{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T07:31:32Z","timestamp":1771918292441,"version":"3.50.1"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"11","license":[{"start":{"date-parts":[[2017,3,10]],"date-time":"2017-03-10T00:00:00Z","timestamp":1489104000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput &amp; Applic"],"published-print":{"date-parts":[[2018,12]]},"DOI":"10.1007\/s00521-017-2931-x","type":"journal-article","created":{"date-parts":[[2017,3,10]],"date-time":"2017-03-10T05:25:05Z","timestamp":1489123505000},"page":"3431-3444","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Coupling of optimal variation of parameters method with Adomian\u2019s polynomials for nonlinear equations representing fluid flow in different geometries"],"prefix":"10.1007","volume":"30","author":[{"given":"Waseem","family":"Sikander","sequence":"first","affiliation":[]},{"given":"Naveed","family":"Ahmed","sequence":"additional","affiliation":[]},{"given":"Umar","family":"Khan","sequence":"additional","affiliation":[]},{"given":"Syed Tauseef","family":"Mohyud-Din","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,3,10]]},"reference":[{"key":"2931_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-016-2830-6","author":"A Majeed","year":"2016","unstructured":"Majeed A, Zeeshan A, Alamri SZ, Ellahi R (2016) Heat transfer analysis in ferromagnetic viscoelastic fluid flow over a stretching sheet with suction. Neural Comput Appl. doi: 10.1007\/s00521-016-2830-6","journal-title":"Neural Comput Appl"},{"issue":"5","key":"2931_CR2","doi-asserted-by":"crossref","first-page":"1433","DOI":"10.1108\/HFF-04-2015-0131","volume":"26","author":"R Ellahi","year":"2016","unstructured":"Ellahi R, Shivanian E, Abbasbandy S, Hayat T (2016) Numerical study of magnetohydrodynamics generalized Couette flow of Eyring\u2013Powell fluid with heat transfer and slip condition. Int J Numer Methods Heat Fluid Flow 26(5):1433\u20131445","journal-title":"Int J Numer Methods Heat Fluid Flow"},{"issue":"5","key":"2931_CR3","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1088\/0253-6102\/66\/5\/547","volume":"66","author":"K Maqbool","year":"2016","unstructured":"Maqbool K, Sohail A, Manzoor N, Ellahi R (2016) Hall effect on Falkner\u2013Skan boundary layer flow of FENE-P fluid over a stretching sheet. Commun Theor Phys 66(5):547\u2013554","journal-title":"Commun Theor Phys"},{"key":"2931_CR4","doi-asserted-by":"publisher","DOI":"10.1186\/s11671-015-1144-4","author":"G Aaiza","year":"2015","unstructured":"Aaiza G, Khan I, Shafie S (2015) Energy transfer in mixed convection MHD flow of nanofluid containing different shapes of nanoparticles in a channel filled with saturated porous medium. Nanoscale Res Lett. doi: 10.1186\/s11671-015-1144-4","journal-title":"Nanoscale Res Lett"},{"key":"2931_CR5","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-016-2688-7","author":"S Aman","year":"2016","unstructured":"Aman S, Khan I, Ismail Z, Salleh MZ (2016) Impacts of gold nanoparticles on MHD mixed convection Poiseuille flow of nanofluid passing through a porous medium in the presence of thermal radiation, thermal diffusion and chemical reaction. Neural Comput Appl. doi: 10.1007\/s00521-016-2688-7","journal-title":"Neural Comput Appl"},{"key":"2931_CR6","doi-asserted-by":"crossref","first-page":"1175","DOI":"10.1016\/j.molliq.2016.06.105","volume":"221","author":"A Khalid","year":"2016","unstructured":"Khalid A, Khan I, Shafie S (2016) Heat transfer in ferrofluid with cylindrical shape nanoparticles past a vertical plate with ramped wall temperature embedded in a porous medium. J Mol Liq 221:1175\u20131183","journal-title":"J Mol Liq"},{"key":"2931_CR7","doi-asserted-by":"crossref","first-page":"544","DOI":"10.1016\/j.ijheatmasstransfer.2016.06.056","volume":"120","author":"M Mamourian","year":"2016","unstructured":"Mamourian M, Shirvan KM, Ellahi R (2016) Optimization of mixed convection heat transfer with entropy generation in a wavy surface square lid-driven cavity by means of Taguchi approach. Int J Heat Mass Transf 120:544\u2013554","journal-title":"Int J Heat Mass Transf"},{"key":"2931_CR8","doi-asserted-by":"crossref","first-page":"446","DOI":"10.1016\/j.molliq.2016.07.052","volume":"222","author":"N Shehzad","year":"2016","unstructured":"Shehzad N, Zeeshan A, Ellahi R, Vafai K (2016) Convective heat transfer of nanofluid in a wavy channel: Buongiorno\u2019s mathematical model. J Mol Liq 222:446\u2013455","journal-title":"J Mol Liq"},{"key":"2931_CR9","doi-asserted-by":"crossref","first-page":"761","DOI":"10.1016\/j.applthermaleng.2016.08.116","volume":"109","author":"KM Shirvan","year":"2016","unstructured":"Shirvan KM, Ellahi R, Mirzakhanlari S, Mamourian M (2016) Enhancement of heat transfer and heat exchanger effectiveness in a double pipe heat exchanger filled with porous media: numerical simulation and sensitivity analysis of turbulent fluid flow. Appl Therm Eng 109:761\u2013774","journal-title":"Appl Therm Eng"},{"issue":"10","key":"2931_CR10","first-page":"1","volume":"11","author":"A Gul","year":"2015","unstructured":"Gul A, Khan I, Shafie S, Khalid A, Khan A (2015) Heat transfer in MHD mixed convection flow of a ferrofluid along a vertical channel. PLoS ONE 11(10):1\u201314","journal-title":"PLoS ONE"},{"key":"2931_CR11","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1016\/j.molliq.2016.06.098","volume":"222","author":"NAM Zin","year":"2016","unstructured":"Zin NAM, Khan I, Shafie S (2016) The impact silver nanoparticles on MHD free convection flow of Jeffrey fluid over an oscillating vertical plate embedded in a porous medium. J Mol Liq 222:138\u2013150","journal-title":"J Mol Liq"},{"key":"2931_CR12","doi-asserted-by":"crossref","first-page":"412","DOI":"10.1016\/j.molliq.2016.08.068","volume":"223","author":"F Ali","year":"2016","unstructured":"Ali F, Gohar M, Khan I (2016) MHD flow of water-based Brinkman type nanofluid over a vertical plate embedded in a porous medium with variable surface velocity, temperature and concentration. J Mol Liq 223:412\u2013419","journal-title":"J Mol Liq"},{"key":"2931_CR13","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1016\/j.ijheatmasstransfer.2016.10.130","volume":"107","author":"M Sheikholeslami","year":"2017","unstructured":"Sheikholeslami M, Rokni HB (2017) Nanofluid two phase model analysis in existence of induced magnetic field. Int J Heat Mass Transf 107:288\u2013299","journal-title":"Int J Heat Mass Transf"},{"key":"2931_CR14","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/j.molliq.2016.12.024","volume":"229","author":"M Sheikholeslami","year":"2017","unstructured":"Sheikholeslami M (2017) Magnetic field influence on nanofluid thermal radiation in a cavity with tilted elliptic inner cylinder. J Mol Liq 229:137\u2013147","journal-title":"J Mol Liq"},{"key":"2931_CR15","doi-asserted-by":"crossref","first-page":"1261","DOI":"10.1016\/j.ijheatmasstransfer.2016.10.107","volume":"106","author":"M Sheikholeslami","year":"2017","unstructured":"Sheikholeslami M, Shehzad S (2017) Magnetohydrodynamic nanofluid convection in a porous enclosure considering heat flux boundary condition. Int J Heat Mass Transf 106:1261\u20131269","journal-title":"Int J Heat Mass Transf"},{"key":"2931_CR16","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1016\/j.ijheatmasstransfer.2016.09.077","volume":"106","author":"M Sheikholeslami","year":"2017","unstructured":"Sheikholeslami M, Hayat T, Alsaedi A (2017) Numerical study for external magnetic source influence on water based nanofluid convective heat transfer. Int J Heat Mass Transf 106:745\u2013755","journal-title":"Int J Heat Mass Transf"},{"key":"2931_CR17","first-page":"272","volume":"298","author":"M Sheikholeslami","year":"2017","unstructured":"Sheikholeslami M, Vajravelu K (2017) Nanofluid flow and heat transfer in a cavity with variable magnetic field. Appl Math Comput 298:272\u2013282","journal-title":"Appl Math Comput"},{"key":"2931_CR18","doi-asserted-by":"crossref","first-page":"750","DOI":"10.1016\/j.molliq.2016.11.001","volume":"225","author":"M Sheikholeslami","year":"2017","unstructured":"Sheikholeslami M, Chamkha AJ (2017) Influence of Lorentz forces on nanofluid forced convection considering Marangoni convection. J Mol Liq 225:750\u2013757","journal-title":"J Mol Liq"},{"key":"2931_CR19","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1016\/j.cma.2016.12.028","volume":"317","author":"M Sheikholeslamia","year":"2017","unstructured":"Sheikholeslamia M, Rokni HB (2017) Numerical modeling of nanofluid natural convection in a semi annulus in existence of Lorentz force. Comput Methods Appl Mech Eng 317:419\u2013430","journal-title":"Comput Methods Appl Mech Eng"},{"key":"2931_CR20","doi-asserted-by":"crossref","first-page":"494","DOI":"10.1016\/j.physleta.2016.11.042","volume":"381","author":"M Sheikholeslami","year":"2017","unstructured":"Sheikholeslami M (2017) Numerical simulation of magnetic nanofluid natural convection in porous media. Phys Lett A 381:494\u2013503","journal-title":"Phys Lett A"},{"key":"2931_CR21","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1016\/j.molliq.2016.11.022","volume":"225","author":"M Sheikholeslami","year":"2017","unstructured":"Sheikholeslami M (2017) Influence of Lorentz forces on nanofluid flow in a porous cylinder considering Darcy model. J Mol Liq 225:903\u2013912","journal-title":"J Mol Liq"},{"key":"2931_CR22","first-page":"129","volume":"2014","author":"MS Kandelousi","year":"2014","unstructured":"Kandelousi MS (2014) Effect of spatially variable magnetic field on ferrofluid flow and heat transfer considering constant heat flux boundary condition. Eur Phys J Plus 2014:129\u2013248","journal-title":"Eur Phys J Plus"},{"issue":"10","key":"2931_CR23","doi-asserted-by":"crossref","first-page":"1186","DOI":"10.1080\/10407782.2015.1125709","volume":"69","author":"M Sheikholeslamia","year":"2016","unstructured":"Sheikholeslamia M, Chamkha AJ (2016) Flow and convective heat transfer of a ferro-nanofluid in a double-sided lid-driven cavity with a wavy wall in the presence of a variable magnetic field. Numer Heat Transf Part A 69(10):1186\u20131200","journal-title":"Numer Heat Transf Part A"},{"key":"2931_CR24","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1016\/j.ijheatmasstransfer.2016.01.059","volume":"96","author":"M Sheikholeslami","year":"2016","unstructured":"Sheikholeslami M, Hayat T, Alsaedi A (2016) MHD free convection of Al2O3\u2013water nanofluid considering thermal radiation: a numerical study. Int J Heat Mass Transf 96:513\u2013524","journal-title":"Int J Heat Mass Transf"},{"issue":"7","key":"2931_CR25","doi-asserted-by":"crossref","first-page":"781","DOI":"10.1080\/10407782.2015.1090819","volume":"69","author":"M Sheikholeslamia","year":"2016","unstructured":"Sheikholeslamia M, Chamkha AJ (2016) Electrohydrodynamic free convection heat transfer of a nanofluid in a semi-annulus enclosure with a sinusoidal wall. Numer Heat Transf Part A 69(7):781\u2013793","journal-title":"Numer Heat Transf Part A"},{"issue":"45","key":"2931_CR26","doi-asserted-by":"crossref","first-page":"3331","DOI":"10.1016\/j.physleta.2014.09.046","volume":"378","author":"MS Kandelousi","year":"2014","unstructured":"Kandelousi MS (2014) KKL correlation for simulation of nanofluid flow and heat transfer in a permeable channel. Phys Lett A 378(45):3331\u20133339","journal-title":"Phys Lett A"},{"key":"2931_CR27","doi-asserted-by":"crossref","first-page":"1623","DOI":"10.1007\/s40430-014-0242-z","volume":"37","author":"M Sheikholeslami","year":"2015","unstructured":"Sheikholeslami M (2015) Effect of uniform suction on nanofluid flow and heat transfer over a cylinder. J Braz Soc Mech Sci Eng 37:1623\u20131633","journal-title":"J Braz Soc Mech Sci Eng"},{"key":"2931_CR28","volume-title":"Differential equations with boundary-value problems","author":"DG Zill","year":"2009","unstructured":"Zill DG, Cullen MR (2009) Differential equations with boundary-value problems. Cengage Learning, Brooks\/Cole"},{"key":"2931_CR29","volume-title":"Elementary differential equations and boundary value problems","author":"WE Boyce","year":"2012","unstructured":"Boyce WE, DiPrima RC (2012) Elementary differential equations and boundary value problems. Wiley, New York"},{"key":"2931_CR30","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1016\/j.chaos.2004.02.011","volume":"22","author":"WX Ma","year":"2004","unstructured":"Ma WX, You Y (2004) Rational solutions of the Toda lattice equation in Casoratian form. Casoratian form. Chaos Solitons Fractals 22:395\u2013406","journal-title":"Chaos Solitons Fractals"},{"key":"2931_CR31","doi-asserted-by":"crossref","first-page":"1753","DOI":"10.1090\/S0002-9947-04-03726-2","volume":"357","author":"WX Ma","year":"2004","unstructured":"Ma WX, You Y (2004) Solving the Korteweg\u2013de Vries equation by its bilinear form: Wronskian solutions. Trans Am Math Soc 357:1753\u20131778","journal-title":"Trans Am Math Soc"},{"key":"2931_CR32","first-page":"622","volume":"11","author":"ST Mohyud-Din","year":"2010","unstructured":"Mohyud-Din ST, Noor MA, Waheed A (2010) Variation of parameter method for initial and boundary value problems. World Appl Sci J 11:622\u2013639","journal-title":"World Appl Sci J"},{"key":"2931_CR33","first-page":"1139","volume":"6","author":"ST Mohyud-Din","year":"2009","unstructured":"Mohyud-Din ST, Noor MA, Waheed A (2009) Modified variation of parameters method for second-order integro-differential equations and coupled systems. World Appl Sci J 6:1139\u20131146","journal-title":"World Appl Sci J"},{"key":"2931_CR34","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1016\/j.aej.2014.02.002","volume":"53","author":"U Khan","year":"2014","unstructured":"Khan U, Ahmed N, Khan SIU, Zaidi ZA, Yang XJ, Mohyud-Din ST (2014) On unsteady two-dimensional and axisymmetric squeezing flow between parallel plates. Alex Eng J 53:463\u2013468","journal-title":"Alex Eng J"},{"key":"2931_CR35","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/j.asej.2013.09.007","volume":"5","author":"U Khan","year":"2014","unstructured":"Khan U, Ahmed N, Zaidi ZA, Asadullah M, Mohyud-Din ST (2014) MHD squeezing flow between two infinite plates. Ain Shams Eng J 5:187\u2013192","journal-title":"Ain Shams Eng J"},{"key":"2931_CR36","first-page":"161","volume":"31","author":"Z Zaidi","year":"2013","unstructured":"Zaidi Z, Jan S, Ahmed N, Khan U, Mohyud-Din S (2013) Variation of parameters method for thin film flow of a third grade fluid down an inclined plane. Ital J Pure Appl Math 31:161\u2013168","journal-title":"Ital J Pure Appl Math"},{"key":"2931_CR37","first-page":"39","volume":"199","author":"J Ramos","year":"2008","unstructured":"Ramos J (2008) On the variational iteration method and other iterative techniques for nonlinear differential equations. Appl Math Comput 199:39\u201369","journal-title":"Appl Math Comput"},{"key":"2931_CR38","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-015-8289-6","volume-title":"Solving Frontier problems of physics: the decomposition method","author":"G Adomian","year":"1994","unstructured":"Adomian G (1994) Solving Frontier problems of physics: the decomposition method. Kluwer, Dordrecht"},{"key":"2931_CR39","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-00251-9","volume-title":"Partial differential equations and solitary waves theory","author":"A Wazwaz","year":"2009","unstructured":"Wazwaz A (2009) Partial differential equations and solitary waves theory. Springer, Berlin"},{"issue":"7","key":"2931_CR40","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1515\/IJNSNS.2010.11.7.495","volume":"11","author":"MM Hosseini","year":"2010","unstructured":"Hosseini MM, Mohyud-Din ST, Ghaneai H, Usman M (2010) Auxiliary parameter in the variational iteration method and its optimal determination. Int J Nonlinear Sci Numer Simul 11(7):495\u2013502","journal-title":"Int J Nonlinear Sci Numer Simul"},{"issue":"12","key":"2931_CR41","doi-asserted-by":"crossref","first-page":"1137","DOI":"10.1515\/zna-2010-1219","volume":"65","author":"SMM Hosseini","year":"2010","unstructured":"Hosseini SMM, Mohyud-Din ST, Ghaneai H (2010) Variational iteration method for nonlinear Age-Structured population models using auxiliary parameter. Zeitschrift fr Naturforschung-A 65(12):1137\u20131142","journal-title":"Zeitschrift fr Naturforschung-A"},{"issue":"5","key":"2931_CR42","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1016\/j.camwa.2014.11.007","volume":"69","author":"H Ghaneai","year":"2015","unstructured":"Ghaneai H, Hosseini MM (2015) Variational iteration method with an auxiliary parameter for solving wave-like and heat-like equations in large domains. Comput Math Appl 69(5):363\u2013373","journal-title":"Comput Math Appl"},{"key":"2931_CR43","doi-asserted-by":"crossref","first-page":"3434","DOI":"10.1016\/j.physleta.2008.02.006","volume":"372","author":"Q Esmaili","year":"2008","unstructured":"Esmaili Q, Ramiar A, Alizadeh E, Ganji D (2008) An approximation of the analytical solution of the Jeffery\u2013Hamel flow by decomposition method. Phys Lett A 372:3434\u20133439","journal-title":"Phys Lett A"},{"key":"2931_CR44","doi-asserted-by":"crossref","first-page":"1317","DOI":"10.1016\/j.chaos.2007.06.019","volume":"39","author":"M Sajid","year":"2009","unstructured":"Sajid M, Hayat T (2009) The application of homotopy analysis method for MHD viscous flow due to a shrinking sheet. Chaos Solitons Fractals 39:1317\u20131323","journal-title":"Chaos Solitons Fractals"},{"issue":"15","key":"2931_CR45","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1016\/j.cnsns.2009.03.034","volume":"15","author":"N Noor","year":"2010","unstructured":"Noor N, Kechil SA, Hashim I (2010) Simple non-perturbative solution for MHD viscous flow due to a shrinking sheet. Commun Nonlinear Sci Numer Simul 15(15):144\u2013148","journal-title":"Commun Nonlinear Sci Numer Simul"},{"issue":"4","key":"2931_CR46","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1515\/IJNSNS.2006.7.4.399","volume":"7","author":"PD Ariel","year":"2006","unstructured":"Ariel PD, Hayat T, Asghar S (2006) Homotopy perturbation method and axisymmetric flow over a stretching sheet. Int J Nonlinear Sci Numer Simul 7(4):399\u2013406","journal-title":"Int J Nonlinear Sci Numer Simul"},{"key":"2931_CR47","doi-asserted-by":"crossref","first-page":"2424","DOI":"10.1016\/j.apm.2006.09.008","volume":"31","author":"T Hayat","year":"2007","unstructured":"Hayat T, Shahzad F, Ayub M (2007) Analytical solution for the steady flow of the third grade fluid in a porous half space. Appl Math Model 31:2424\u20132432","journal-title":"Appl Math Model"},{"key":"2931_CR48","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/j.aml.2008.03.019","volume":"22","author":"V Marinca","year":"2009","unstructured":"Marinca V, Heri\u015fanu N, Bota C, Marinca B (2009) An optimal homotopy asymptotic method applied to the steady flow of a fourth-grade fluid past a porous plate. Appl Math Lett 22:245\u2013251","journal-title":"Appl Math Lett"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00521-017-2931-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-017-2931-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-017-2931-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,3]],"date-time":"2020-10-03T17:35:50Z","timestamp":1601746550000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00521-017-2931-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3,10]]},"references-count":48,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2018,12]]}},"alternative-id":["2931"],"URL":"https:\/\/doi.org\/10.1007\/s00521-017-2931-x","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,3,10]]}}}