluids. ASME J Heat Transf 128:240\u2013250","journal-title":"ASME J Heat Transf"},{"key":"3770_CR30","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1016\/j.ijthermalsci.2009.07.015","volume":"49","author":"AV Kuznetsov","year":"2010","unstructured":"Kuznetsov AV, Nield DA (2010) Natural convective boundary-layer flow of a nanofluid past a vertical plate. Int J Therm Sci 49:243\u2013247","journal-title":"Int J Therm Sci"},{"key":"3770_CR31","doi-asserted-by":"publisher","first-page":"682","DOI":"10.1016\/j.ijheatmasstransfer.2013.06.054","volume":"65","author":"AV Kuznetsov","year":"2013","unstructured":"Kuznetsov AV, Nield DA (2013) The Cheng\u2013Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by a nanofluid: a revised model. Int J Heat Mass Transf 65:682\u2013685","journal-title":"Int J Heat Mass Transf"},{"key":"3770_CR32","doi-asserted-by":"publisher","first-page":"5792","DOI":"10.1016\/j.ijheatmasstransfer.2009.07.024","volume":"52","author":"DA Nield","year":"2000","unstructured":"Nield DA, Kuznetsov AV (2000) The Cheng\u2013Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by a nanofluid. Int J Heat Mass Transf 52:5792\u20135795","journal-title":"Int J Heat Mass Transf"},{"key":"3770_CR33","doi-asserted-by":"publisher","first-page":"771","DOI":"10.1016\/j.ijheatfluidflow.2011.03.010","volume":"32","author":"DA Nield","year":"2011","unstructured":"Nield DA, Kuznetsov AV (2011) The onset of double-diffusive convection in a nanofluid layer. Int J Heat Fluid Flow 32:771\u2013776","journal-title":"Int J Heat Fluid Flow"},{"key":"3770_CR34","doi-asserted-by":"publisher","first-page":"102","DOI":"10.1016\/j.ijheatmasstransfer.2013.05.061","volume":"65","author":"NC Ro\u015fca","year":"2013","unstructured":"Ro\u015fca NC, Pop I (2013) Mixed convection stagnation point flow past a vertical flat plate with a second order slip: heat flux case. Int J Heat Mass Transf 65:102\u2013109","journal-title":"Int J Heat Mass Transf"},{"key":"3770_CR35","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1108\/HFF-10-2014-0315","volume":"26","author":"MM Rahman","year":"2016","unstructured":"Rahman MM, Grosan T, Pop I (2016) Oblique stagnation-point flow of a nanofluid past a shrinking sheet. Int J Numer Methods Heat Fluid Flow 26:189\u2013213","journal-title":"Int J Numer Methods Heat Fluid Flow"},{"key":"3770_CR36","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1007\/BF00052913","volume":"14","author":"JH Merkin","year":"1980","unstructured":"Merkin JH (1980) Mixed convection boundary layer flow on a vertical surface in a saturated porous medium. J Eng Math 14:301\u2013313","journal-title":"J Eng Math"},{"key":"3770_CR37","doi-asserted-by":"publisher","first-page":"730","DOI":"10.1016\/j.ijengsci.2006.04.005","volume":"44","author":"PD Weidman","year":"2006","unstructured":"Weidman PD, Kubitschek DG, Davis AMJ (2006) The effects of transpiration on self-similar boundary layer flow over moving surfaces. Int J Eng Sci 44:730\u2013737","journal-title":"Int J Eng Sci"},{"key":"3770_CR38","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1007\/s11242-008-9309-6","volume":"77","author":"SD Harris","year":"2009","unstructured":"Harris SD, Ingham DB, Pop I (2009) Mixed convection boundary-layer flow near the stagnation point on a vertical surface in a porous medium: Brinkman model with slip. Transp Porous Medium 77:267\u2013285","journal-title":"Transp Porous Medium"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-018-3770-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00521-018-3770-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-018-3770-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T01:19:25Z","timestamp":1775265565000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00521-018-3770-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,12]]},"references-count":38,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2020,5]]}},"alternative-id":["3770"],"URL":"https:\/\/doi.org\/10.1007\/s00521-018-3770-0","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,11,12]]},"assertion":[{"value":"24 March 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 September 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 November 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}