{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T16:49:24Z","timestamp":1776098964760,"version":"3.50.1"},"reference-count":48,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,15]],"date-time":"2022-11-15T00:00:00Z","timestamp":1668470400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"NSRF","award":["B05F650018"],"award-info":[{"award-number":["B05F650018"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The Darcy ternary hybrid nanofluid flow comprising titanium dioxide (TiO2), cobalt ferrite (CoFe2O4) and magnesium oxide (MgO) nanoparticles (NPs) through wedge, cone, and plate surfaces is reported in the present study. TiO2, CoFe2O4, and MgO NPs were dispersed in water to synthesize a trihybrid nanofluid. For this purpose, a mathematical model was calculated to augment the energy transport rate and efficiency for variety of commercial and medical functions. The consequences of heat source\/sink, activation energy, and the magnetic field are also analyzed. Such problems mostly occur in symmetrical phenomena and are applicable to engineering, physics, and applied mathematics. The phenomena were formulated in the form of a nonlinear system of PDEs, which are simplified to the system of dimensionless ODEs through similarity replacement (obtained from symmetry analysis). The obtained set of differential equations is resolved through a parametric continuation approach (PCM). Graphical depictions are used to evaluate and address the impact of significant factors on energy, mass, and flow exchange rates. The velocity and energy propagation rates over a cone surface were greater than those of a wedge and plate versus the variation of Grashof number, porosity effect, and heat source, while the mass transfer ratio under the impact of a chemical reaction and activation energy over a wedge surface was higher than that of a plate.<\/jats:p>","DOI":"10.3390\/sym14112419","type":"journal-article","created":{"date-parts":[[2022,11,16]],"date-time":"2022-11-16T02:31:27Z","timestamp":1668565887000},"page":"2419","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":49,"title":["Numerical Simulations through PCM for the Dynamics of Thermal Enhancement in Ternary MHD Hybrid Nanofluid Flow over Plane Sheet, Cone, and Wedge"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7773-4844","authenticated-orcid":false,"given":"Muhammad","family":"Bilal","sequence":"first","affiliation":[{"name":"Department of Mathematics, City University of Science and IT, Peshawar 25000, Pakistan"}]},{"given":"Ikram","family":"Ullah","sequence":"additional","affiliation":[{"name":"Department of Natural Sciences and Humanities, University of Engineering and Technology, Mardan 23200, Pakistan"}]},{"given":"Mohammad Mahtab","family":"Alam","sequence":"additional","affiliation":[{"name":"Department of Basic Medical Sciences, College of Applied Medical Science, King Khalid University, Abha 61421, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9595-6096","authenticated-orcid":false,"given":"Wajaree","family":"Weera","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3541-9704","authenticated-orcid":false,"given":"Ahmed M.","family":"Galal","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, College of Engineering in Wadi Alddawasir, Prince Sattam Bin Abdulaziz University, Wadi Alddawasir 11991, Saudi Arabia"},{"name":"Production Engineering and Mechanical Design Department, Faculty of Engineering, Mansoura University, Mansoura P.O. Box 35516, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4787","DOI":"10.1016\/j.aej.2021.03.062","article-title":"Fractional simulation for Darcy-Forchheimer hybrid nanoliquid flow with partial slip over a spinning disk","volume":"60","author":"Li","year":"2021","journal-title":"Alex. Eng. J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"651","DOI":"10.12989\/sem.2014.51.4.651","article-title":"Relaxed Saint-Venant principle for thermoelastic micropolar diffusion","volume":"51","author":"Marin","year":"2014","journal-title":"Struct. Eng. Mech."},{"key":"ref_3","first-page":"1","article-title":"Gyrotactic micro-organism flow of Maxwell nanofluid between two parallel plates","volume":"11","author":"Xu","year":"2021","journal-title":"Sci. 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