{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T18:44:29Z","timestamp":1770489869070,"version":"3.49.0"},"reference-count":55,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2019,8,22]],"date-time":"2019-08-22T00:00:00Z","timestamp":1566432000000},"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>In the present work we consider a numerical solution for laminar, incompressible, and steady oblique stagnation point flow of     Cu \u2212 water     nanofluid over a stretching\/shrinking sheet with mass suction    S   . We make use of the Cattaneo\u2013Christov heat flux model to develop the equation of energy and investigate the qualities of surface heat transfer. The governing flow and energy equations are modified into the ordinary differential equations by similarity method for reasonable change. The subsequent ordinary differential equations are illuminated numerically through the function bvp4c in MATLAB. The impact of different flow parameters for example thermal relaxation parameter, suction parameter, stretching\/shrinking parameter, free stream parameter, and nanoparticles volume fraction on the skin friction coefficient, local Nusselt number, and streamlines are contemplated and exposed through graphs. It turns out that the lower branch solution for the skin friction coefficient becomes singular in shrinking area, although the upper branch solution is smooth in both stretching and shrinking domain. For oblique stagnation-point flow the streamlines pattern are not symmetric, and reversed phenomenon are detected close to the shrinking surface. Also, we observed that the free stream parameter changes the direction of the oncoming flow and controls the obliqueness of the flow. The existing work mostly includes heat and mass transfer as a mechanism for improving the heat transfer rate, which is the main objective of the authors.<\/jats:p>","DOI":"10.3390\/sym11091070","type":"journal-article","created":{"date-parts":[[2019,8,23]],"date-time":"2019-08-23T10:15:07Z","timestamp":1566555307000},"page":"1070","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":88,"title":["Oblique Stagnation Point Flow of Nanofluids over Stretching\/Shrinking Sheet with Cattaneo\u2013Christov Heat Flux Model: Existence of Dual Solution"],"prefix":"10.3390","volume":"11","author":[{"given":"Xiangling","family":"Li","sequence":"first","affiliation":[{"name":"Department of Mathematics and Physics, Hebei University of Architecture, Zhangjiakou 075024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Arif Ullah","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Gomal University, D.I. Khan 29050, Khyber Pakhtoonkhwa, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muhammad Riaz","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Quaid-i-Azam University, 45320, Islamabad 44000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sohail","family":"Nadeem","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Quaid-i-Azam University, 45320, Islamabad 44000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sami Ullah","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Gomal University, D.I. Khan 29050, Khyber Pakhtoonkhwa, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"33881","DOI":"10.1038\/srep33881","article-title":"Transport Phenomena of Water in Molecular Fluidic Channels","volume":"6","author":"Vo","year":"2016","journal-title":"Sci. Rep."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"186101","DOI":"10.1103\/PhysRevLett.96.186101","article-title":"Thermal conductance of hydrophilic and hydrophobic interfaces","volume":"96","author":"Ge","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"ref_3","first-page":"83","article-title":"Sulla conduzione del calore","volume":"3","author":"Cattaneo","year":"1948","journal-title":"Atti Sem. Mat. Fis. Univ. 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