{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T04:57:18Z","timestamp":1773291438580,"version":"3.50.1"},"reference-count":67,"publisher":"Springer Science and Business Media LLC","issue":"32","license":[{"start":{"date-parts":[[2025,9,20]],"date-time":"2025-09-20T00:00:00Z","timestamp":1758326400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,9,20]],"date-time":"2025-09-20T00:00:00Z","timestamp":1758326400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"Anusandhan National Research Foundation, Government of India through State University Research Excellence Program","award":["SUR\/2022\/000701"],"award-info":[{"award-number":["SUR\/2022\/000701"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput & Applic"],"published-print":{"date-parts":[[2025,11]]},"DOI":"10.1007\/s00521-025-11658-9","type":"journal-article","created":{"date-parts":[[2025,9,20]],"date-time":"2025-09-20T08:45:27Z","timestamp":1758357927000},"page":"27083-27115","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Shape factor effect on the thermal variation of a wavy fin wetted by ternary hybrid nanofluid using an extended physics-informed Laguerre neural network"],"prefix":"10.1007","volume":"37","author":[{"given":"R. S. Varun","family":"Kumar","sequence":"first","affiliation":[]},{"given":"G.","family":"Sowmya","sequence":"additional","affiliation":[]},{"given":"Chander","family":"Prakash","sequence":"additional","affiliation":[]},{"given":"K.","family":"Chandan","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1950-4666","authenticated-orcid":false,"given":"B. C.","family":"Prasannakumara","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,9,20]]},"reference":[{"key":"11658_CR1","unstructured":"Choi SUS, Eastman JA (2024) Enhancing thermal conductivity of fluids with nanoparticles, Argonne National Lab. (ANL), Argonne, IL (United States), 1995. https:\/\/www.osti.gov\/biblio\/196525 (accessed March 6)."},{"key":"11658_CR2","doi-asserted-by":"publisher","first-page":"757","DOI":"10.1016\/j.aej.2014.04.003","volume":"53","author":"K Das","year":"2014","unstructured":"Das K (2014) Flow and heat transfer characteristics of nanofluids in a rotating frame. Alexandria Eng J 53:757\u2013766. https:\/\/doi.org\/10.1016\/j.aej.2014.04.003","journal-title":"Alexandria Eng J"},{"key":"11658_CR3","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1016\/j.aej.2015.01.001","volume":"54","author":"S Das","year":"2015","unstructured":"Das S, Jana RN (2015) Natural convective magneto-nanofluid flow and radiative heat transfer past a moving vertical plate. Alexandria Eng J 54:55\u201364. https:\/\/doi.org\/10.1016\/j.aej.2015.01.001","journal-title":"Alexandria Eng J"},{"key":"11658_CR4","doi-asserted-by":"publisher","first-page":"1899","DOI":"10.1007\/s10973-018-7066-5","volume":"132","author":"I Tlili","year":"2018","unstructured":"Tlili I, Hamadneh NN, Khan WA, Atawneh S (2018) Thermodynamic analysis of MHD Couette-Poiseuille flow of water-based nanofluids in a rotating channel with radiation and Hall effects. J Therm Anal Calorim 132:1899\u20131912. https:\/\/doi.org\/10.1007\/s10973-018-7066-5","journal-title":"J Therm Anal Calorim"},{"key":"11658_CR5","doi-asserted-by":"publisher","first-page":"194","DOI":"10.1016\/j.rinp.2018.05.032","volume":"10","author":"SA Mohammadein","year":"2018","unstructured":"Mohammadein SA, Raslan K, Abdel-Wahed MS, Abedel-Aal EM (2018) KKL-model of MHD CuO-nanofluid flow over a stagnation point stretching sheet with nonlinear thermal radiation and suction\/injection. Results Phys 10:194\u2013199. https:\/\/doi.org\/10.1016\/j.rinp.2018.05.032","journal-title":"Results Phys"},{"key":"11658_CR6","doi-asserted-by":"publisher","first-page":"473","DOI":"10.1016\/j.ijheatmasstransfer.2018.11.124","volume":"132","author":"AS Dogonchi","year":"2019","unstructured":"Dogonchi AS, Waqas M, Seyyedi SM, Hashemi-Tilehnoee M, Ganji DD (2019) CVFEM analysis for Fe3O4\u2013H2O nanofluid in an annulus subject to thermal radiation. Int J Heat Mass Transf 132:473\u2013483. https:\/\/doi.org\/10.1016\/j.ijheatmasstransfer.2018.11.124","journal-title":"Int J Heat Mass Transf"},{"key":"11658_CR7","doi-asserted-by":"publisher","first-page":"2419","DOI":"10.3390\/sym14112419","volume":"14","author":"M Bilal","year":"2022","unstructured":"Bilal M, Ullah I, Alam MM, Weera W, Galal AM (2022) Numerical simulations through PCM for the dynamics of thermal enhancement in ternary MHD hybrid nanofluid flow over plane sheet, cone, and wedge. Symmetry 14:2419. https:\/\/doi.org\/10.3390\/sym14112419","journal-title":"Symmetry"},{"key":"11658_CR8","doi-asserted-by":"publisher","first-page":"129525","DOI":"10.1016\/j.jclepro.2021.129525","volume":"328","author":"H Adun","year":"2021","unstructured":"Adun H, Kavaz D, Dagbasi M (2021) Review of ternary hybrid nanofluid: synthesis, stability, thermophysical properties, heat transfer applications, and environmental effects. J Clean Prod 328:129525. https:\/\/doi.org\/10.1016\/j.jclepro.2021.129525","journal-title":"J Clean Prod"},{"key":"11658_CR9","doi-asserted-by":"publisher","first-page":"588","DOI":"10.3390\/mi13040588","volume":"13","author":"KAM Alharbi","year":"2022","unstructured":"Alharbi KAM, Ahmed AE-S, Ould Sidi M, Ahammad NA, Mohamed A, El-Shorbagy MA, Bilal M, Marzouki R (2022) Computational valuation of Darcy ternary-hybrid nanofluid flow across an extending cylinder with induction effects. Micromachines 13:588. https:\/\/doi.org\/10.3390\/mi13040588","journal-title":"Micromachines"},{"key":"11658_CR10","doi-asserted-by":"publisher","first-page":"122338","DOI":"10.1016\/j.molliq.2023.122338","volume":"385","author":"A Shahsavar","year":"2023","unstructured":"Shahsavar A, Sepehrnia M, Maleki H, Darabi R (2023) Thermal conductivity of hydraulic oil-GO\/Fe3O4\/TiO2 ternary hybrid nanofluid: experimental study, RSM analysis, and development of optimized GPR model. J Mol Liq 385:122338. https:\/\/doi.org\/10.1016\/j.molliq.2023.122338","journal-title":"J Mol Liq"},{"key":"11658_CR11","doi-asserted-by":"publisher","first-page":"981","DOI":"10.3390\/math11040981","volume":"11","author":"B Souayeh","year":"2023","unstructured":"Souayeh B, Ramesh K (2023) Numerical scrutinization of ternary nanofluid flow over an exponentially stretching sheet with gyrotactic microorganisms. Mathematics 11:981. https:\/\/doi.org\/10.3390\/math11040981","journal-title":"Mathematics"},{"key":"11658_CR12","doi-asserted-by":"publisher","first-page":"125257","DOI":"10.1016\/j.molliq.2024.125257","volume":"408","author":"MII Rabby","year":"2024","unstructured":"Rabby MII, Uddin MW, Hassan NMS, Al Nur M, Uddin R, Istiaque S, Abir MMM (2024) Recent progresses in tri-hybrid nanofluids: a comprehensive review on preparation, stability, thermo-hydraulic properties, and applications. J Mol Liq 408:125257. https:\/\/doi.org\/10.1016\/j.molliq.2024.125257","journal-title":"J Mol Liq"},{"key":"11658_CR13","doi-asserted-by":"publisher","first-page":"2183","DOI":"10.1080\/10407782.2023.2219834","volume":"85","author":"M Nagapavani","year":"2024","unstructured":"Nagapavani M, Ramana Reddy G, Venkata A, Amal K, Raman RJ, Gowda P (2024) Three-dimensional swirling flow of a ternary composite nanofluid induced by the torsional motion of a cylinder considering non-Fourier law. Numer Heat Trans, Part A: Appl 85:2183\u20132196. https:\/\/doi.org\/10.1080\/10407782.2023.2219834","journal-title":"Numer Heat Trans, Part A: Appl"},{"key":"11658_CR14","doi-asserted-by":"publisher","first-page":"758","DOI":"10.1140\/epjp\/s13360-024-05549-6","volume":"139","author":"T Shivanna","year":"2024","unstructured":"Shivanna T, Hanumagowda BN, Subray PVA, Prasad KV, Varma SVK, Muhammad T, Punith Gowda RJ (2024) Heat and mass transfer of ternary nanofluid in permeable vertical channel sandwiched between nanofluid zones with Soret and Dufour effects using sensitivity analysis. Eur Phys J Plus 139:758. https:\/\/doi.org\/10.1140\/epjp\/s13360-024-05549-6","journal-title":"Eur Phys J Plus"},{"key":"11658_CR15","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1016\/j.molliq.2014.03.001","volume":"196","author":"ShM Vanaki","year":"2014","unstructured":"Vanaki ShM, Mohammed HA, Abdollahi A, Wahid MA (2014) Effect of nanoparticle shapes on the heat transfer enhancement in a wavy channel with different phase shifts. J Mol Liq 196:32\u201342. https:\/\/doi.org\/10.1016\/j.molliq.2014.03.001","journal-title":"J Mol Liq"},{"key":"11658_CR16","doi-asserted-by":"publisher","first-page":"030042","DOI":"10.1063\/1.4965162","volume":"1775","author":"S Shafie","year":"2016","unstructured":"Shafie S, Gul A, Khan I (2016) Molybdenum disulfide nanoparticles suspended in water-based nanofluids with mixed convection and flow inside a channel filled with saturated porous medium. AIP Conf Proc 1775:030042. https:\/\/doi.org\/10.1063\/1.4965162","journal-title":"AIP Conf Proc"},{"key":"11658_CR17","doi-asserted-by":"publisher","first-page":"633","DOI":"10.1016\/j.rinp.2017.12.077","volume":"8","author":"EN Maraj","year":"2018","unstructured":"Maraj EN, Iqbal Z, Azhar E, Mehmood Z (2018) A comprehensive shape factor analysis using transportation of MoS2-SiO2\/H2O inside an isothermal semi vertical inverted cone with porous boundary. Results Phys 8:633\u2013641. https:\/\/doi.org\/10.1016\/j.rinp.2017.12.077","journal-title":"Results Phys"},{"key":"11658_CR18","doi-asserted-by":"publisher","first-page":"092002","DOI":"10.1063\/5.0168503","volume":"35","author":"CM Mohana","year":"2023","unstructured":"Mohana CM, Rushi Kumar B (2023) Shape effects of Darcy-Forchheimer unsteady three-dimensional CdTe-C\/H2O hybrid nanofluid flow over a stretching sheet with convective heat transfer. Phys Fluids 35:092002. https:\/\/doi.org\/10.1063\/5.0168503","journal-title":"Phys Fluids"},{"key":"11658_CR19","doi-asserted-by":"publisher","first-page":"790","DOI":"10.1115\/1.1371922","volume":"123","author":"S Kiwan","year":"2000","unstructured":"Kiwan S, Al-Nimr MA (2000) Using porous fins for heat transfer enhancement. J Heat Transf 123:790\u2013795. https:\/\/doi.org\/10.1115\/1.1371922","journal-title":"J Heat Transf"},{"key":"11658_CR20","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1007\/s11242-006-0010-3","volume":"67","author":"S Kiwan","year":"2007","unstructured":"Kiwan S (2007) Thermal analysis of natural convection porous fins. Transp Porous Media 67:17\u201329. https:\/\/doi.org\/10.1007\/s11242-006-0010-3","journal-title":"Transp Porous Media"},{"key":"11658_CR21","doi-asserted-by":"publisher","first-page":"1046","DOI":"10.1016\/j.ijthermalsci.2006.11.013","volume":"46","author":"S Kiwan","year":"2007","unstructured":"Kiwan S (2007) Effect of radiative losses on the heat transfer from porous fins. Int J Therm Sci 46:1046\u20131055. https:\/\/doi.org\/10.1016\/j.ijthermalsci.2006.11.013","journal-title":"Int J Therm Sci"},{"key":"11658_CR22","doi-asserted-by":"publisher","first-page":"638","DOI":"10.1016\/j.icheatmasstransfer.2010.12.024","volume":"38","author":"RSR Gorla","year":"2011","unstructured":"Gorla RSR, Bakier AY (2011) Thermal analysis of natural convection and radiation in porous fins. Int Commun Heat Mass Transfer 38:638\u2013645. https:\/\/doi.org\/10.1016\/j.icheatmasstransfer.2010.12.024","journal-title":"Int Commun Heat Mass Transfer"},{"key":"11658_CR23","doi-asserted-by":"publisher","first-page":"806","DOI":"10.2514\/1.T4348","volume":"28","author":"M Turkyilmazoglu","year":"2014","unstructured":"Turkyilmazoglu M (2014) Heat transfer through longitudinal fins. J Thermophys Heat Transf 28:806\u2013811. https:\/\/doi.org\/10.2514\/1.T4348","journal-title":"J Thermophys Heat Transf"},{"key":"11658_CR24","doi-asserted-by":"publisher","first-page":"188","DOI":"10.1016\/j.jppr.2020.03.002","volume":"9","author":"PL Ndlovu","year":"2020","unstructured":"Ndlovu PL, Moitsheki RJ (2020) Steady state heat transfer analysis in a rectangular moving porous fin. Propuls Power Res 9:188\u2013196. https:\/\/doi.org\/10.1016\/j.jppr.2020.03.002","journal-title":"Propuls Power Res"},{"key":"11658_CR25","doi-asserted-by":"publisher","first-page":"101012","DOI":"10.1016\/j.padiff.2024.101012","volume":"13","author":"S Singh","year":"2025","unstructured":"Singh S, Kaur P, Kumar D, Rai KN (2025) Wavelet collocation solution for fully wet semi-spherical porous fin. Partial Diff Equ Appl Math 13:101012. https:\/\/doi.org\/10.1016\/j.padiff.2024.101012","journal-title":"Partial Diff Equ Appl Math"},{"key":"11658_CR26","doi-asserted-by":"publisher","first-page":"867","DOI":"10.1016\/j.nonrwa.2010.08.011","volume":"12","author":"RJ Moitsheki","year":"2011","unstructured":"Moitsheki RJ (2011) Steady heat transfer through a radial fin with rectangular and hyperbolic profiles. Nonlinear Anal Real World Appl 12:867\u2013874. https:\/\/doi.org\/10.1016\/j.nonrwa.2010.08.011","journal-title":"Nonlinear Anal Real World Appl"},{"key":"11658_CR27","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1016\/j.enconman.2014.05.033","volume":"86","author":"S Mosayebidorcheh","year":"2014","unstructured":"Mosayebidorcheh S, Farzinpoor M, Ganji DD (2014) Transient thermal analysis of longitudinal fins with internal heat generation considering temperature-dependent properties and different fin profiles. Energy Convers Manag 86:365\u2013370. https:\/\/doi.org\/10.1016\/j.enconman.2014.05.033","journal-title":"Energy Convers Manag"},{"key":"11658_CR28","doi-asserted-by":"publisher","first-page":"110408","DOI":"10.18280\/mmep.110408","volume":"13","author":"AHM AlEssa","year":"2024","unstructured":"AlEssa AHM, Hussien AA, Al-Tahaineh H, Qasem I, Janvekar AA (2024) Enhancement of natural convection heat dissipation using longitudinal elliptic perforations fins. Math Model Eng Probl 13:110408. https:\/\/doi.org\/10.18280\/mmep.110408","journal-title":"Math Model Eng Probl"},{"key":"11658_CR29","doi-asserted-by":"publisher","first-page":"108397","DOI":"10.1016\/j.icheatmasstransfer.2024.108397","volume":"161","author":"RSV Kumar","year":"2025","unstructured":"Kumar RSV, Sowmya G, Abhilasha SK, Prasannakumara BC (2025) Solution by operational matrix based Vieta-Lucas collocation method to analyze the thermal performance of the convex spine fin applicable in air conditioning systems. Int Commun Heat Mass Transf 161:108397. https:\/\/doi.org\/10.1016\/j.icheatmasstransfer.2024.108397","journal-title":"Int Commun Heat Mass Transf"},{"key":"11658_CR30","doi-asserted-by":"publisher","first-page":"126820","DOI":"10.1016\/j.applthermaleng.2025.126820","volume":"275","author":"RSV Kumar","year":"2025","unstructured":"Kumar RSV, Abhilasha SK, Banakar VR, Gamaoun F, Prasannakumara BC (2025) Computational analysis of wetted triangular spine fin using Lerch polynomial collocation method. Appl Therm Eng 275:126820. https:\/\/doi.org\/10.1016\/j.applthermaleng.2025.126820","journal-title":"Appl Therm Eng"},{"key":"11658_CR31","doi-asserted-by":"publisher","first-page":"768","DOI":"10.1016\/j.ijthermalsci.2006.10.004","volume":"46","author":"YB Tao","year":"2007","unstructured":"Tao YB, He YL, Huang J, Wu ZG, Tao WQ (2007) Numerical study of local heat transfer coefficient and fin efficiency of wavy fin-and-tube heat exchangers\u2606. Int J Therm Sci 46:768\u2013778. https:\/\/doi.org\/10.1016\/j.ijthermalsci.2006.10.004","journal-title":"Int J Therm Sci"},{"key":"11658_CR32","doi-asserted-by":"publisher","first-page":"892","DOI":"10.1108\/HFF-06-2014-0174","volume":"25","author":"AA Khaled","year":"2015","unstructured":"Khaled AA (2015) Thermal performance of six different types of wavy-fins. Int J Numer Methods Heat Fluid Flow 25:892\u2013911. https:\/\/doi.org\/10.1108\/HFF-06-2014-0174","journal-title":"Int J Numer Methods Heat Fluid Flow"},{"key":"11658_CR33","doi-asserted-by":"publisher","DOI":"10.18280\/ijht.370310","author":"H Sertel","year":"2019","unstructured":"Sertel H, Bilen K (2019) The effect of using sinusoidal profile in fins on thermal performance. Int J Heat Technol. https:\/\/doi.org\/10.18280\/ijht.370310","journal-title":"Int J Heat Technol"},{"key":"11658_CR34","doi-asserted-by":"publisher","first-page":"1658","DOI":"10.1002\/htj.21684","volume":"49","author":"A Maji","year":"2020","unstructured":"Maji A, Choubey G (2020) Improvement of heat transfer through fins: a brief review of recent developments. Heat Transf 49:1658\u20131685. https:\/\/doi.org\/10.1002\/htj.21684","journal-title":"Heat Transf"},{"key":"11658_CR35","doi-asserted-by":"publisher","first-page":"4307","DOI":"10.1007\/s12206-020-0921-x","volume":"34","author":"N Chimres","year":"2020","unstructured":"Chimres N, Chittiphalungsri T, Asirvatham LG, Dalk\u0131l\u0131\u00e7 AS, Mahian O, Wongwises S (2020) Experimental and numerical studies on heat transfer enhancement for air conditioner condensers using a wavy fin with a rectangular winglet. J Mech Sci Technol 34:4307\u20134322. https:\/\/doi.org\/10.1007\/s12206-020-0921-x","journal-title":"J Mech Sci Technol"},{"key":"11658_CR36","doi-asserted-by":"publisher","first-page":"20680","DOI":"10.1016\/j.ijhydene.2023.01.088","volume":"48","author":"P Xu","year":"2023","unstructured":"Xu P, Wen J, Wang S, Chen Q, Li Y (2023) Numerical simulation on flow and heat transfer performances of serrated and wavy fins in plate-fin heat exchanger for hydrogen liquefaction. Int J Hydrogen Energy 48:20680\u201320693. https:\/\/doi.org\/10.1016\/j.ijhydene.2023.01.088","journal-title":"Int J Hydrogen Energy"},{"key":"11658_CR37","doi-asserted-by":"publisher","first-page":"2401","DOI":"10.3390\/math11102401","volume":"11","author":"RSV Kumar","year":"2023","unstructured":"Kumar RSV, Alsulami MD, Sarris IE, Sowmya G, Gamaoun F (2023) Stochastic Levenberg\u2013Marquardt neural network implementation for analyzing the convective heat transfer in a wavy fin. Mathematics 11:2401. https:\/\/doi.org\/10.3390\/math11102401","journal-title":"Mathematics"},{"key":"11658_CR38","doi-asserted-by":"publisher","first-page":"725","DOI":"10.1109\/TIM.2010.2082390","volume":"60","author":"JC Patra","year":"2011","unstructured":"Patra JC, Meher PK, Chakraborty G (2011) Development of Laguerre neural-network-based intelligent sensors for wireless sensor networks. IEEE Trans Instrum Meas 60:725\u2013734. https:\/\/doi.org\/10.1109\/TIM.2010.2082390","journal-title":"IEEE Trans Instrum Meas"},{"key":"11658_CR39","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1016\/j.advengsoft.2016.02.010","volume":"97","author":"B Stojanovic","year":"2016","unstructured":"Stojanovic B, Milivojevic M, Milivojevic N, Antonijevic D (2016) A self-tuning system for dam behavior modeling based on evolving artificial neural networks. Adv Eng Softw 97:85\u201395. https:\/\/doi.org\/10.1016\/j.advengsoft.2016.02.010","journal-title":"Adv Eng Softw"},{"key":"11658_CR40","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1007\/s00779-016-0916-x","volume":"20","author":"X Luo","year":"2016","unstructured":"Luo X, Lv Y, Zhou M, Wang W, Zhao W (2016) A laguerre neural network-based ADP learning scheme with its application to tracking control in the Internet of Things. Pers Ubiquit Comput 20:361\u2013372. https:\/\/doi.org\/10.1007\/s00779-016-0916-x","journal-title":"Pers Ubiquit Comput"},{"key":"11658_CR41","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1016\/j.asoc.2015.10.069","volume":"43","author":"S Mall","year":"2016","unstructured":"Mall S, Chakraverty S (2016) Application of Legendre neural network for solving ordinary differential equations. Appl Soft Comput 43:347\u2013356. https:\/\/doi.org\/10.1016\/j.asoc.2015.10.069","journal-title":"Appl Soft Comput"},{"key":"11658_CR42","unstructured":"Bello I, Zoph B, Vasudevan V, Le QV (2024) Neural Optimizer Search with Reinforcement Learning, In: Proceedings of the 34th International Conference on Machine Learning, PMLR, 2017: pp. 459\u2013468. https:\/\/proceedings.mlr.press\/v70\/bello17a.html (accessed March 6)."},{"key":"11658_CR43","doi-asserted-by":"publisher","first-page":"686","DOI":"10.1016\/j.jcp.2018.10.045","volume":"378","author":"M Raissi","year":"2019","unstructured":"Raissi M, Perdikaris P, Karniadakis GE (2019) Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J Comput Phys 378:686\u2013707. https:\/\/doi.org\/10.1016\/j.jcp.2018.10.045","journal-title":"J Comput Phys"},{"key":"11658_CR44","doi-asserted-by":"publisher","first-page":"103003","DOI":"10.1016\/j.dsp.2021.103003","volume":"112","author":"Y Chen","year":"2021","unstructured":"Chen Y, Yu H, Meng X, Xie X, Hou M, Chevallier J (2021) Numerical solving of the generalized Black-Scholes differential equation using Laguerre neural network. Digit Signal Process 112:103003. https:\/\/doi.org\/10.1016\/j.dsp.2021.103003","journal-title":"Digit Signal Process"},{"key":"11658_CR45","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1186\/s13662-022-03676-x","volume":"2022","author":"NA Khan","year":"2022","unstructured":"Khan NA, Sulaiman M, Kumam P, Alarfaj FK (2022) Application of Legendre polynomials based neural networks for the analysis of heat and mass transfer of a non-Newtonian fluid in a porous channel. Adv Contin Discrete Models 2022:7. https:\/\/doi.org\/10.1186\/s13662-022-03676-x","journal-title":"Adv Contin Discrete Models"},{"key":"11658_CR46","doi-asserted-by":"publisher","first-page":"48","DOI":"10.1016\/j.camwa.2022.12.008","volume":"132","author":"S Tang","year":"2023","unstructured":"Tang S, Feng X, Wu W, Xu H (2023) Physics-informed neural networks combined with polynomial interpolation to solve nonlinear partial differential equations. Comput Math Appl 132:48\u201362. https:\/\/doi.org\/10.1016\/j.camwa.2022.12.008","journal-title":"Comput Math Appl"},{"key":"11658_CR47","doi-asserted-by":"publisher","first-page":"101757","DOI":"10.1016\/j.csite.2022.101757","volume":"30","author":"S Hosseinzadeh","year":"2022","unstructured":"Hosseinzadeh S, Hosseinzadeh Kh, Hasibi A, Ganji DD (2022) Thermal analysis of moving porous fin wetted by hybrid nanofluid with trapezoidal, concave parabolic and convex cross sections. Case Stud Therm Eng 30:101757. https:\/\/doi.org\/10.1016\/j.csite.2022.101757","journal-title":"Case Stud Therm Eng"},{"key":"11658_CR48","doi-asserted-by":"publisher","first-page":"102825","DOI":"10.1016\/j.csite.2023.102825","volume":"44","author":"MM AlBaidani","year":"2023","unstructured":"AlBaidani MM, Mishra NK, Alam MM, Eldin SM, AL-Zahrani AA, Akgul A, (2023) Numerical analysis of magneto-radiated annular fin natural-convective heat transfer performance using advanced ternary nanofluid considering shape factors with heating source. Case Stud Therm Eng 44:102825. https:\/\/doi.org\/10.1016\/j.csite.2023.102825","journal-title":"Case Stud Therm Eng"},{"key":"11658_CR49","doi-asserted-by":"publisher","first-page":"680","DOI":"10.1108\/MMMS-08-2022-0153","volume":"19","author":"J Raza","year":"2023","unstructured":"Raza J, Raza M, Mustaq T, Qureshi MI (2023) Supervised machine learning techniques for optimization of heat transfer rate of Cu-H2O nanofluid flow over a radial porous fin. Multidiscip Model Mater Struct 19:680\u2013706. https:\/\/doi.org\/10.1108\/MMMS-08-2022-0153","journal-title":"Multidiscip Model Mater Struct"},{"key":"11658_CR50","doi-asserted-by":"publisher","first-page":"112010","DOI":"10.1063\/5.0176926","volume":"35","author":"CS Raju","year":"2023","unstructured":"Raju CS, Sajjan K, Yook SJ (2023) Heat transfer characteristics of rectangular\/triangular\/convex-shaped fins filled with hybrid nanoparticles under dry and wet conditions. Phys Fluids 35:112010. https:\/\/doi.org\/10.1063\/5.0176926","journal-title":"Phys Fluids"},{"key":"11658_CR51","doi-asserted-by":"publisher","first-page":"9528","DOI":"10.1038\/s41598-023-36418-4","volume":"13","author":"KAM Alharbi","year":"2023","unstructured":"Alharbi KAM, Adnan MZ, Bani-Fwaz SM, Eldin AA (2023) Thermal management in annular fin using ternary nanomaterials influenced by magneto-radiative phenomenon and natural convection. Sci Rep 13:9528. https:\/\/doi.org\/10.1038\/s41598-023-36418-4","journal-title":"Sci Rep"},{"key":"11658_CR52","doi-asserted-by":"publisher","first-page":"861","DOI":"10.1140\/epjp\/s13360-023-04459-3","volume":"138","author":"M Ouada","year":"2023","unstructured":"Ouada M, Kezzar M, Talbi N, Eid MR, Sari MR, Yousef WM, Elsaid EM (2023) Heat transfer characteristics of moving longitudinal porous fin wetted with ternary (Cu\u2013Al2O3\u2013TiO2) hybrid nanofluid: ADM solution. Eur Phys J Plus 138:861. https:\/\/doi.org\/10.1140\/epjp\/s13360-023-04459-3","journal-title":"Eur Phys J Plus"},{"key":"11658_CR53","doi-asserted-by":"publisher","first-page":"101438","DOI":"10.1016\/j.jrras.2025.101438","volume":"18","author":"S Riasat","year":"2025","unstructured":"Riasat S, Naz A, Ghachem K, Mir A, Alshammari BM, Kolsi L (2025) Thermal stress analysis of radiated annular fin by considering platelet, hexahedron, and tetrahedron nanoparticles in the presence of magnetic field. J Radiat Res Appl Sci 18:101438. https:\/\/doi.org\/10.1016\/j.jrras.2025.101438","journal-title":"J Radiat Res Appl Sci"},{"key":"11658_CR54","doi-asserted-by":"publisher","DOI":"10.1007\/s10999-025-09761-9","author":"CG Pavithra","year":"2025","unstructured":"Pavithra CG, Gireesha BJ, Gowtham KJ, Sushma S (2025) Hermite wavelet method in thermal performance of porous fin in MoS2-Go-C6H6O2-H2O hybrid nanofluid: a comparative analysis of rectangular, triangular and convex configurations. Int J Mech Mater Des. https:\/\/doi.org\/10.1007\/s10999-025-09761-9","journal-title":"Int J Mech Mater Des"},{"key":"11658_CR55","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1007\/s10483-025-3218-9","volume":"46","author":"CG Pavithra","year":"2025","unstructured":"Pavithra CG, Gireesha BJ, Sushma S, Gowtham KJ (2025) Analysis of convective-radiative heat transfer in dovetail longitudinal fins with shape-dependent hybrid nanofluids: a study using the Hermite wavelet method. Appl Math Mech-Engl Ed 46:357\u2013372. https:\/\/doi.org\/10.1007\/s10483-025-3218-9","journal-title":"Appl Math Mech-Engl Ed"},{"key":"11658_CR56","doi-asserted-by":"publisher","first-page":"106069","DOI":"10.1016\/j.icheatmasstransfer.2022.106069","volume":"135","author":"W Cao","year":"2022","unstructured":"Cao W, I.l. A, Yook S-J, V.a. O, Ji X (2022) Simulation of the dynamics of colloidal mixture of water with various nanoparticles at different levels of partial slip: ternary-hybrid nanofluid. Int Commun Heat Mass Transf 135:106069. https:\/\/doi.org\/10.1016\/j.icheatmasstransfer.2022.106069","journal-title":"Int Commun Heat Mass Transf"},{"key":"11658_CR57","doi-asserted-by":"publisher","first-page":"103214","DOI":"10.1016\/j.csite.2023.103214","volume":"49","author":"R Girish","year":"2023","unstructured":"Girish R, Salma A, Ananth Subray PV, Hanumagowda BN, Varma SVK, Nagaraja KV, chohan J, Khan U, Hassan AM, Gamaoun F (2023) Effect of temperature-dependent internal heat generation over exponential and dovetail convective-radiative porous fin wetted in hybrid nanofluid. Case Stud Therm Eng 49:103214. https:\/\/doi.org\/10.1016\/j.csite.2023.103214","journal-title":"Case Stud Therm Eng"},{"key":"11658_CR58","doi-asserted-by":"publisher","first-page":"121903","DOI":"10.1063\/5.0179798","volume":"35","author":"BK Sharma","year":"2023","unstructured":"Sharma BK, Gandhi R (2023) Entropy-driven optimization of radiative Jeffrey tetrahybrid nanofluid flow through a stenosed bifurcated artery with Hall effects. Phys Fluids 35:121903. https:\/\/doi.org\/10.1063\/5.0179798","journal-title":"Phys Fluids"},{"key":"11658_CR59","doi-asserted-by":"publisher","first-page":"123114","DOI":"10.1063\/5.0177221","volume":"35","author":"P Mushahary","year":"2023","unstructured":"Mushahary P, Surender O (2023) Mixed convective magnetohydrodynamic and thermally radiative flow of reactive couple stress MWCNT\u2013Ag\/C2H6O2 hybrid nanofluid in a porous vertical channel: entropy analysis. Phys Fluids 35:123114. https:\/\/doi.org\/10.1063\/5.0177221","journal-title":"Phys Fluids"},{"key":"11658_CR60","doi-asserted-by":"publisher","first-page":"102008","DOI":"10.1063\/5.0169236","volume":"35","author":"C Rath","year":"2023","unstructured":"Rath C, Nayak A (2023) A numerical study on MHD Cu-Al2O3\/H2O hybrid nanofluid with Hall current and cross-diffusion effect. Phys Fluids 35:102008. https:\/\/doi.org\/10.1063\/5.0169236","journal-title":"Phys Fluids"},{"key":"11658_CR61","doi-asserted-by":"publisher","first-page":"106241","DOI":"10.1016\/j.icheatmasstransfer.2022.106241","volume":"137","author":"W Xiu","year":"2022","unstructured":"Xiu W, Animasaun IL, Al-Mdallal QM, Alzahrani AK, Muhammad T (2022) Dynamics of ternary-hybrid nanofluids due to dual stretching on wedge surfaces when volume of nanoparticles is small and large: forced convection of water at different temperatures. Int Commun Heat Mass Transf 137:106241. https:\/\/doi.org\/10.1016\/j.icheatmasstransfer.2022.106241","journal-title":"Int Commun Heat Mass Transf"},{"key":"11658_CR62","doi-asserted-by":"publisher","first-page":"987","DOI":"10.1109\/72.712178","volume":"9","author":"IE Lagaris","year":"1998","unstructured":"Lagaris IE, Likas A, Fotiadis DI (1998) Artificial neural networks for solving ordinary and partial differential equations. IEEE Trans Neural Netw 9:987\u20131000. https:\/\/doi.org\/10.1109\/72.712178","journal-title":"IEEE Trans Neural Netw"},{"issue":"15","key":"11658_CR63","doi-asserted-by":"publisher","first-page":"8963","DOI":"10.1007\/s00521-025-11040-9","volume":"37","author":"A Habib","year":"2025","unstructured":"Habib A, Yildirim U (2025) Developing block-based physics-informed multi-layered neural network model for simulating the inelastic response of base-isolated structures. Neural Comput Applic 37(15):8963\u20138986. https:\/\/doi.org\/10.1007\/s00521-025-11040-9","journal-title":"Neural Comput Applic"},{"issue":"22","key":"11658_CR64","doi-asserted-by":"publisher","first-page":"13665","DOI":"10.1007\/s00521-024-09791-y","volume":"36","author":"MA Rahman","year":"2024","unstructured":"Rahman MA, Zhang T, Lu Y (2024) PINN-CHK: physics-informed neural network for high-fidelity prediction of early-age cement hydration kinetics. Neural Comput Appl 36(22):13665\u201313687. https:\/\/doi.org\/10.1007\/s00521-024-09791-y","journal-title":"Neural Comput Appl"},{"issue":"30","key":"11658_CR65","doi-asserted-by":"publisher","first-page":"19097","DOI":"10.1007\/s00521-024-10177-3","volume":"36","author":"J Shi","year":"2024","unstructured":"Shi J, Yang X, Liu X (2024) A novel fractional physics-informed neural networks method for solving the time-fractional Huxley equation. Neural Comput Appl 36(30):19097\u201319119. https:\/\/doi.org\/10.1007\/s00521-024-10177-3","journal-title":"Neural Comput Appl"},{"issue":"16","key":"11658_CR66","doi-asserted-by":"publisher","first-page":"12159","DOI":"10.1007\/s00521-023-08347-w","volume":"35","author":"RA Genedy","year":"2023","unstructured":"Genedy RA, Chung M, Ogejo JA (2023) Physics-informed neural networks for predicting liquid dairy manure temperature during storage. Neural Comput Appl 35(16):12159\u201312174. https:\/\/doi.org\/10.1007\/s00521-023-08347-w","journal-title":"Neural Comput Appl"},{"key":"11658_CR67","doi-asserted-by":"publisher","unstructured":"Lu Y, Weng F, Sun H (2021) Numerical solution for initial and boundary value problems of high-order ordinary differential equations using Hermite neural network algorithm with improved extreme learning machine, https:\/\/doi.org\/10.21203\/rs.3.rs-818207\/v1.","DOI":"10.21203\/rs.3.rs-818207\/v1"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-025-11658-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00521-025-11658-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-025-11658-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T20:15:54Z","timestamp":1761077754000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00521-025-11658-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,20]]},"references-count":67,"journal-issue":{"issue":"32","published-print":{"date-parts":[[2025,11]]}},"alternative-id":["11658"],"URL":"https:\/\/doi.org\/10.1007\/s00521-025-11658-9","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9,20]]},"assertion":[{"value":"4 June 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 September 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 September 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declared no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}