{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T13:32:12Z","timestamp":1778851932660,"version":"3.51.4"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2014,11,14]],"date-time":"2014-11-14T00:00:00Z","timestamp":1415923200000},"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":["Numer Algor"],"published-print":{"date-parts":[[2015,9]]},"DOI":"10.1007\/s11075-014-9934-9","type":"journal-article","created":{"date-parts":[[2014,11,14]],"date-time":"2014-11-14T16:52:35Z","timestamp":1415983955000},"page":"43-59","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":45,"title":["Series solutions of non-similarity boundary layer flows of nano-fluids over stretching surfaces"],"prefix":"10.1007","volume":"70","author":[{"given":"U.","family":"Farooq","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"T.","family":"Hayat","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.","family":"Alsaedi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S. J.","family":"Liao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2014,11,14]]},"reference":[{"key":"9934_CR1","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1007\/BF01587695","volume":"21","author":"LJ Crane","year":"1970","unstructured":"Crane, L.J.: Flow past a stretching sheet. Z. Angew. Math. Phys. (ZAMP) 21, 645\u2013647 (1970)","journal-title":"Z. Angew. Math. Phys. (ZAMP)"},{"key":"9934_CR2","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1016\/j.ijheatmasstransfer.2013.03.004","volume":"62","author":"MM Rashidi","year":"2013","unstructured":"Rashidi, M.M., Abelman, S., Mehr, N.F.: Entropy generation in a steady MHD flow due to a rotating porous disk in a nanofluid. Int. J. Heat Mass Transfer 62, 515\u2013525 (2013)","journal-title":"Int. J. Heat Mass Transfer"},{"key":"9934_CR3","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/j.compfluid.2012.01.009","volume":"70","author":"M Turkyilmazoglu","year":"2012","unstructured":"Turkyilmazoglu, M.: Dual and triple solutions for MHD slip flow of non-Newtonian fluid over a shrinking surface. Comput. Fluids 70, 53\u201358 (2012)","journal-title":"Comput. Fluids"},{"key":"9934_CR4","doi-asserted-by":"crossref","first-page":"123","DOI":"10.3329\/jname.v9i2.12541","volume":"9","author":"S Mukhopadhyay","year":"2012","unstructured":"Mukhopadhyay, S., Gorla, S.R.: Unsteady MHD boundary layer flow of an upper convected Maxwell fluid past a stretching sheet with first order constructive\/destructive chemical reaction. J. Naval Architecture Eng. 9, 123\u2013133 (2012)","journal-title":"J. Naval Architecture Eng."},{"key":"9934_CR5","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/j.nucengdes.2011.11.005","volume":"243","author":"T Hayat","year":"2012","unstructured":"Hayat, T., Shehzad, S.A., Qasim, M., Obaidat, S.: Radiative flow of Jeffery fluid in a porous medium with power law heat flux and heat source. Nucl. Eng. Des. 243, 15\u201319 (2012)","journal-title":"Nucl. Eng. Des."},{"key":"9934_CR6","doi-asserted-by":"crossref","first-page":"2144","DOI":"10.1016\/j.cnsns.2008.06.013","volume":"14","author":"SJ Liao","year":"2009","unstructured":"Liao, S.J.: A general approach to get series solution of non-similarity boundary-layer flows. J. Commun. Nonlinear Sci. Nummer. Simulat. 14, 2144\u20132159 (2009)","journal-title":"J. Commun. Nonlinear Sci. Nummer. Simulat."},{"key":"9934_CR7","doi-asserted-by":"crossref","unstructured":"You, X.Ch., Xu, H., Liao, S.J.: On the nonsimilarity boundary-layer flows of second-order fluids over a stretching sheet, ASME. J. Applied Mechanics 77 (2010). doi: 10.1115\/1.3173764","DOI":"10.1115\/1.3173764"},{"issue":"2","key":"9934_CR8","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1007\/s11433-010-0124-z","volume":"53","author":"N Kousar","year":"2010","unstructured":"Kousar, N., Liao, S.J.: Series solution of non-similarity natural convection boundary-layer flows over permeable vertical surface. Sci. China Ser. G Phys. Mech. Astron. 53(2), 360\u2013368 (2010)","journal-title":"Sci. China Ser. G Phys. Mech. Astron."},{"issue":"10","key":"9934_CR9","doi-asserted-by":"crossref","first-page":"104703","DOI":"10.1088\/0256-307X\/29\/10\/104703","volume":"29","author":"ME Nakhehi","year":"2012","unstructured":"Nakhehi, M.E., Nobari, M.R.H., Tabrizi, H.B.: Non-similarity thermal boundary layer flow over a stretching flat plate. Chinese Phys. Letters 29(10), 104703 (2012)","journal-title":"Chinese Phys. Letters"},{"key":"9934_CR10","doi-asserted-by":"crossref","first-page":"127","DOI":"10.4236\/am.2013.48A018","volume":"4","author":"N Kousar","year":"2013","unstructured":"Kousar, N., Mahmood, R.: Series solution of non-similarity boundary-layer flow in porous medium. J. Applied Mathematics 4, 127\u2013136 (2013)","journal-title":"J. Applied Mathematics"},{"key":"9934_CR11","doi-asserted-by":"crossref","first-page":"1326","DOI":"10.1016\/j.ijthermalsci.2011.02.019","volume":"50","author":"OD Makinde","year":"2011","unstructured":"Makinde, O.D., Aziz, A.: Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition. Int. J. Thermal Sci. 50, 1326\u20131332 (2011)","journal-title":"Int. J. Thermal Sci."},{"key":"9934_CR12","doi-asserted-by":"crossref","first-page":"4210","DOI":"10.1016\/j.cnsns.2012.03.008","volume":"17","author":"A Alsaedi","year":"2012","unstructured":"Alsaedi, A., Awais, M., Hayat, T.: Effects of heat generation\/absorption on stagnation point flow nanofluid over a surface with convective boundary conditions. Comm. Nonlinear Sci. Num. Simulat. 17, 4210\u20134223 (2012)","journal-title":"Comm. Nonlinear Sci. Num. Simulat."},{"key":"9934_CR13","doi-asserted-by":"crossref","first-page":"7552","DOI":"10.1016\/j.ijheatmasstransfer.2012.07.054","volume":"55","author":"M Narayana","year":"2012","unstructured":"Narayana, M., Sibanda, P.: Laminar flow of a nanofluid over an unsteady streching sheet. Int. J. Heat Mass Transfer 55, 7552\u20137560 (2012)","journal-title":"Int. J. Heat Mass Transfer"},{"key":"9934_CR14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ijheatmasstransfer.2012.08.034","volume":"56","author":"W Ibrahim","year":"2013","unstructured":"Ibrahim, W., Shankarand, B., Nandepponavar, M.M.: MHD stagnation point flow and heat transfer due to nanofluid towards a stretching sheet. Int. J. Heat Mass Transfer 56, 1\u20139 (2013)","journal-title":"Int. J. Heat Mass Transfer"},{"key":"9934_CR15","doi-asserted-by":"crossref","first-page":"13","DOI":"10.5383\/ijtee.04.01.003","volume":"4","author":"MM Rashidi","year":"2012","unstructured":"Rashidi, M.M., Anwar, O., Asadi, M., Rastegari, M.T.: DTM-Pade modelling of natural convective boundary layer flow of a nanofluid past a vertical surface. Int. J. Thermal Enviorment Eng 4, 13\u201324 (2012)","journal-title":"Int. J. Thermal Enviorment Eng"},{"key":"9934_CR16","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/j.ijheatmasstransfer.2012.12.009","volume":"59","author":"M Turkyilmazoglu","year":"2013","unstructured":"Turkyilmazoglu, M., Pop, I.: Heat and mass transfer of unsteady natural convection flow of some nanofluids past a vertical infinite flat plate with radiation effect. Int. J. Heat Mass Transfer 59, 167\u2013171 (2013)","journal-title":"Int. J. Heat Mass Transfer"},{"key":"9934_CR17","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1016\/j.molliq.2013.11.002","volume":"190","author":"M Sheikholeslami","year":"2014","unstructured":"Sheikholeslami, M., Hatam, M., Ganji, D.D.: Heat flux boundary condition for nanofluid filled enclosure in presence of magnetic field. J. Molecular Liquids 190, 112\u2013120 (2014)","journal-title":"J. Molecular Liquids"},{"key":"9934_CR18","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1007\/s00231-012-1087-6","volume":"49","author":"M Turkyilmazoglu","year":"2013","unstructured":"Turkyilmazoglu, M., Ashorynejad, H.R., Sheikholeslami, M., Pop, I., Ganji, D.D.: Nanofluid flow and heat transfer due to a stretching cylinder in the presence of magnetic field. Int. J. Heat Mass Transfer 49, 427\u2013436 (2013)","journal-title":"Int. J. Heat Mass Transfer"},{"key":"9934_CR19","doi-asserted-by":"crossref","first-page":"031704","DOI":"10.1115\/1.4025730","volume":"136","author":"M Turkyilmazoglu","year":"2013","unstructured":"Turkyilmazoglu, M.: Unsteady convection flow of some nanofluids past a moving vertical flat plate with heat transfer, ASME. J. Heat Transfer 136, 031704 (2013)","journal-title":"J. Heat Transfer"},{"key":"9934_CR20","doi-asserted-by":"crossref","first-page":"2477","DOI":"10.1016\/j.ijheatmasstransfer.2010.01.032","volume":"53","author":"WA Khan","year":"2010","unstructured":"Khan, W.A.: Boundary-layer flow of a nanofluid past a stretching sheet. Int. J. Heat Mass Transfer 53, 2477\u20132483 (2010)","journal-title":"Int. J. Heat Mass Transfer"},{"key":"9934_CR21","doi-asserted-by":"crossref","first-page":"5792","DOI":"10.1016\/j.ijheatmasstransfer.2009.07.024","volume":"52","author":"DA Nield","year":"2009","unstructured":"Nield, D.A., Kuznetsov, A.V.: The Cheng-Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by a nanofluid. Int. J. Heat Mass Transfer 52, 5792\u20135795 (2009)","journal-title":"Int. J. Heat Mass Transfer"},{"key":"9934_CR22","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.ijthermalsci.2009.07.015","volume":"49","author":"AV Kuznetsov","year":"2010","unstructured":"Kuznetsov, A.V., Nield, D.A.: Natural convective boundary-layer flow of a nanofluid past a vertical plate. Int. J. Therm. Sci. 49, 243\u2013247 (2010)","journal-title":"Int. J. Therm. Sci."},{"key":"9934_CR23","doi-asserted-by":"crossref","first-page":"1494","DOI":"10.1016\/j.cnsns.2009.06.004","volume":"15","author":"RAV Gorder","year":"2010","unstructured":"Gorder, R.A.V., Sweet, E., Vajravelu, K.: Nano boundary layers over stretching surfaces. Commun. Nonlinear Sci. Numm. Simulat. 15, 1494\u20131500 (2010)","journal-title":"Commun. Nonlinear Sci. Numm. Simulat."},{"key":"9934_CR24","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1016\/S0020-7462(96)00101-1","volume":"32","author":"SJ Liao","year":"1997","unstructured":"Liao, S.J.: A kind of approximate solution technique which does not depend upon small parameters (II)- An application in fluid mechanics. Int. J. Nonlinear Mech. 32, 815\u2013822 (1997)","journal-title":"Int. J. Nonlinear Mech."},{"key":"9934_CR25","first-page":"2315","volume":"15","author":"SJ Liao","year":"2010","unstructured":"Liao, S.J.: An optimal homotopy analysis approach for strongly nonlinear differential equations. Commun. Nonlinear Sci. Numm. Simulat. 15, 2315\u20132332 (2010)","journal-title":"Commun. Nonlinear Sci. Numm. Simulat."},{"key":"9934_CR26","doi-asserted-by":"crossref","first-page":"1163","DOI":"10.1016\/j.cnsns.2011.08.003","volume":"17","author":"M Ghoreishi","year":"2012","unstructured":"Ghoreishi, M., Ismail, A.I.B.Md., Alomari, A.k., Bataineh, A.S: The comparison between homotopy analysis method and optimal homotopy asymtotic method for nonlinear age structured population models. Commun. Nonlinear Sci. Numm. Simulat. 17, 1163\u20131177 (2012)","journal-title":"Commun. Nonlinear Sci. Numm. Simulat."},{"key":"9934_CR27","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1007\/s11075-012-9554-1","volume":"61","author":"RAV Gorder","year":"2012","unstructured":"Gorder, R.A.V.: Control of error in the homotopy analysis of semi-linear elliptic boundary value problems. Numer. Algoritm. 61, 613\u2013629 (2012)","journal-title":"Numer. Algoritm."},{"key":"9934_CR28","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1007\/s11075-012-9587-5","volume":"62","author":"F Tao","year":"2013","unstructured":"Tao, F., You, X.Ch.: Optimal homotopy analysis method for nonlinear differential equations in the boundary layer. Numer. Algoritm. 62, 337\u2013354 (2013)","journal-title":"Numer. Algoritm."},{"key":"9934_CR29","doi-asserted-by":"crossref","first-page":"2026","DOI":"10.1016\/j.cnsns.2009.08.014","volume":"15","author":"N Zhao","year":"2010","unstructured":"Zhao, N., Wang, C.: A one-step optimal homotopy analysis method for nonlinear differential equations. Commun. Nonlinear Sci. Numm. Simulat. 15, 2026\u20132036 (2010)","journal-title":"Commun. Nonlinear Sci. Numm. Simulat."},{"key":"9934_CR30","first-page":"843","volume":"66","author":"K Mallory","year":"2013","unstructured":"Mallory, K., Gorder, R.A.V.: Optimal homotopy analysis and control of error for solution to the non-local Whitham equation. Numer. Algoritm. 66, 843\u2013863 (2013)","journal-title":"Numer. Algoritm."},{"key":"9934_CR31","doi-asserted-by":"crossref","DOI":"10.1201\/9780203491164","volume-title":"Beyond perturbation: Introduction to the homotopy analysis method","author":"SJ Liao","year":"2003","unstructured":"Liao, S.J.: Beyond perturbation: Introduction to the homotopy analysis method. Chapman and Hall\/CRC Press, Boca Raton (2003)"},{"key":"9934_CR32","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-25132-0","volume-title":"Homotopy analysis method in non-linear differential equations","author":"SJ Liao","year":"2012","unstructured":"Liao, S.J.: Homotopy analysis method in non-linear differential equations. Higher education press, Beijing (2012)"},{"key":"9934_CR33","doi-asserted-by":"crossref","unstructured":"Farooq, U., Liang, L.Z.: Non-linear heat transfer in a two layer flow with nanofluids by OHAM, ASME. J. Heat Mass Transfer 2(136) (2014). doi: 10.1115\/1.4025432","DOI":"10.1115\/1.4025432"},{"key":"9934_CR34","doi-asserted-by":"crossref","first-page":"983","DOI":"10.1016\/j.cnsns.2008.04.013","volume":"14","author":"SJ Liao","year":"2009","unstructured":"Liao, S.J.: Notes on the homotopy analysis method- Some defnitions and theorems. J. Commun. Nonlinear Sci. Nummer. Simulat. 14, 983\u2013997 (2009)","journal-title":"J. Commun. Nonlinear Sci. Nummer. Simulat."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-014-9934-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-014-9934-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-014-9934-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,17]],"date-time":"2019-08-17T10:46:23Z","timestamp":1566038783000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-014-9934-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,11,14]]},"references-count":34,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2015,9]]}},"alternative-id":["9934"],"URL":"https:\/\/doi.org\/10.1007\/s11075-014-9934-9","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,11,14]]}}}