{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T12:53:23Z","timestamp":1774356803291,"version":"3.50.1"},"reference-count":62,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2020,5,2]],"date-time":"2020-05-02T00:00:00Z","timestamp":1588377600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The physical problem under consideration is the boundary layer problem of an incompressible, laminar flow, taking place over a flat plate in the presence of a pressure gradient and radiation. For the mathematical formulation of the problem, the partial differential equations of continuity, energy, and momentum are taken into consideration with the boundary layer simplifications. Using the dimensionless Falkner\u2013Skan transformation, a nonlinear, nonhomogeneous, coupled system of partial differential equations (PDEs) is obtained, which is solved via the homotopy analysis method. The obtained analytical solution describes radiation and pressure gradient effects on the boundary layer flow. These analytical results reveal that the adverse or favorable pressure gradient influences the dimensionless velocity and the dimensionless temperature of the boundary layer. An adverse pressure gradient causes significant changes on the dimensionless wall shear parameter and the dimensionless wall heat-transfer parameter. Thermal radiation influences the thermal boundary layer. The analytical results are in very good agreement with the corresponding numerical ones obtained using a modification of the Keller\u2019s-box method.<\/jats:p>","DOI":"10.3390\/sym12050710","type":"journal-article","created":{"date-parts":[[2020,5,5]],"date-time":"2020-05-05T06:41:20Z","timestamp":1588660880000},"page":"710","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["Solving the Nonlinear Boundary Layer Flow Equations with Pressure Gradient and Radiation"],"prefix":"10.3390","volume":"12","author":[{"given":"Michalis A.","family":"Xenos","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece"}]},{"given":"Eugenia N.","family":"Petropoulou","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, Geotechnical Engineering Laboratory, University of Patras, 26504 Patras, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4695-0354","authenticated-orcid":false,"given":"Anastasios","family":"Siokis","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece"}]},{"given":"U. S.","family":"Mahabaleshwar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Davangere University, Shivagangotri, Davangere 577 007, India"}]}],"member":"1968","published-online":{"date-parts":[[2020,5,2]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"Grenzschichten in fl\u00fcssigkeiten mit kleiner reibung","volume":"56","author":"Blasius","year":"1908","journal-title":"Z. Angew. Math. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1098\/rspa.1938.0037","article-title":"On the solution of the laminar boundary layer equations","volume":"164","author":"Howarth","year":"1938","journal-title":"Proc. R. Soc. Lond. Ser. A"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Cebeci, T., and Bradshaw, P. (1984). Physical and Computational Aspects of Convective Heat Transfer, Springer.","DOI":"10.1007\/978-3-662-02411-9"},{"key":"ref_4","unstructured":"Howell, J.R., Siegel, R., and Meng\u00fc\u00e7, M.P. 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