{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T15:44:29Z","timestamp":1767368669536,"version":"3.48.0"},"reference-count":38,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2025,12,13]],"date-time":"2025-12-13T00:00:00Z","timestamp":1765584000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100023674","name":"Deanship of Scientific Research at King Khalid University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100023674","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Research Project","award":["RGP.2\/51\/46"],"award-info":[{"award-number":["RGP.2\/51\/46"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,1,2]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>The implication of buoyancy reveals complex, non-linear behavior in numerous mass and thermal transfer processes. Quadratic thermal and solutal buoyancy effects become significant in high-temperature and high-concentration systems where density variations are strongly non-linear. Additionally, cross thermo-solutal buoyancy interactions play a crucial role in alloy solidification, geophysical flows, and oceanography, where the stability and density of the flow are influenced by the combined action of thermal and solutal gradients. This study aims to investigate quadratic thermal and solutal buoyancy effects in nanofluid convection through a vertical frustum of a cone, emphasizing the Soret phenomenon. The partial differential equations derived from the mathematical formulation using non-similarity variables were solved numerically. The governing non-similar partial differential equations are solved numerically using the bivariate pseudo-spectral local linearization method, which combines quasi-linearization and spectral collocation for enhanced accuracy. The results are compared to asymptotic series solutions in order to evaluate the reliability of the proposed methodology. Graphical results illustrate how quadratic and mixed buoyancy parameters influence momentum, heat, and mass transfer characteristics. The findings provide new insights into the physics of non-linear buoyancy-driven nanofluid convection in conical geometries relevant to thermal, geophysical, and chemical systems.<\/jats:p>","DOI":"10.1093\/jcde\/qwaf133","type":"journal-article","created":{"date-parts":[[2025,12,13]],"date-time":"2025-12-13T12:44:07Z","timestamp":1765629847000},"page":"217-238","source":"Crossref","is-referenced-by-count":0,"title":["Quadratic convection and quadratic solutal convection on the nanofluid flow over a vertical frustum of a cone under Soret impact: An implementation of a spectral computational approach"],"prefix":"10.1093","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5681-0051","authenticated-orcid":false,"given":"Zheng","family":"Mingliang","sequence":"first","affiliation":[{"name":"School of Mechanical and Electrical Engineering, Huainan Normal University , Huainan 232038 ,","place":["China"]},{"name":"School of Intelligent Manufacturing, Zhejiang Guangsha Vocational and Technical University of Construction , Jinhua 322100 ,","place":["China"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4882-512X","authenticated-orcid":false,"given":"Rosana","family":"Manea","sequence":"additional","affiliation":[{"name":"Transilvania University of Brasov Faculty of Medicine, Department of Medical and Surgical Specialties, , Brasov 500036 ,","place":["Romania"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3219-7579","authenticated-orcid":false,"given":"Muhammad M","family":"Bhatti","sequence":"additional","affiliation":[{"name":"College of Mathematics and Systems Science, Shandong University of Science and Technology , Qingdao 266590 ,","place":["China"]},{"name":"Material Science Innovation and Modelling (MaSIM) Research Focus Area, North-West University (Mafikeng Campus) , Private Bag X2046, Mmabatho 2735 ,","place":["South Africa"]},{"name":"College of Science, Korea University Department of Physics, , 145 Anam-ro, Seongbuk-gu, Seoul 02841 ,","place":["Republic of Korea"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6217-3626","authenticated-orcid":false,"given":"Salman","family":"Saleem","sequence":"additional","affiliation":[{"name":"College of Science, King Khalid University Department of Mathematics, , Abha 61413 ,","place":["Saudi Arabia"]},{"name":"Center for Artificial Intelligence (CAI), King Khalid University , Abha 61421 ,","place":["Saudi Arabia"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2161-0639","authenticated-orcid":false,"given":"Hakan F","family":"\u00d6ztop","sequence":"additional","affiliation":[{"name":"Technology Faculty, Firat University Department of Mechanical Engineering, , 23119 Elazig ,","place":["Turkey"]},{"name":"China Medical University Hospital, China Medical University Department of Medical Research, , Taichung 40447 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