Home Numerical treatment of squeezing unsteady nanofluid flow using optimized stochastic algorithm
Article
Licensed
Unlicensed Requires Authentication

Numerical treatment of squeezing unsteady nanofluid flow using optimized stochastic algorithm

  • Ahcene Nouar , Amar Dib , Mohamed Kezzar , Mohamed R. Sari and Mohamed R. Eid EMAIL logo
Published/Copyright: July 29, 2021

Abstract

In this paper, very efficient, intelligent techniques have been used to solve the fourth-order nonlinear ordinary differential equations arising from squeezing unsteady nanofluid flow. The activation functions used to develop the three models are log-sigmoid, radial basis, and tan-sigmoid. The neural network of each scheme is optimized with the interior point method (IPM) to find the weights of the networks. The confrontation of the obtained results with the numerical solutions shows good accuracy of the three schemes. The obtained solutions by utilizing the neural network technique of our variables field (velocity and temperature) are continuous contrary to the discrete form obtained by the numerical scheme.


Corresponding author: Mohamed R. Eid, Department of Mathematics, Faculty of Science, New Valley University, El-Kharga, Al-Wadi Al-Gadid 72511, Egypt; and Department of Mathematics, Faculty of Science, Northern Border University, Arar 1321, Saudi Arabia, E-mail:

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

References

[1] S. U. S. Choi, “Enhancing thermal conductivity of fluids with nanoparticle,” in ASME FED, vol. 231, 1995, pp. 99–105.Search in Google Scholar

[2] J. Buongiorno, “Convective transport in nanofluids,” J. Heat Transfer, vol. 128, pp. 240–250, 2006. https://doi.org/10.1115/1.2150834.Search in Google Scholar

[3] W. Daungthongsuk and S. Wongwises, “A critical review of convective heat transfer nanofluids,” Renew. Sustain. Energy Rev., vol. 11, pp. 797–817, 2007. https://doi.org/10.1016/j.rser.2005.06.005.Search in Google Scholar

[4] X. Q. Wang and A. S. Mujumdar, “A review on nanofluids—part I: theoretical and numerical investigations,” Braz. J. Chem. Eng., vol. 25, pp. 613–630, 2008. https://doi.org/10.1590/s0104-66322008000400001.Search in Google Scholar

[5] X. Q. Wang and A. S. Mujumdar, “A review on nanofluids—part II: experiments and applications,” Braz. J. Chem. Eng., vol. 25, pp. 631–648, 2008. https://doi.org/10.1590/s0104-66322008000400002.Search in Google Scholar

[6] S. Kakaç and A. Pramuanjaroenkij, “Review of convective heat transfer enhancement with nanofluids,” Int. J. Heat Mass Tran., vol. 52, pp. 3187–3196, 2009. https://doi.org/10.1016/j.ijheatmasstransfer.2009.02.006.Search in Google Scholar

[7] M. Sheikholeslami and D. D. Ganji, “Nanofluid flow and heat transfer between parallel plates considering Brownian motion using DTM,” Comput. Methods Appl. Mech. Eng., vol. 283, pp. 651–663, 2015. https://doi.org/10.1016/j.cma.2014.09.038.Search in Google Scholar

[8] A. K. Pandey and M. Kumar, “Squeezing unsteady MHD Cu–water nanofluid flow between two parallel plates in porous medium with suction/injection,” Comput. Appl. Math., vol. 4, no. 2, pp. 31–42, 2018.Search in Google Scholar

[9] A. Dib, A. Haiahem, and B. Bou-said, “Approximate analytical solution of squeezing unsteady nanofluid flow,” Powder Technol., vol. 269, pp. 193–199, 2015. https://doi.org/10.1016/j.powtec.2014.08.074.Search in Google Scholar

[10] M. Turkyilmazoglu, “Natural convective flow of nanofluids past a radiative and impulsive vertical plate,” J. Aero. Eng., vol. 29, no. 6, p. 04016049, 2016. https://doi.org/10.1061/(asce)as.1943-5525.0000643.Search in Google Scholar

[11] M. A. Sheremet and I. Pop, “Mixed convection in a lid-driven square cavity filled by nanofluid: Buongiorno’s mathematical model,” Appl. Math. Comput., vol. 266, pp. 792–808, 2015. https://doi.org/10.1016/j.amc.2015.05.145.Search in Google Scholar

[12] M. Rahimi-Gorji, O. Pourmehran, M. Gorji-Bandpy, and D. D. Ganji, “Unsteady squeezing nanofluid simulation and investigation of its effect on important heat transfer parameters in presence of magnetic field,” J. Taiwan Inst. Chem. Eng., vol. 67, pp. 467–475, 2016. https://doi.org/10.1016/j.jtice.2016.08.001.Search in Google Scholar

[13] T. Hayat, M. Khan, T. Muhammad, and A. Alsaedi, “A useful model for squeezing flow of nanofluid,” J. Mol. Liq., vol. 237, pp. 447–454, 2017. https://doi.org/10.1016/j.molliq.2017.04.111.Search in Google Scholar

[14] S. H. Seyedi, B. N. Saray, and A. Ramazani, “On the multiscale simulation of squeezing nanofluid flow by a high precision scheme,” Powder Technol., vol. 340, pp. 264–273, 2018. https://doi.org/10.1016/j.powtec.2018.08.088.Search in Google Scholar

[15] A. G. Madaki, R. Roslan, M. S. Rusiman, and C. S. K. Raju, “Analytical and numerical solutions of squeezing unsteady Cu and TiO2-nanofluid flow in the presence of thermal radiation and heat generation/absorption,” Alexandria Eng. J., vol. 57, pp. 1033–1040, 2018. https://doi.org/10.1016/j.aej.2017.02.011.Search in Google Scholar

[16] M. I. Khan, M. U. Hafeez, T. Hayat, M. I. Khan, and A. Alsaedi, “Magneto rotating flow of hybrid nanofluid with entropy generation,” Comput. Methods Progr. Biomed., vol. 183, p. 105093, 2020. https://doi.org/10.1016/j.cmpb.2019.105093.Search in Google Scholar PubMed

[17] S. Muhammad, S. I. A. Shah, G. Ali, M. Ishaq, S. A. Hussain, and H. Ullah, “Squeezing nanofluid flow between two parallel plates under the influence of MHD and thermal radiation,” Asian J. Math., vol. 10, no. 1, pp. 1–20, 2018. https://doi.org/10.9734/arjom/2018/42092.Search in Google Scholar

[18] M. Turkyilmazoglu, “Nanoliquid film flow due to a moving substrate and heattransfer,” Eur. Phys. J. Plus, vol. 135, p. 781, 2020. https://doi.org/10.1140/epjp/s13360-020-00812-y.Search in Google Scholar

[19] M. Turkyilmazoglu, “Magnetic field and slip effects on the flow and heat transfer of stagnation point Jeffrey fluid over deformable surfaces,” Z. Naturforsch. A, vol. 71, no. 6, pp. 549–556, 2016. https://doi.org/10.1515/zna-2016-0047.Search in Google Scholar

[20] O. A. Akbari, D. Toghraie, A. Karimipour, et al.., “Investigation of rib’s height effect on heat transfer and flow parameters of laminar water–Al2 O3nanofluid in a rib-microchannel,” Appl. Math. Comput., vol. 290, pp. 135–153, 2016. https://doi.org/10.1016/j.amc.2016.05.053.Search in Google Scholar

[21] H. Upreti, A. K. Pandey, and M. Kumar, “Unsteady squeezing flow of magnetic hybrid nanofluids with in parallel plates and entropy generation,” Heat Transfer, vol. 50, no. 1, pp. 105–125, 2021. https://doi.org/10.1002/htj.21994.Search in Google Scholar

[22] A. K. Pandey and M. Kumar, “Effect of viscous dissipation and suction/injection on MHD nanofluid flow over a wedge with porous medium and slip,” Alexandria Eng. J., vol. 55, no. 4, pp. 3115–3123, 2016. https://doi.org/10.1016/j.aej.2016.08.018.Search in Google Scholar

[23] A. K. Pandey and M. Kumar, “Boundary layer flow and heat transfer analysis on Cu-water nanofluid flow over a stretching cylinder with slip,” Alexandria Eng. J., vol. 56, no. 4, pp. 671–677, 2017. https://doi.org/10.1016/j.aej.2017.01.017.Search in Google Scholar

[24] A. K. Pandey and M. Kumar, “MHD flow inside a stretching/shrinking convergent/divergent channel with heat generation/absorption and viscous-ohmic dissipation utilizing cu–water nanofluid,” Comput. Therm. Sci., vol. 10, no. 5, pp. 457–471, 2018. https://doi.org/10.1615/computthermalscien.2018020807.Search in Google Scholar

[25] A. Mishra, A. K. Pandey, and M. Kumar, “Velocity, thermal and concentration slip effects on MHD silver–water nanofluid flow past a permeable cone with suction/injection and viscous-ohmic dissipation,” Heat Tran. Res., vol. 50, no. 14, pp. 1351–1367, 2019. https://doi.org/10.1615/heattransres.2018020420.Search in Google Scholar

[26] M. A. Z. Raja and R. Samar, “Numerical treatment for nonlinear MHD Jeffery–Hamel problem using neural networks optimized with interior point algorithm,” Neurocomputing, vol. 124, pp. 178–193, 2014. https://doi.org/10.1016/j.neucom.2013.07.013.Search in Google Scholar

[27] M. H. Esfe and S. M. S. Tilebon, “Statistical and artificial based optimization on thermo-physical properties of an oil based hybrid nanofluid using NSGA-II and RSM,” Physica A, vol. 537, p. 122126, 2020. https://doi.org/10.1016/j.physa.2019.122126.Search in Google Scholar

[28] M. A. Abchouyeh, O. S. Fard, R. Mohebbi, and M. A. Sheremet, “Enhancement of heat transfer of nanofluids in the presence of sinusoidal side obstacles between two parallel plates through the lattice Boltzmann method,” Int. J. Mech. Sci., vol. 156, pp. 159–169, 2019. https://doi.org/10.1016/j.ijmecsci.2019.03.035.Search in Google Scholar

[29] S. A. Bagherzadeh, M. T. Sulgani, V. Nikkhah, M. Bahrami, A. Karimipour, and Y. Jiang, “Minimize pressure drop and maximize heat transfer coefficient by the new proposed multi-objective optimization/statistical model composed of “ANN+Genetic Algorithm” based on empirical data of CuO/paraffin nanofluid in a pipe,” Physica A, vol. 527, p. 121056, 2019. https://doi.org/10.1016/j.physa.2019.121056.Search in Google Scholar

[30] A. Jafarian, S. M. Nia, A. K. Golmankhaneh, and D. Baleanu, “On artificial neural networks approach with new cost functions,” Appl. Math. Comput., vol. 339, pp. 546–555, 2018. https://doi.org/10.1016/j.amc.2018.07.053.Search in Google Scholar

[31] Z. Sabir, H. Abdul Wahab, M. Umar, and F. Erdogan, “Stochastic numerical approach for solving second order nonlinear singular functional differential equation,” Appl. Math. Comput., vol. 363, p. 124605, 2019. https://doi.org/10.1016/j.amc.2019.124605.Search in Google Scholar

[32] M. Ghazvini, H. Maddah, R. Peymanfar, M. H. Ahmadi, and R. Kumar, “Experimental evaluation and artificial neural network modeling of thermal conductivity of water based nanofluid containing magnetic copper nanoparticles,” Physica A, vol. 551, p. 124127, 2020. https://doi.org/10.1016/j.physa.2019.124127.Search in Google Scholar

[33] M. Hojjat, “Nanofluids as coolant in a shell and tube heat exchanger: ANN modeling and multi-objective optimization,” Appl. Math. Comput., vol. 365, p. 124710, 2020. https://doi.org/10.1016/j.amc.2019.124710.Search in Google Scholar

[34] H. F. Oztop and E. Abu-Nada, “Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids,” Int. J. Heat Fluid Flow, vol. 29, pp. 1326–1336, 2008. https://doi.org/10.1016/j.ijheatfluidflow.2008.04.009.Search in Google Scholar

[35] G. Domairry and A. Aziz, “Approximate analysis of MHD squeeze flow between two parallel disks with suction or injection by homotopy perturbation method,” Math. Probl Eng., vol. 2009, p. 603916, 2009. https://doi.org/10.1155/2009/603916.Search in Google Scholar

[36] M. Sheikholeslami, D. D. Ganji, and H. R. Ashorynejad, “Investigation of squeezing unsteady nanofluid flow using ADM,” Powder Technol., vol. 239, pp. 259–265, 2013. https://doi.org/10.1016/j.powtec.2013.02.006.Search in Google Scholar

[37] G. Domairry and M. Hatami, “Squeezing Cu–water nanofluid flow analysis between parallel plates by DTM–Padé method,” J. Mol. Liq., vol. 193, pp. 37–44, 2014. https://doi.org/10.1016/j.molliq.2013.12.034.Search in Google Scholar

[38] R. S. Beidokhti and A. Malek, “Solving initial-boundary value problems for systems of partial differential equations using neural networks and optimization techniques,” J. Franklin Inst., vol. 346, no. 9, pp. 898–913, 2009. https://doi.org/10.1016/j.jfranklin.2009.05.003.Search in Google Scholar

[39] D. R. Parisi, M. C. Mariani, and M. A. Laborde, “Solving differential equations with unsupervised neural networks,” Chem. Eng. Process, vol. 42, nos. 8–9, pp. 715–721, 2003. https://doi.org/10.1016/s0255-2701(02)00207-6.Search in Google Scholar

[40] N. Karmarkar, “A new, polynomial time algorithm for linear programming,” Combinatorica, vol. 4, pp. 373–395, 1984. https://doi.org/10.1007/bf02579150.Search in Google Scholar

[41] S. J. Wright, Primal-Dual Interior-Point Methods, Philadelphia, PA, SIAM, 1997.10.1137/1.9781611971453Search in Google Scholar

[42] M. H. Wright, “The interior-point revolution in optimization: history, recent developments, and lasting consequences,” Bull. Am. Math. Soc., vol. 42, pp. 39–56, 2005.10.1090/S0273-0979-04-01040-7Search in Google Scholar

[43] W. Yan, L. Wen, W. Li, C. Y. Chung, and K. P. Wong, “Decomposition–coordination interior point method and its application to multi-area optimal reactive power flow,” Int. J. Electr. Power Energy Syst., vol. 33, no. 1, pp. 55–60, 2011. https://doi.org/10.1016/j.ijepes.2010.08.004.Search in Google Scholar

Received: 2021-06-09
Revised: 2021-07-06
Accepted: 2021-07-07
Published Online: 2021-07-29
Published in Print: 2021-10-26

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 2.12.2025 from https://www.degruyterbrill.com/document/doi/10.1515/zna-2021-0163/html
Scroll to top button