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Artificial neural network modeling of MHD slip-flow over a permeable stretching surface

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Abstract

In this work, we consider the flow of magnetohydrodynamic (MHD) fluid over a permeable surface due to continuous stretching. The stretching surface is subject to a constant magnetic field along normal direction and velocity-slip conditions. This flow is governed by nonlinear partial differential equations (PDEs) subject to associated boundary conditions. The similarity transformation technique was applied to obtain their non-dimensional form, coupled with nonlinear ordinary differential equations (ODEs). MATLAB-based program “bvp5c” was then used to obtain their numerical solution. Two artificial neural network models were also presented for predicting the coefficients of skin friction \(- f^{\prime \prime } \left( 0 \right)\) and heat transfer rate \(- \theta^{\prime } \left( 0 \right)\). The present study revealed that heat transfer rate is decreased due to increases in first- and second-order slip parameters. Results also showed that neural network models can predict thermal conductivity with high accuracy. High R squared values of 0.99 were achieved for predicting coefficients of skin friction \(- f^{\prime \prime } \left( 0 \right)\) and heat transfer rate \(- \theta^{\prime } \left( 0 \right)\). This shows the effectiveness of neural network models for predicting those characteristics and thus reducing the time required for numerical models for predicting MHD slip flow over a permeable stretching surface. Moreover, in comparison with the other numerical methods, the present ANN model can be applied to more complex mathematical models because it reduces the time and processing capacity required for solving the problem.

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References

  1. Fischer, E.G.: Extrusion of Plastics. Wiley, New York (1976)

    Google Scholar 

  2. Sakiadis, B.C.: Boundary layer behaviour on continuous solid surfaces: II. Boundary layer on a continuous flat surface. AIChE J. 7, 221–225 (1961)

    Article  Google Scholar 

  3. Crane, L.: Flow past a stretching plate. MJ. Math. Phys. 21, 645–647 (1970)

    Google Scholar 

  4. Wang, C.Y.: The three-dimensional flow due to a stretching flat surface. Phys. Fluids 27, 1915–1917 (1984)

    Article  MathSciNet  Google Scholar 

  5. Cortell, R.: Flow and heat transfer of an electrically conducting fluid of second grade over a stretching sheet subject to suction and to a transverse magnetic field. Int. J. Heat Mass Transf. 49, 1851–1856 (2006)

    Article  Google Scholar 

  6. Arnold, J.C., Asir, A.A., Somasundaram, A., Christopher, T.: Heat transfer in a viscoelastic boundary layer flow over a stretching sheet. Int. J. Heat Mass Transf. 53, 1112–1118 (2010)

    Article  Google Scholar 

  7. Maxwell, J.C.: On stresses in rarified gases arising from inequalities of temperature. Philos. Trans. R. Soc. 170, 231–256 (1879)

    Article  Google Scholar 

  8. Hsia, Y.T., Domoto, G.A.: An experimental investigation of molecular rarefaction effects in gas lubricated bearings at ultra-low clearances. J. Lubr. Technol. 105, 120–129 (1983)

    Article  Google Scholar 

  9. Fukui, S., Kaneko, R.: A database for interpolation of poiseuille flow rates for high knudsen number lubrication problems. J. Tribol. 112, 78–83 (1990)

    Article  Google Scholar 

  10. Mitsuya, Y.: Modified Reynolds equation for ultra-thin film gas lubrication using 1.5-Order slip-flow model and considering surface accommodation coefficient. J. Tribol. 115, 289–294 (1993)

    Article  Google Scholar 

  11. Wu, L.: A slip model for rarefied gas flows at arbitrary Knudsen number. Appl. Phys. Lett. 93, 253103 (2008)

    Article  Google Scholar 

  12. Fang, T., Yao, S., Zhang, J., Aziz, A.: Viscous flow over a shrinking sheet with a second order slip flow model. Commun. Nonlinear Sci. Numer. Simulat. 15, 1831–1842 (2010)

    Article  MathSciNet  Google Scholar 

  13. Rosca, A.V., Pop, I.: Flow and heat transfer over a vertical permeable stretching/shrinking sheet with a second order slip. Int. J. Heat Mass Transf. 60, 355–364 (2013)

    Article  Google Scholar 

  14. Mishra, U., Singh, G.: Dual solutions of mixed convection flow with momentum and thermal slip flow over a permeable shrinking cylinder. Comput. Fluids 93, 107–115 (2014)

    Article  MathSciNet  Google Scholar 

  15. Aly, E.H., Vajravelu, K.: Exact and numerical solutions of MHD nano boundary layer flow over stretching surfaces in a porous medium. Appl. Math. Comput. 232, 191–204 (2014)

    MathSciNet  MATH  Google Scholar 

  16. Abdul Hakeem, A.K., VishnuGanesh, N., Ganga, B.: Magnetic field effect on second order slip flow of nanofluid over a stretching/shrinking sheet with thermal radiation effect. J. Magn. Magn. Mater. 381, 243–257 (2015)

    Article  Google Scholar 

  17. Nandeppanavar, M.M., Vajravelu, K., SubhasAbel, M., Siddalingappa, M.N.: Second order slip flow and heat transfer over a stretching sheet with non-linear Navier boundary condition. Int. J. Therm. Sci. 58, 143–150 (2012)

    Article  Google Scholar 

  18. Turkyilmazoglu, M.: Heat and mass transfer of MHD second order slip flow. Comput. Fluids 71, 426–434 (2013)

    Article  MathSciNet  Google Scholar 

  19. Soomro, F.A., Usman, M., Haq, R.U., Wang, W.: Thermal and velocity slip effects on MHD mixed convection flow of Williamson nanofluid along a vertical surface: Modified Legendre wavelets approach. Physica E 104, 130–137 (2018)

    Article  Google Scholar 

  20. Bhatti, M.M., Phali, L., Khalique, C.M.: Heat transfer effects on electro-magnetohydrodynamic Carreau fluid flow between two micro-parallel plates with Darcy–Brinkman–Forchheimer medium. Arch. Appl. Mech. 91, 1683–1695 (2021)

    Article  Google Scholar 

  21. Zhang, L., Bhatti, M.M., Michaelides, E.E., Marin, M., Ellahi, R.: Hybrid nanofluid flow towards an elastic surface with tantalum and nickel nanoparticles, under the influence of an induced magnetic field. Eur. Phys. J. Special Topics (2021). https://doi.org/10.1140/epjs/s11734-021-00409-1

    Article  Google Scholar 

  22. Bhatti, M.M., Al-Khaled, K., Khan, S.U., Chamman, W., Awais, M.: Dracy-Forchheimer higher-order flow of Erying–Powell nanofluid with nonlinear thermal radiation and bioconvection phenomenon. Sci. Technol. J. Dispers. (2021). https://doi.org/10.1080/01932691.2021.1942035

    Article  Google Scholar 

  23. Alamir, M.A.: A Novel acoustic sciene classification model using the late fusion of convolutional neural networks and different ensembles classifiers. Appl. Acoust. 175, 107829 (2021)

    Article  Google Scholar 

  24. Alamir, M.A.: An enhanced artificial neural network model using the Harris Hawks optimizer for predicting food liking in the presence of background noise. Appl. Acoust. 178, 108022 (2021)

    Article  Google Scholar 

  25. Asghar, A., Mirjalili, S., Faris, H., Aljarah, I.: Harris hawks optimization: algorithm and applications. Future Gener. Comput. Syst. 97, 849–872 (2019)

    Article  Google Scholar 

  26. Bala AnkiReddy, P., Das, R.: 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)

    Google Scholar 

  27. Ziaei-Rad, M., Saeedan, M., Afshari, E.: Simulation and prediction of MHD dissipative nanofluid flow on a permeable stretching surface using artificial neural network. Appl. Therm. Eng. 99, 373–382 (2016)

    Article  Google Scholar 

  28. Elayarani, M., Shanmugapriya, M.: Artificial neural network modeling of MHD stagnation point flow and heat transfer towards a porous stretching sheet. AIP Conf. Proc. 2161, 020043 (2019)

    Article  Google Scholar 

  29. Shafiq, A., Colak, A.B., Sindhu, T.N., Al-Mdallal, Q.M., Abdelijawad, T.: Estimation of unsteady hydromagnetic Williamson fluid flow in a radiative surface through numerical and artificial neural network modeling. Sci. Rep. 11, 14509 (2021)

    Article  Google Scholar 

  30. Soomro, F.A., Haq, R.U., Hamid, M.: Brownian motion and thermophoretic effects on non-Newtonian nanofluid flow via Crank–Nicolson Scheme. Arch. Appl. Mech. (2021). https://doi.org/10.1007/s00419-021-01966-6

    Article  Google Scholar 

  31. Essa, F.A., Elaziz, M.A., Elsheikh, A.H.: An enhanced productivity prediction model of active solar still using artificial neural network and Harris Hawks optimizer. Appl. Therm. Eng. 10, 115020 (2020)

    Article  Google Scholar 

  32. Karlik, B., Olgac, A.V.: Performance analysis of various activation functions in generalized MLP architectures of neural networks. Int. J. Artif. Intell. Expert Syst. 1(4), 111–122 (2011)

    Google Scholar 

  33. Zamanlooy, B., Mirhassani, M.: Efficient VLSI implementation of neural networks with hyperbolic tangent activation function. IEEE Trans. Very Large Scale Integr. Syst 22(1), 39–48 (2013)

    Article  Google Scholar 

  34. Alamir, M.A.: An artificial neural network model for predicting the performance of thermoacoustic refrigerator. Int. J. Heat Mass Transf. 164, 120551 (2021)

    Article  Google Scholar 

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Acknowledgements

This study was supported by Princess Nourah bint Abdulrahman University through Researchers Supporting Project number (PNURSP2022R154), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.

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Authors and Affiliations

  1. Department of Basic Sciences and Related Studies, Quaid-e-Awam University of Engineering, Science and Technology, Larkana, 77150, Pakistan

    Feroz Ahmed Soomro

  2. VIPAC Engineers and Scientists, 279 Normanby Rd, Port Melbourne, VIC, 3207, Australia

    Mahmoud A. Alamir

  3. Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P. O. Box 84428, Riyadh, 11671, Saudi Arabia

    Shreen El-Sapa

  4. Department of Electrical Engienering, Bahria University, Islamabad, Pakistan

    Rizwan Ul Haq

  5. Department of Mathematics and Statistics, Quaid-e-Awam University of Engineering, Science and Technology, Nawabshah, 67480, Pakistan

    Muhammad Afzal Soomro

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  1. Feroz Ahmed Soomro
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  2. Mahmoud A. Alamir
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  3. Shreen El-Sapa
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  4. Rizwan Ul Haq
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Correspondence to Feroz Ahmed Soomro.

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Soomro, F.A., Alamir, M.A., El-Sapa, S. et al. Artificial neural network modeling of MHD slip-flow over a permeable stretching surface. Arch Appl Mech 92, 2179–2189 (2022). https://doi.org/10.1007/s00419-022-02168-4

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  • DOI: https://doi.org/10.1007/s00419-022-02168-4

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