{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T00:08:42Z","timestamp":1774483722145,"version":"3.50.1"},"reference-count":69,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,12,28]],"date-time":"2024-12-28T00:00:00Z","timestamp":1735344000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"FCT","award":["UI\/BD\/153761\/2022"],"award-info":[{"award-number":["UI\/BD\/153761\/2022"]}]},{"name":"FCT","award":["UIDB\/00144\/2020"],"award-info":[{"award-number":["UIDB\/00144\/2020"]}]},{"name":"CMUP","award":["UI\/BD\/153761\/2022"],"award-info":[{"award-number":["UI\/BD\/153761\/2022"]}]},{"name":"CMUP","award":["UIDB\/00144\/2020"],"award-info":[{"award-number":["UIDB\/00144\/2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>This study explores the optimization of a Cu\u2013Al2O3\/water hybrid nanofluid within an irregular wavy enclosure under inclined periodic MHD effects. Hybrid nanofluids, with different mixture ratios of copper (Cu) and alumina (Al2O3) nanoparticles in water, are used in this study. Numerical simulations using the Galerkin residual-based finite-element method (FEM) are conducted to solve the governing PDEs. At the same time, artificial neural networks (ANNs) and response surface methodology (RSM) are employed to optimize thermal performance by maximizing the average Nusselt number (Nuav), the key indicator of thermal transport efficiency. Thermophysical properties such as viscosity and thermal conductivity are evaluated for validation against experimental data. The results include visual representations of heatlines, streamlines, and isotherms for various physical parameters. Additionally, Nuav, friction factors, and thermal efficiency index are analyzed using different nanoparticle ratios. The findings show that buoyancy and MHD parameters significantly influence heat transfer, friction, and thermal efficiency. The addition of Cu nanoparticles improves heat transport compared to Al2O3 nanofluid, demonstrating the superior thermal conductivity of the Cu\u2013Al2O3\/water hybrid nanofluid. The results also indicate that adding Al2O3 nanoparticles to the Cu\/water nanofluid diminishes the heat transport rate. The waviness of the geometry shows a significant impact on thermal management as well. Moreover, the statistical RSM analysis indicates a high R2 value of 98.88% for the response function, which suggests that the model is well suited for predicting Nuav. Furthermore, the ANN model demonstrates high accuracy with a mean squared error (MSE) of 0.00018, making it a strong alternative to RSM analysis. Finally, this study focuses on the interaction between the hybrid nanofluid, a wavy geometry, and MHD effects, which can optimize heat transfer and contribute to energy-efficient cooling or heating technologies.<\/jats:p>","DOI":"10.3390\/math13010078","type":"journal-article","created":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T14:35:42Z","timestamp":1735742142000},"page":"78","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Artificial Neural Network and Response Surface Methodology-Driven Optimization of Cu\u2013Al2O3\/Water Hybrid Nanofluid Flow in a Wavy Enclosure with Inclined Periodic Magnetohydrodynamic Effects"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0220-6996","authenticated-orcid":false,"given":"Tarikul","family":"Islam","sequence":"first","affiliation":[{"name":"Mathematics Center of the Porto University (CMUP), Department of Mathematics, Science Faculty, University of Porto, 4169-007 Porto, Portugal"},{"name":"Department of Mathematics, Bangabandhu Sheikh Mujibur Rahman Science and Technology University, Gopalganj 8100, Bangladesh"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0852-8892","authenticated-orcid":false,"given":"S\u00edlvio","family":"Gama","sequence":"additional","affiliation":[{"name":"Mathematics Center of the Porto University (CMUP), Department of Mathematics, Science Faculty, University of Porto, 4169-007 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3928-1482","authenticated-orcid":false,"given":"Marco","family":"Martins Afonso","sequence":"additional","affiliation":[{"name":"Mathematics Center of the Porto University (CMUP), Department of Mathematics, Science Faculty, University of Porto, 4169-007 Porto, Portugal"},{"name":"SIT Technologies, Via Montallegro 1, 16145 Genoa, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1260","DOI":"10.1016\/j.solener.2021.06.072","article-title":"Numerical study of a photovoltaic thermal (PV\/T) system using mono and hybrid nanofluid","volume":"224","author":"Karaaslan","year":"2021","journal-title":"Sol. Energy"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1959","DOI":"10.1007\/s10973-020-09998-w","article-title":"A review on the properties, preparation, models and stability of hybrid nanofluids to optimize energy consumption","volume":"144","author":"Eshgarf","year":"2021","journal-title":"J. Therm. Anal. Calorim."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"105341","DOI":"10.1016\/j.icheatmasstransfer.2021.105341","article-title":"Role of hybrid-nanofluid in heat transfer enhancement\u2013A review","volume":"125","author":"Muneeshwaran","year":"2021","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"135875","DOI":"10.1016\/j.jclepro.2023.135875","article-title":"Applicability of mono-nanofluid and hybrid-nanofluid as a technique to improve the performance of solar still: A critical review","volume":"387","author":"Modi","year":"2023","journal-title":"J. Clean. Prod."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Margoum, S., Hajji, B.S., Aneli, S., Tina, G.M., and Gagliano, A. (2024). Optimizing Nanofluid Hybrid Solar Collectors through Artificial Intelligence Models. Energies, 17.","DOI":"10.3390\/en17102307"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"118751","DOI":"10.1016\/j.ijheatmasstransfer.2019.118751","article-title":"An experimental study on stability and thermal conductivity of water-graphene oxide\/aluminum oxide nanoparticles as a cooling hybrid nanofluid","volume":"145","author":"Taherialekouhi","year":"2019","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"474","DOI":"10.1016\/j.ijheatmasstransfer.2017.10.036","article-title":"Heat transfer efficiency of Al2O3-MWCNT\/thermal oil hybrid nanofluid as a cooling fluid in thermal and energy management applications: An experimental and theoretical investigation","volume":"117","author":"Asadi","year":"2018","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Alghamdi, W., Alsubie, A., Kumam, P., Saeed, A., and Gul, T. (2021). MHD hybrid nanofluid flow comprising the medication through a blood artery. Sci. Rep., 11.","DOI":"10.1038\/s41598-021-91183-6"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1637","DOI":"10.1007\/s10973-020-09717-5","article-title":"Effect of hybrid nanofluid on heat transfer performance of parabolic trough solar collector receiver","volume":"143","author":"Ekiciler","year":"2021","journal-title":"J. Therm. Anal. Calorim."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"119134","DOI":"10.1016\/j.molliq.2022.119134","article-title":"Insight into the investigation of diamond (C) and Silica (SiO2) nanoparticles suspended in water-based hybrid nanofluid with application in solar collector","volume":"357","author":"Bhatti","year":"2022","journal-title":"J. Mol. Liq."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2450015","DOI":"10.1142\/S0217984924500155","article-title":"Analysis of free bioconvective flow of hybrid nanofluid induced by convectively heated cone with entropy generation","volume":"38","author":"Ahmad","year":"2024","journal-title":"Mod. Phys. Lett. B"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"122006","DOI":"10.1016\/j.molliq.2023.122006","article-title":"Experimental Investigation with ANN Modeling of Thermal Conductivity and Viscosity of a Ternary Nanofluid at Different Mixing Ratios and Volume Concentrations","volume":"383","author":"Kishore","year":"2023","journal-title":"J. Mol. Liq."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"112207","DOI":"10.1016\/j.solmat.2023.112207","article-title":"The stability and thermophysical properties of Al2O3-graphene oxide hybrid nanofluids for solar energy applications: Application of robust autoregressive modern machine learning technique","volume":"253","author":"Kanti","year":"2023","journal-title":"Sol. Energy Mater. Sol. Cells"},{"key":"ref_14","first-page":"811","article-title":"Predicting heat transfer performance of Fe3O4-Cu\/water hybrid nanofluid under constant magnetic field using ANN","volume":"9","author":"Dirik","year":"2023","journal-title":"J. Therm. Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1969","DOI":"10.1007\/s12008-022-00906-0","article-title":"Modeling of viscosity of composite of TiO2\u2013Al2O3 and ethylene glycol nanofluid by artificial neural network: Experimental correlation","volume":"18","author":"Ajuka","year":"2024","journal-title":"Int. J. Interact. Des. Manuf. (IJIDeM)"},{"key":"ref_16","first-page":"1","article-title":"Artificial neural network approach to simulate the impact of concentration in optimizing heat transfer rate on water-based hybrid nanofluid under slip conditions: A regression analysis","volume":"85","author":"Panda","year":"2024","journal-title":"Numer. Heat Transf. Part B Fundam."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"104444","DOI":"10.1016\/j.icheatmasstransfer.2019.104444","article-title":"Established prediction models of thermal conductivity of hybrid nanofluids based on artificial neural network (ANN) models in waste heat system","volume":"110","author":"Wang","year":"2020","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1779","DOI":"10.1007\/s10973-019-08618-6","article-title":"Experimental investigation of thermal conductivity and its ANN modeling for glycol-based Ag\/ZnO hybrid nanofluids with low concentration","volume":"139","author":"Barewar","year":"2020","journal-title":"J. Therm. Anal. Calorim."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"4149","DOI":"10.1007\/s10973-020-09372-w","article-title":"Influence of base fluid, temperature, and concentration on the thermophysical properties of hybrid nanofluids of alumina\u2013ferrofluid: Experimental data, modeling through enhanced ANN, ANFIS, and curve fitting","volume":"143","author":"Giwa","year":"2021","journal-title":"J. Therm. Anal. Calorim."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"104930","DOI":"10.1016\/j.icheatmasstransfer.2020.104930","article-title":"A neural network-based predictive model for the thermal conductivity of hybrid nanofluids","volume":"119","author":"Adun","year":"2020","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"126562","DOI":"10.1016\/j.colsurfa.2021.126562","article-title":"Efficacy evaluation of oxide-MWCNT water hybrid nanofluids: An experimental and artificial neural network approach","volume":"620","author":"Kumar","year":"2021","journal-title":"Colloids Surf. A Physicochem. Eng. Asp."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Islam, T., Alam, M.N., Niazai, S., Khan, I., Fayz-Al-Asad, M., and Alqahtani, S. (2023). Heat generation\/absorption effect on natural convective heat transfer in a wavy triangular cavity filled with nanofluid. Sci. Rep., 13.","DOI":"10.1038\/s41598-023-48704-2"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2367","DOI":"10.1007\/s10973-020-09910-6","article-title":"Heat transfer analysis of Cu\u2013Al2O3 hybrid nanofluid with heat flux and viscous dissipation","volume":"143","author":"Ali","year":"2021","journal-title":"J. Therm. Anal. Calorim."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1197","DOI":"10.1007\/s10973-018-7546-7","article-title":"Experimental investigation of natural convection heat transfer characteristics in MWCNT-thermal oil nanofluid","volume":"135","author":"Ilyas","year":"2019","journal-title":"J. Therm. Anal. Calorim."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"657","DOI":"10.1016\/j.aej.2020.01.028","article-title":"Cu-Al2O3\/water hybrid nanofluid flow over a permeable moving surface in presence of hydromagnetic and suction effects","volume":"59","author":"Aladdin","year":"2020","journal-title":"Alex. Eng. J."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"7198","DOI":"10.1002\/er.5417","article-title":"Experimental study for predicting the specific heat of water based Cu-Al2O3 hybrid nanofluid using artificial neural network and proposing new correlation","volume":"44","author":"Bayrak","year":"2020","journal-title":"Int. J. Energy Res."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1943","DOI":"10.1016\/j.aej.2017.03.047","article-title":"Performance of hybrid nanofluid (Cu-CuO\/water) on MHD rotating transport in oscillating vertical channel inspired by Hall current and thermal radiation","volume":"57","author":"Iqbal","year":"2018","journal-title":"Alex. Eng. J."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1016\/j.jppr.2022.06.002","article-title":"Heat transfer attributes of Al2O3-Fe3O4\/H2O hybrid nanofluid flow over a yawed cylinder","volume":"11","author":"Patil","year":"2022","journal-title":"Propuls. Power Res."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1016\/j.molliq.2018.12.104","article-title":"Variable magnetic forces impact on magnetizable hybrid nanofluid heat transfer through a circular cavity","volume":"277","author":"Sheikholeslami","year":"2019","journal-title":"J. Mol. Liq."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"122136","DOI":"10.1016\/j.physa.2019.122136","article-title":"Macroscopic modeling for convection of Hybrid nanofluid with magnetic effects","volume":"534","author":"Tlili","year":"2019","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"100605","DOI":"10.1016\/j.tsep.2020.100605","article-title":"Natural convection and entropy production in hybrid nanofluid filled-annular elliptical cavity with internal heat generation or absorption","volume":"19","author":"Tayebi","year":"2020","journal-title":"Therm. Sci. Eng. Prog."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"104676","DOI":"10.1016\/j.icheatmasstransfer.2020.104676","article-title":"Influence of the Lorentz force on the ventilation cavity having a centrally placed heated baffle filled with the Cu\u2212Al2O3\u2212H2O hybrid nanofluid","volume":"116","author":"Du","year":"2020","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"171612","DOI":"10.1016\/j.jmmm.2023.171612","article-title":"Hydrothermal scenario of buoyancy-driven magnetized multi-walled carbon nanotube-Fe3O4-water hybrid nanofluid flow within a discretely heated circular chamber fitted with fins","volume":"589","author":"Acharya","year":"2024","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"100571","DOI":"10.1016\/j.ijft.2024.100571","article-title":"Magnetic field effect on mixed convection flow inside an oval-shaped annulus enclosure filled by a non-Newtonian nanofluid","volume":"21","author":"Hameed","year":"2024","journal-title":"Int. J. Thermofluids"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"107232","DOI":"10.1016\/j.rinp.2023.107232","article-title":"A Galerkin finite element-based study of MHD mixed convective of Ostwald-de Waele nanofluids in a lid-driven wavy chamber","volume":"56","author":"Abderrahmane","year":"2024","journal-title":"Results Phys."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1016\/j.cjph.2020.03.006","article-title":"Natural convection of a hybrid nanofluid affected by an inclined periodic magnetic field within a porous medium","volume":"65","author":"Izadi","year":"2020","journal-title":"Chin. J. Phys."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Islam, T., Yavuz, M., Parveen, N., and Fayz-Al-Asad, M. (2022). Impact of Non-Uniform Periodic Magnetic Field on Unsteady Natural Convection Flow of Nanofluids in Square Enclosure. Fractal Fract., 6.","DOI":"10.3390\/fractalfract6020101"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"510","DOI":"10.1016\/j.molliq.2018.04.119","article-title":"Natural convection and entropy generation of a ferrofluid in a square enclosure under the effect of a horizontal periodic magnetic field","volume":"263","author":"Mehryan","year":"2018","journal-title":"J. Mol. Liq."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"106015","DOI":"10.1016\/j.icheatmasstransfer.2022.106015","article-title":"Mixed bioconvection flow of Ag-MgO\/water in the presence of oxytactic bacteria and inclined periodic magnetic field","volume":"134","author":"Hussain","year":"2022","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"e202300194","DOI":"10.1002\/zamm.202300194","article-title":"Generalized thermal properties of hybrid NANOLIQUID composed of aluminum oxide (Al2O3) and silver (Ag) nanoparticles with water (H2O) as base liquid","volume":"104","author":"Parveen","year":"2024","journal-title":"ZAMM J. Appl. Math. Mech. Z. Angew. Math. Mech."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/10407782.2024.2329312","article-title":"Neural network and thermodynamic optimization of magnetized hybrid nanofluid dissipative radiative convective flow with energy activation","volume":"85","author":"Ferdows","year":"2024","journal-title":"Numer. Heat Transf. A Appl."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"8321","DOI":"10.1007\/s10973-024-13123-6","article-title":"Optimizing microelectronic module cooling under magnetic fields through hybrid nanofluid: A computational fluid dynamics-artificial neural network approach","volume":"149","author":"Salehin","year":"2024","journal-title":"J. Therm. Anal. Calorim."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"108169","DOI":"10.1016\/j.mtcomm.2024.108169","article-title":"Artificial neural network modeling of thermal characteristics of WO3-CuO (50: 50)\/water hybrid nanofluid with a back-propagation algorithm","volume":"38","author":"Qu","year":"2024","journal-title":"Mater. Today Commun."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Jakeer, S., Basha, H.T., Reddy, S.R.R., Abbas, M., Alqahtani, M.S., Loganathan, K., and Anand, A.V. (2023). Entropy analysis on EMHD 3D micropolar tri-hybrid nanofluid flow of solar radiative slendering sheet by a machine learning algorithm. Sci. Rep., 13.","DOI":"10.1038\/s41598-023-45469-6"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"9619","DOI":"10.1007\/s10973-023-12317-8","article-title":"A novel hybrid nanofluid including MWCNT and ZrO2 nanoparticles: Implementation of response surface methodology and artificial neural network","volume":"148","author":"Mustafa","year":"2023","journal-title":"J. Therm. Anal. Calorim."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/10407790.2024.2325027","article-title":"Response surface method and finite element-based investigation of uniform\/nonuniform hydromagnetic convection of nanofluids inside a quarter-circular enclosure","volume":"85","author":"Islam","year":"2024","journal-title":"Numer. Heat Transf. Part B Fundam."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"121150","DOI":"10.1016\/j.molliq.2022.121150","article-title":"Experimental examination of the properties of Fe3O4\/water nanofluid, and an estimation of a correlation using an artificial neural network","volume":"374","author":"Eshgarf","year":"2023","journal-title":"J. Mol. Liq."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"108608","DOI":"10.1016\/j.ijthermalsci.2023.108608","article-title":"Heat transfer, and friction factor of Fe3O4\u2013SiO2\/Water hybrid nanofluids in a plate heat exchanger: Experimental and ANN predictions","volume":"195","author":"Alklaibi","year":"2024","journal-title":"Int. J. Therm. Sci."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"100383","DOI":"10.1016\/j.ijft.2023.100383","article-title":"AI predicts MHD double-diffusive mixed convection and entropy generation in hybrid-nanofluids for different magnetic field inclination angles by ANN","volume":"19","author":"Prince","year":"2023","journal-title":"Int. J. Thermofluids"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"e19228","DOI":"10.1016\/j.heliyon.2023.e19228","article-title":"Modelling the effects of mixing ratio and temperature on the thermal conductivity of GNP-Alumina hybrid nanofluids: A comparison of ANN, RSM, and linear regression methods","volume":"9","author":"Borode","year":"2023","journal-title":"Heliyon"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"3801","DOI":"10.1007\/s12648-023-02737-5","article-title":"ANN model of three-dimensional micropolar dusty hybrid nanofluid flow with coriolis force: Biomedical applications","volume":"97","author":"Reddy","year":"2023","journal-title":"Indian J. Phys."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"103949","DOI":"10.1016\/j.csite.2023.103949","article-title":"Effectiveness and number of transfer units of plate heat exchanger with Fe3O4\u2013SiO2\/Water hybrid nanofluids: Experimental and artificial neural network predictions","volume":"53","author":"Sundar","year":"2024","journal-title":"Case Stud. Therm. Eng."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"2455","DOI":"10.1108\/HFF-01-2024-0058","article-title":"Optimisation of MHD flow within trapezoidal cavity containing hybrid nanofluid by artificial neural network","volume":"34","author":"Tanveer","year":"2024","journal-title":"Int. J. Numer. Methods Heat Fluid Flow"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1140\/epjp\/s13360-024-05359-w","article-title":"Levenberg\u2013Marquardt neural network for entropy optimization on Casson hybrid nanofluid flow with nonlinear thermal radiation: A comparative study","volume":"139","author":"Kumar","year":"2024","journal-title":"Eur. Phys. J. Plus"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"101940","DOI":"10.1016\/j.csite.2022.101940","article-title":"Experimental study and sensitivity analysis of a new generation of special ternary hybrid nanofluids (THNFs) and investigation of factors affecting its thermal conductivity","volume":"34","author":"Esfe","year":"2022","journal-title":"Case Stud. Therm. Eng."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"801","DOI":"10.1007\/s10973-020-09271-0","article-title":"Experimental investigation of the hydrothermal aspects of water\u2013Fe3O4 nanofluid inside a twisted tube","volume":"143","author":"Niknejadi","year":"2021","journal-title":"J. Therm. Anal. Calorim."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"108576","DOI":"10.1016\/j.compositesa.2024.108576","article-title":"Effect of soft magnetic particles content on multi-physics field of magnetorheological composite gel clutch with complex flow channel excited by Halbach array arrangement","volume":"188","author":"Zhang","year":"2025","journal-title":"Compos. Part A Appl. Sci. Manuf."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"022021","DOI":"10.1063\/5.0190569","article-title":"Study on performance optimization of double screw-magnetic fluid combination seal","volume":"36","author":"Li","year":"2024","journal-title":"Phys. Fluids"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"130026","DOI":"10.1016\/j.physleta.2024.130026","article-title":"Electromagnetohydrodynamic (EMHD) flow of Jeffrey fluid through parallel plate microchannels with surface charge-dependent asymmetric slip","volume":"528","author":"Li","year":"2024","journal-title":"Phys. Lett. A"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"e09015","DOI":"10.1016\/j.heliyon.2022.e09015","article-title":"Mathematical Modeling of Unsteady Flow with Uniform\/Non-Uniform Thermal and Magnetic Fields in a Half-Moon Shaped Domain","volume":"8","author":"Islam","year":"2021","journal-title":"Heliyon"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.colsurfa.2011.08.005","article-title":"Synthesis of Al2O3\u2013Cu\/water hybrid nanofluids using two step method and its thermo physical properties","volume":"388","author":"Suresh","year":"2011","journal-title":"Colloids Surf. A Physicochem. Eng. Asp."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1021\/i160003a005","article-title":"Thermal Conductivity of Heterogeneous Two-Component Systems","volume":"1","author":"Hamilton","year":"1062","journal-title":"Ind. Eng. Chem. Fundam."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"147059","DOI":"10.1155\/2014\/147059","article-title":"Augmentation of the Heat Transfer Performance of a Sinusoidal Corrugated Enclosure by Employing Hybrid Nanofluid","volume":"6","author":"Takabi","year":"2014","journal-title":"Adv. Mech. Eng."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1108\/HFF-11-2020-0748","article-title":"Free convective heat transfer efficiency in Al2O3\u2013Cu\/water hybrid nanofluid inside a rectotrapezoidal enclosure","volume":"32","author":"Rahman","year":"2022","journal-title":"Int. J. Numer. Methods Heat Fluid Flow"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1016\/j.enganabound.2023.06.009","article-title":"Numerical and machine learning approaches in nanofluid natural convection flow in a wavy cavity","volume":"155","author":"Geridonmez","year":"2023","journal-title":"Eng. Anal. Bound. Elem."},{"key":"ref_66","first-page":"764","article-title":"Energetic thermo-physical analysis of MLP-RBF feed-forward neural network compared with RLS Fuzzy to predict CuO\/liquid paraffin mixture properties","volume":"16","author":"Zhang","year":"2022","journal-title":"Eng. Appl. Comput. Fluid Mech."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"999","DOI":"10.2514\/1.T5430","article-title":"Impact of periodic magnetic field on entropy generation and mixed convection","volume":"32","author":"Hussain","year":"2018","journal-title":"J. Thermophys. Heat Transf."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"100661","DOI":"10.1016\/j.ijft.2024.100661","article-title":"Natural convective heat transfer of Al2O3-Cu\/water hybrid nanofluid in a rectotrapezoidal enclosure under the influence of periodic magnetic field","volume":"22","author":"Haque","year":"2024","journal-title":"Int. J. Thermofluids"},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1016\/j.ces.2012.07.003","article-title":"Numerical study of substrate assimilation by a microorganism exposed to fluctuating concentration","volume":"81","author":"Fede","year":"2012","journal-title":"Chem. Eng. Sci."}],"container-title":["Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2227-7390\/13\/1\/78\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:55:29Z","timestamp":1760115329000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2227-7390\/13\/1\/78"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,28]]},"references-count":69,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,1]]}},"alternative-id":["math13010078"],"URL":"https:\/\/doi.org\/10.3390\/math13010078","relation":{},"ISSN":["2227-7390"],"issn-type":[{"value":"2227-7390","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,12,28]]}}}