Analysis of incompressible viscous fluid flow in convergent and divergent channels with a hybrid meta-heuristic optimization techniques in ANN: An intelligent approach

Abstract

In this research article, we introduce a numerical investigation through artificial neural networks (ANN) integrated with evolutionary algorithm especially Archimedean optimization algorithm (AOA) hybrid with the water cycle algorithm (WCA) to address and enhance the analysis of the non-linear magneto-hydrodynamic (MHD) Jeffery-Hamel problem, especially stretching/shrinking in convergent and divergent channel. This combined technique is referred to as ANN-AOA-WCA. The complex nonlinear magneto-hydrodynamic Jeffery-Hamel problem based partial differential equations are transformed into non-linear system of ordinary differential equations for velocity and temperature. We formulate the ANN based fitness function to find the solution of non-linear differential. Subsequently, we employ a novel hybridization of AOA and WCA (AOA-WCA) to optimize the ANN based fitness function and identify the best optimal weights and biases for ANN. To demonstrate the effectiveness and versatility of our proposed hybrid method, we explore MHD models across a range of Reynolds numbers, channel angles and stretchable boundary value leading to the development of two distinct cases. ANN-AOA-WCA numerical results closely align with reference solutions (NDSOLVE) and the absolute error between NDSOLVE and ANN-AOA-WCA is up to 3.35 × 10⁻⁸, particularly critical to the understanding of stretchable convergent and divergent channel. Furthermore, to validate the ANN-AOA-WCA technique, we conducted a statistical analysis over 150 independence runs to find the fitness value.

Keywords

ANN / Archimedes optimization / water cycle algorithm / stretching/shrinking surface / convergent/divergent channel

References

[1] JefferyG B L. The two-dimensional steady motion of a viscous fluid [J]. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1915, 29(172): 455-465

[2] HamelG. Spiralförmige Bewegungen zäher Flüssigkeiten [J]. Jahresbericht der Deutschen Mathematiker-Vereinigung, 1917, 25: 34-60

[3] PapavasileiouP, KoronakiE D, PozzettiG, et al. . An efficient chemistry-enhanced CFD model for the investigation of the rate-limiting mechanisms in industrial Chemical Vapor Deposition reactors [J]. Chemical Engineering Research and Design, 2022, 186: 314-325

[4] DingE, LiuP, KhanA T, et al. . Towards the synthesis of semiconducting single-walled carbon nanotubes by floating-catalyst chemical vapor deposition: Challenges of reproducibility [J]. Carbon, 2022, 195: 92-100

[5] ArainM B, ZeeshanA, BhattiM M, et al. . Description of non-Newtonian bioconvective Sutterby fluid conveying tiny particles on a circular rotating disk subject to induced magnetic field [J]. Journal of Central South University, 2023, 30(8): 2599-2615

[6] ZHANG Ze-long, SUN Qiang, WANG Cheng, et al. Numerical simulation and experimental study on a DC multi-cathode arc plasma generator [J]. Plasma Chemistry and Plasma Processing, 2023: 1–17. DOI: https://doi.org/10.1007/s11090-023-10377-0.

[7] LiuE, PengY, JiY, et al. . Energy consumption optimization model of large parallel natural gas pipeline network: Using compressors with multiple operating modes [J]. Energy & Fuels, 2023, 37(1): 774-784

[8] RosenheadL. The steady two-dimensional radial flow of viscous fluid between two inclined plane walls [J]. Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences, 1940, 175(963): 436-467

[9] MillsapsK, PohlhausenK. Thermal distributions in Jeffery-Hamel flows between nonparallel plane walls [J]. Journal of the Aeronautical Sciences, 1953, 20(3): 187-196

[10] RileyN. Heat transfer in jeffery-hamel flow [J]. The Quarterly Journal of Mechanics and Applied Mathematics, 1989, 42(2): 203-211

[11] FraenkelL E. Laminar flow in symmetrical channels with slightly curved walls, I. On the Jeffery-Hamel solutions for flow between plane walls [J]. Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences, 1962, 267(1328): 119-138

[12] TerrillR M. Slow laminar flow in a converging or diverging channel with suction at one wall and blowing at the other wall [J]. Journal of Applied Mathematics and Physics (ZAMP), 1965, 16(2): 306-308

[13] Schlichting DeceasedH, GerstenKBoundarylayer control (suction/blowing) [M], 2017, Berlin, Heidelberg, Springer: 291320

[14] RoyJ S, NayakP. Steady two dimensional incompressible laminar visco-elastic flow in a converging or diverging channel with suction and injection [J]. Acta Mechanica, 1982, 43(1): 129-136

[15] AhmadS, FarooqM. Double-diffusive Hamel-Jeffrey flow of nanofluid in a convergent/divergent permeable medium under zero mass flux [J]. Scientific Reports, 2023, 13: 1102

[16] KumbinarasaiahS, RaghunathaK R. Numerical solution of the Jeffery–Hamel flow through the wavelet technique [J]. Heat Transfer, 2022, 51(2): 1568-1584

[17] HaddoutY, EssaghirE, RafikiA, et al. . The Graetz problem extended to Jeffery-Hamel flow through a convergent plate channel with step-change in wall temperature and streamwise conduction [J]. International Communications in Heat and Mass Transfer, 2022, 134105986

[18] RaghunathaK R, SiddanagowdruS O. Investigation of Jeffery–Hamel flow with high magnetic field and nanoparticle by DTM [J]. Heat Transfer, 2022, 51(4): 3562-3572

[19] AsgharZ, SaifR S, GhaffariA Z. Numerical study of boundary stresses on Jeffery-Hamel flow subject to Soret/Dufour effects [J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2023, 237(5): 1088-1105

[20] HassanM, RizwanM, BhattiM M. Investigating the influence of temperature-dependent rheological properties on nanofluid behavior in heat transfer [J]. Nanotechnology, 2023, 34(50): 505404

[21] AliF M, NazarR, ArifinN M, et al. . MHD stagnationpoint flow and heat transfer towards stretching sheet with induced magnetic field [J]. Applied Mathematics and Mechanics, 2011, 324409-418

[22] UstaO B, ButlerJ E, LaddA J C. Flow-induced migration of polymers in dilute solution [J]. Physics of Fluids, 2006, 18(3): 031703

[23] FatimaA, SagheerM, HussainS. A study of inclined magnetically driven Casson nanofluid using the Cattaneo-Christov heat flux model with multiple slips towards a chemically reacting radially stretching sheet [J]. Journal of Central South University, 2023, 30113721-3736

[24] FarhanaK, MahamudeA S F, KadirgamaK. Numerical study of solar tray with noble Mxene nanofluids [J]. Journal of Central South University, 2023, 30(11): 3656-3669

[25] AkinshiloA T, IlegbusiA O, AliH M, et al. . Impact of melting and radiation on MHD mixed convective heat transfer slip flow through vertical porous embedded microchannel [J]. Journal of Central South University, 2023, 30(11): 3670-3681

[26] KumbinarasaiahS, RaghunathaK R, PreethamM P. Applications of Bernoulli wavelet collocation method in the analysis of Jeffery-Hamel flow and heat transfer in Eyring-Powell fluid [J]. Journal of Thermal Analysis and Calorimetry, 2023, 148(3): 1173-1189

[27] UmavathiJ C. Jeffery-hamel flow in conducting nanofluid: Non-darcy model [J]. Nanoscience and Technology: an International Journal, 2023, 14(4): 17-30

[28] ChandraP, DasR. A hybrid RSA-IPA optimizer for designing an artificial neural network to study the Jeffery-Hamel blood flow with copper nanoparticles: Application to stenotic tapering artery [J]. Results in Engineering, 2023, 20101542

[29] SelimefendigilF, ÖztopH F, Abu-HamdehN. Phase change dynamics in a triangular elastic walled vented cavity having phase change material packed bed during nanofluid forced convection [J]. Journal of Central South University, 2023, 30(11): 3630-3640

[30] AzharE, KamranA. Analysis of magnetomicrostructural improvisation of Jeffery-Hamel flow of a viscoelastic fluid [J]. Journal of Central South University, 2023, 30(6): 1763-1775

[31] YangL, ZhangD, KarniadakisG E. Physics-informed generative adversarial networks for stochastic differential equations [J]. SIAM Journal on Scientific Computing, 2020, 42(1): A292-A317

[32] RAISSI M. Forward-backward stochastic neural networks: Deep learning of high-dimensional partial differential equations [EB/OL]. 2018: arXiv: 1804.07010. https://arxiv.org/abs/1804.07010.pdf

[33] MattheakisM, SondakD, DograA S, et al. . Hamiltonian neural networks for solving equationsof motion [J]. Physical Review E, 2022, 105(6): 065305

[34] MATTHEAKIS M, PROTOPAPAS P, SONDAK D, et al. Physical symmetries embedded in neural networks [EB/OL]. 2019: arXiv: 1904.08991. https://arxiv.org/abs/1904.08991.pdf

[35] RaissiM, PerdikarisP, KarniadakisG E. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations [J]. Journal of Computational Physics, 2019, 378686-707

[36] PiscopoM L, SpannowskyM, WaiteP. Solving differential equations with neural networks: Applications to the calculation of cosmological phase transitions [J]. Physical Review D, 2019, 100016002

[37] HAGGE T, STINIS P, YEUNG E, et al. Solving differential equations with unknown constitutive relations as recurrent neural networks [EB/OL]. 2017: arXiv: 1710.02242. https://arxiv.org/abs/1710.02242.pdf

[38] LiuH, DengD H. An enhanced hybrid ensemble deep learning approach for forecasting daily PM_2.5 [J]. Journal of Central South University, 2022, 29(6): 2074-2083

[39] XueZ, LiT, PengS T, ZhangC Y, et al. . A data-driven method to predict future bottlenecks in a remanufacturing system with multi-variant uncertainties [J]. Journal of Central South University, 2022, 29(1): 129-145

[40] AzarW A, NazarP S. An optimized and chaotic intelligent system for a 3DOF rehabilitation robot for lower limbs based on neural network and genetic algorithm [J]. Biomedical Signal Processing and Control, 2021, 69102864

[41] ASLAM M N, RIAZ A, SHAUKAT N, et al. Machine learning analysis of heat transfer and electroosmotic effects on multiphase wavy flow: A numerical approach [J]. International Journal of Numerical Methods for Heat & Fluid Flow. 2023. DOI: https://doi.org/10.1108/hff-07-2023-0387.2023

[42] RAISSI M. Forward - backward stochastic neural networks: Deep learning of high-dimensional partial differential equations [M]//Peter Carr Gedenkschrift. 637–655: WORLD Scientific, 2023: 637–655. DOI: https://doi.org/10.1142/9789811280306_0018.

[43] AslamM N, ShaheenA, RiazA, et al. . An ANN-PSO approach for mixed convection flow in an inclined tube with ciliary motion of Jeffrey six constant fluid [J]. Case Studies in Thermal Engineering, 2023, 52103740

[44] AdelW, BiçerK E, SezerM. A novel numerical approach for simulating the nonlinear MHD jeffery-hamel flow problem [J]. International Journal of Applied and Computational Mathematics, 2021, 7(3): 1-15

[45] RanaS, MehmoodR, BhattiM M, et al. . Swimming of motile gyrotactic microorganisms and suspension of nanoparticles in a rheological Jeffery fluid with Newtonian heating along elastic surface [J]. Journal of Central South University, 2021, 28(11): 3279-3296

[46] ZhangL, BhattiM M, MichaelidesE E, et al. . Characterizing quadratic convection and electromagnetically induced flow of couple stress fluids in microchannels [J]. Qualitative Theory of Dynamical Systems, 2024, 23(1): 35

[47] TurkyilmazogluM. Extending the traditional Jeffery-Hamel flow to stretchable convergent/divergent channels [J]. Computers & Fluids, 2014, 100196-203

[48] BuhlJ, SumpterD J T, CouzinI D, et al. . From disorder to order in marching locusts [J]. Science, 2006, 312(5778): 1402-1406

[49] BlumC, LiXBlumC, MerkleD. Swarm intelligence in optimization [M]. Swarm Intelligence, 2008, Berlin, Heidelberg, Springer: 43-85

[50] HashimF A, HussainK, HousseinE H, et al. . Archimedes optimization algorithm: A new metaheuristic algorithm for solving optimization problems [J]. Applied Intelligence, 2021, 51(3): 1531-1551

[51] SadollahA, EskandarH, LeeH M, et al. . Water cycle algorithm: A detailed standard code [J]. SoftwareX, 2016, 5: 37-43

[52] JiangQ, WangL, HeiX. Parameter identification of chaotic systems using artificial raindrop algorithm [J]. Journal of Computational Science, 2015, 8: 20-31