{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T21:40:38Z","timestamp":1775943638364,"version":"3.50.1"},"reference-count":56,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,5,24]],"date-time":"2023-05-24T00:00:00Z","timestamp":1684886400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Higher Education Malaysia, Fundamental Research Grant Scheme","award":["FRGS\/1\/2021\/STG06\/UPNM\/02\/1"],"award-info":[{"award-number":["FRGS\/1\/2021\/STG06\/UPNM\/02\/1"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Exploration related to chemical processes in nanomaterial flows contains astonishing features. Nanoparticles have unique physical and chemical properties, so they are continuously used in almost every field of nanotechnology and nanoscience. The motive behind this article is to investigate the Cross nanofluid model along with its chemical processes via auto catalysts, inclined magnetic field phenomena, heat generation, Brownian movement, and thermophoresis phenomena over a symmetric shrinking (stretching) wedge. The transport of heat via nonuniform heat sources\/sinks, the impact of thermophoretic diffusion, and Brownian motion are considered. The Buongiorno nanofluid model is used to investigate the impact of nanofluids on fluid flow. Modeled PDEs are transformed into ODEs by utilizing similarity variables and handling dimensionless ODEs numerically with the adoption of MATLAB\u2019s developed bvp4c technique. This software performs a finite difference method that uses the collocation method with a three-stage LobattoIIIA strategy. Obtained outcomes are strictly for the case of a symmetric wedge. The velocity field lessens due to amplification in the magneto field variable. Fluid temperature is amplified through the enhancement of Brownian diffusion and the concentration field improves under magnification in a homogeneous reaction effect.<\/jats:p>","DOI":"10.3390\/sym15061145","type":"journal-article","created":{"date-parts":[[2023,5,25]],"date-time":"2023-05-25T01:36:28Z","timestamp":1684978588000},"page":"1145","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Cubic Chemical Autocatalysis and Oblique Magneto Dipole Effectiveness on Cross Nanofluid Flow via a Symmetric Stretchable Wedge"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0857-0935","authenticated-orcid":false,"given":"Nor Ain Azeany Mohd","family":"Nasir","sequence":"first","affiliation":[{"name":"Department of Mathematics, Centre for Defence Foundation Studies, Universiti Pertahanan Nasional Malaysia, Kem Sungai Besi, Kuala Lumpur 57000, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6130-3660","authenticated-orcid":false,"given":"Tanveer","family":"Sajid","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Capital University of Science and Technology, Islamabad 44000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9438-6132","authenticated-orcid":false,"given":"Wasim","family":"Jamshed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Capital University of Science and Technology, Islamabad 44000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7936-1495","authenticated-orcid":false,"given":"Gilder Cieza","family":"Altamirano","sequence":"additional","affiliation":[{"name":"Universidad Nacional Aut\u00f3noma de Chota, Cajamarca 06003, Per\u00fa-Fizmako Research Group, Bogot\u00e1 110110, Colombia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2479-9809","authenticated-orcid":false,"given":"Mohamed R.","family":"Eid","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, New Valley University, Al-Kharga 72511, Al-Wadi Al-Gadid, Egypt"},{"name":"Department of Mathematics, Faculty of Science, Northern Border University, Arar 1321, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fayza Abdel Aziz","family":"ElSeabee","sequence":"additional","affiliation":[{"name":"Mathematics Department, Faculty of Science, Helwan University, Cairo 12612, Egypt"},{"name":"Department of Mathematics, College of Science and Arts, Alasyah, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,24]]},"reference":[{"key":"ref_1","first-page":"99","article-title":"Enhancing thermal conductivity of fluids with nanoparticles","volume":"231","author":"Choi","year":"1995","journal-title":"ASME-Publ.-Fed."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1115\/1.2825978","article-title":"Measuring thermal conductivity of fluids containing oxide nanoparticles","volume":"121","author":"Lee","year":"1999","journal-title":"J. Heat Transf."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1115\/1.2150834","article-title":"Convective transport in nanofluids","volume":"128","author":"Buongiorno","year":"2006","journal-title":"J. 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