{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T20:52:14Z","timestamp":1783975934128,"version":"3.55.0"},"reference-count":43,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T00:00:00Z","timestamp":1762819200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University","award":["IMSIU-DDRSP2502"],"award-info":[{"award-number":["IMSIU-DDRSP2502"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This article investigates the impact of Arrhenius energy and the radius of a nanoparticle subject to an irregular heat source on tangent-hyperbolic nanofluid flow over a stretching sheet with nonlinear radiation. The convective boundary effect, higher-order slip, and micropolarity are all included for a water-based Cu nanofluid. The present study investigates the significance of a nanoparticle\u2019s radius under inclined MHD conditions. The thermally convective flow of the nanofluid is optimized for the heat-transfer rate using the response surface technique. The modeled governing equations are converted into a system of first-order ODEs using the proper similarity transformations, and the BVP5C algorithm\u2014a finite-difference-based solver\u2014is then used to solve these ODEs numerically. Microrotation, thermal boundary-layer thickness, and the skin-friction coefficient all decrease as the nanoparticle radius increases. The thermal layer thickens as the Biot number increases. As the higher-order slip parameter coefficient increases, the results indicate that the skin friction and local Nusselt number fall. Using tables, figures, contour plots, and surface plots, the effects of several influencing factors on the rates of heat and mass transfer, as well as on the skin-friction factor, are demonstrated. The study uses \u201cResponse Surface Methodology\u201d (RSM) in conjunction with \u201cAnalysis of Variance\u201d (ANOVA) to optimize the most important factors, which are probably the magnetic parameter and the nanoparticle radius that control the flow and heat-transfer properties. Additionally, with a Nusselt number R2 value of 99.96, indicating an excellent fit, the suggested model exhibits amazing precision. The reliability and efficiency of the estimated model are assessed using the residual versus fitted plot.<\/jats:p>","DOI":"10.3390\/sym17111928","type":"journal-article","created":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T08:57:41Z","timestamp":1762851461000},"page":"1928","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Relevance of Inclined Magnetohydrodynamics and Nanoparticle Radius on Tangent-Hyperbolic Flow over a Stretching Sheet: A Symmetric Modeling Perspective with Higher-Order Slip"],"prefix":"10.3390","volume":"17","author":[{"given":"Dipika","family":"Yadav","sequence":"first","affiliation":[{"name":"School of Basic and Applied Sciences, KR Mangalam University, Gurugram 122103, Haryana, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6876-8276","authenticated-orcid":false,"given":"Pardeep","family":"Kumar","sequence":"additional","affiliation":[{"name":"School of Basic and Applied Sciences, KR Mangalam University, Gurugram 122103, Haryana, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9343-0725","authenticated-orcid":false,"given":"Md","family":"Aquib","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 65892, Riyadh 11566, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Partap Singh","family":"Malik","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering, Guru Jambheshwar University of Science and Technology, Hisar 125001, Haryana, India"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,11]]},"reference":[{"key":"ref_1","unstructured":"Choi, S.U., and Eastman, J.A. (1995). Enhancing Thermal Conductivity of Fluids with Nanoparticles, Argonne National Lab. (ANL). Technical Report."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Ali, B., Ahammad, N.A., Awan, A.U., Oke, A.S., Tag-ElDin, E.M., Shah, F.A., and Majeed, S. (2022). The dynamics of water-based nanofluid subject to the nanoparticle\u2019s radius with a significant magnetic field: The case of rotating micropolar fluid. 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