AnalysisofMicro-polarFluidFlowPastaPorousSphereusinganArtificialNeural NetworkApproach
DOI:
https://doi.org/10.5269/bspm.82379Abstract
The study examines the continuous flow of a micro-polar fluid through a porous sphere that is
saturated with a viscous fluid,using an Artificial Neural Network (ANN )approach to determine the optimal
conditions. The stream function describes the velocity field both inside and outside the sphere. The flow is
regulated by non-linear partial differential equations (PDE’s) inrelation to the stream function, which are
subjected to the corresponding boundary conditions. A novel approach to estimate solutions the Navier-Stokes
equations has been developed based on artificial neural networks. We assess the scheme performance and result
correct ness by comparing it with established analytical methods and solutions in the literature. Tables and
graphics present numerical results from analytical and ANN solutions for awide range of physical parameter
values.The results effectiveness improves when the number of neurons and the number of data points in the
neural network increase. Furthermore, incontrast to the analytical approach, the existing ANN model applies
to more complex mathematical frame worksas it diminishes the time and computational resources necessary
for problem solving.
References
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[21] Mohib Hussain ., Hassan Waqas., Bagh Ali., Nehad Ali Shah.: Predicting radiative flow and heat transfer in ternary nanofluids: A hybried graph neural network and finite difference framework with Cattaneo-Christov theory. Thermal Science and Engineering Progress.66,2025, 103982.
[22] Mohib Hussain , Du Lin , Hassan Waqas, Qasem M.AI-Mdallal.:An artificial intelligence and machine learning – driven CFD simulation for optimizing thermal performance of blood-integrated ternary nano-fluid.19,2025, 2459664, https://doi.org/10.1080/19942060.2025.2459664
[23] P. Aparna, V.Ganesh Kumar, P. Padmaja, H. Niranjan.: Viscous fluid flow past a permeable sphere-ANN approach, International Journal of Thermo fluids,30(2025),101475, https://doi.org/10.1016/j.ijft.2025.101475
[24] Ajed Akbar, Hakeem Ullaha, Muhammad Asif Zahoor Raja, Kottakkaran Sooppy Nisar, Saeed Islam, Muhammad Shoaib, A Design of Neural Networks to Study MHD and Heat Transfer in Two Phase Model of Nano-Fluid Flow in the Presence of Thermal Radiation (2022), https://doi.org/10.1080/ 17455030.2022.2152905.
[25] I. E. Lagaris, A. Likas, D. I. Fotiadis, Artificial neural networks for solving ordinary and partial differential equations, IEEE Trans. Neural Networks. 9(5)(1998) 987–1000.
[26] M. L. Piscopo, M. Spannowsky, P. Waite, Solving differential equations with neural networks: Applications to the calculation of cosmological phase transitions, Phys. Rev. D. 100 (2019) 016002
[27] Pothanna Nalimela, Chinthakuntla Thirmal, V. Ganesh Kumar, G. Jithender Reddy, Artificial neural networks analysis of an unsteady fluid flow through a horizontal oscillating flat plate in a porous slab, Physics of Fluids 37, 023140 (2025), https://doi.org/10.1063/5.0253605
[28] Parikshit Sharma, Bhupendra K. Sharma, Madhu Sharma, Bandar Almohse, Kamil Urbanowicz, Entropy generation prediction for nanofluid flow using artificial neural networks: a comparative study of training algorithms, Journal of Thermal Analysis and Calorimetry,150,14477-14500(2025)
[2] E.A. Ashmawy, Slip at the surface of a general axi-symmetric body rotating in a viscous fluid, Arch. Mech. 63 (4) (2011) 341– 36
[3] P. Aparna, J.V. Ramana Murthy, G. Nagaraju, Couple on a rotating permeable sphere in a couple stress fluid, Ain Shams Eng. J. (2016)
[4] Srinivasacharya D, Krishna Prasad M. Steady rotation of a composite sphere in a concentric spherical cavity. Acta Mech Sin 2012;28(3):653–8.
[5] Podila Aparna, Podila Padmaja, Nalimela Pothanna, Josyula Venkata Ramana Murthy, Uniform Flow of Viscous Fluid Past a Porous Sphere Saturated with Micro Polar Fluid, Biointerface Research in Applied Chemistry, 13 (1) (2023) 69.
[6] D.Srinivasacharya, I.Rajyalakshmi,Creeping flow of micropolar fluid past a porous sphere, Applied Mathematics and Computation,153(3)(2004),843-854.
[7] P. Aparna and J.V. Ramana Murthy , Uniform flow of an incompressible micropolar fluid past a permeable sphere, International e-Journal of Engineering Mathematics: Theory and Application, Volume (8), March, 2010, pp.1-10
[8] Nagaraju Gajjela and Podila Aparna, Unsteady Rotatory Oscillations of a Vertical Cylinder In Jeffery Fluid With Ion Slip Currents and Porous Medium, International Journal of Engineering & Technology, 7 (4) (2018) 6592-6596
[9] D. T. Pham and X. Liu, Neural Networks for Identification, Prediction and Control (Springer, London, 1995).
[10] Atul Kaushik and J.V.RamanaMurthy, Computational Analysis of Magnetohydrodynamic Jeffery–Hamel Flow for Couple Stress Fluids in Stretching/Shrinking Channels via Artificial Neural Network, International Journal for Numerical Methods in Engineering, 2025; 126:e70174, https://doi.org/10.1002/nme.70174
[11] H. Lee and I. S. Kang, “Neural algorithm for solving differential equations,” J. Comput. Phys. 91, 110–131 (1990).
[12] N. Yadav, A. Yadav, and M. Kumar, An Introduction to Neural Network Methods for Differential Equations(Springer, Dordrecht, 2015).https://doi.org/10.1007/978-94-017-9816-7
[13] S. Chakraverty and S. Mall, Artificial Neural Networks for Engineers and Scientists: Solving Ordinary Differential Equations (CRC Press, Boca Raton, FL, 2017).https://doi.org/10.1201/9781315155265
[14] A. J. Meade Jr. and A. A. Fernandez, “Solution of nonlinear ordinary differential equations by feedforward neural networks,” Math. Comput. Modell. 20, 19–44 (1994).https://doi.org/10.1016/0895-7177(94)00160-X
[15] M. F. Shahri and A. H. Nezhad, “Estimation of the flow and heat transfer in MHD flow of a power law fluid over a porous plate using artificial neural networks,” Middle East J. Sci. Res. 22 , 1422–1429 (2014).
[16] M. Ziaei-Rad, M. Saeedan, and E. Afshari, “Simulation and prediction of MHD dissipative nanofluid flow on a permeable stretching surface using artificial neural network,” Appl. Therm. Eng. 99, 373–382 (2016).https://doi.org/10.1016/j.applthermaleng.2016.01.063
[17] P. B. A. Reddy and R. Das, “Estimation of MHD boundary layer slip flow over a permeable stretching cylinder in the presence of chemical reaction through numerical and artificial neural network modeling,” Eng. Sci. Technol.,Int. J. 19, 1108–1116 (2016).https://doi.org/10.1016/j.jestch.2015.12.013
[18] M. Elayarani and M. Shanmugapriya, “Artificial neural network modeling of MHD stagnation point flow and heat transfer towards a porous stretching sheet,” AIP Conf. Proc. 2161, 020043 (2019). https://doi.org/10.1063/1.5127634
[19] Mohamed I. Nouha,, Emad A-B Abdel-Salamb , Yosry A. Azzam, Artificial Neural Network Approach for Relativistic Polytropes, Scientific African,20, 2023, e01696, https://doi.org/10.1016/j.sciaf.2023.e01696
[20] H. Mutuk, “A neural network study of Blasius equation,” Neural Process. Lett. 51, 2179–2194 (2020).
[21] Mohib Hussain ., Hassan Waqas., Bagh Ali., Nehad Ali Shah.: Predicting radiative flow and heat transfer in ternary nanofluids: A hybried graph neural network and finite difference framework with Cattaneo-Christov theory. Thermal Science and Engineering Progress.66,2025, 103982.
[22] Mohib Hussain , Du Lin , Hassan Waqas, Qasem M.AI-Mdallal.:An artificial intelligence and machine learning – driven CFD simulation for optimizing thermal performance of blood-integrated ternary nano-fluid.19,2025, 2459664, https://doi.org/10.1080/19942060.2025.2459664
[23] P. Aparna, V.Ganesh Kumar, P. Padmaja, H. Niranjan.: Viscous fluid flow past a permeable sphere-ANN approach, International Journal of Thermo fluids,30(2025),101475, https://doi.org/10.1016/j.ijft.2025.101475
[24] Ajed Akbar, Hakeem Ullaha, Muhammad Asif Zahoor Raja, Kottakkaran Sooppy Nisar, Saeed Islam, Muhammad Shoaib, A Design of Neural Networks to Study MHD and Heat Transfer in Two Phase Model of Nano-Fluid Flow in the Presence of Thermal Radiation (2022), https://doi.org/10.1080/ 17455030.2022.2152905.
[25] I. E. Lagaris, A. Likas, D. I. Fotiadis, Artificial neural networks for solving ordinary and partial differential equations, IEEE Trans. Neural Networks. 9(5)(1998) 987–1000.
[26] M. L. Piscopo, M. Spannowsky, P. Waite, Solving differential equations with neural networks: Applications to the calculation of cosmological phase transitions, Phys. Rev. D. 100 (2019) 016002
[27] Pothanna Nalimela, Chinthakuntla Thirmal, V. Ganesh Kumar, G. Jithender Reddy, Artificial neural networks analysis of an unsteady fluid flow through a horizontal oscillating flat plate in a porous slab, Physics of Fluids 37, 023140 (2025), https://doi.org/10.1063/5.0253605
[28] Parikshit Sharma, Bhupendra K. Sharma, Madhu Sharma, Bandar Almohse, Kamil Urbanowicz, Entropy generation prediction for nanofluid flow using artificial neural networks: a comparative study of training algorithms, Journal of Thermal Analysis and Calorimetry,150,14477-14500(2025)
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2026-06-19
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Conf. Issue: Recent Trends in Mathematical Sciences and Technological Applic.
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How to Cite
Podila, A., Kuruva Krishna Murthy, D. Sarath Chandra, Muduganti, M. K. R., & Atul Kaushik. (2026). AnalysisofMicro-polarFluidFlowPastaPorousSphereusinganArtificialNeural NetworkApproach. Boletim Da Sociedade Paranaense De Matemática, 44(17), 1-14. https://doi.org/10.5269/bspm.82379
