Skip to main content
SpringerLink
Log in

Backpropagated Intelligent Networks for the Entropy Generation and Joule Heating in Hydromagnetic Nanomaterial Rheology Over Surface with Variable Thickness

  • Research Article-Physics
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

In the current study, strength of backpropagated intelligent networks (BINs) is exploited for numerical investigations of entropy characteristics in magnetohydrodynamics (MHD) nanofluidic flow model by varying surface thickness using trained artificial neural networks by Levenberg–Marquardt backpropagation (ANNLMB) procedure. The effects of joule heating, viscous dissipation and heat generation/absorption in the expressions of energy are also considered. The conventional expressions for the governing flow in terms of system of ODEs are taken as a system model. A dataset of the system model is generated by utilizing the strength of Adam numerical method (ANM) for the implementation of proposed ANNLMB for the different scenarios of entropy optimized MHD nanomaterial by varying Hartmann number, power index, Prandtl number, Brownian motion parameter, Brinkman number and Lewis number. The approximate solution of BINs-based solver for different cases of entropy optimized MHD nanomaterial is achieved by performing the training, testing and validation process and comparison with reference result is done for proving the validity and correctness of proposed ANNLMB approach. The performance of the designed ANNLMB for the numerical treatment of entropy optimized MHD nanomaterial problem, to study the influence of prominent parameters on velocity profile, temperature field, concentration profile, is validated on mean squared errors, histograms and regression analyses.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28

Similar content being viewed by others

Abbreviations

u, v :

Velocity component

µ :

Dynamic viscosity

ρ :

Density

ν :

Kinematic viscosity

c p :

Specific heat

τ :

Heat capacity ratio

σ :

Thermal diffusivity

C :

Concentration

T :

Temperature

Q :

Heat generation/absorption coefficient

T ∞ :

Ambient temperature

C∞ :

Ambient concentration

Br :

Brinkman number

D B :

Brownian movement coefficient

Be :

Bejan number

D T :

Thermophoresis diffusion coefficient

N b :

Brownian movement parameter

α:

Thickness parameter

\(L\) :

Diffusion parameter

N G :

Entropy generation rate

H a :

Hartmann number

β:

Heat generation/absorption variable

Le :

Lewis number

n :

Power indices

Pr :

Prandtl number

α 1 :

Temperature difference parameter

N t :

Thermophoresis parameter

\( \varphi (\xi ) \) :

Concentration profile

\(\theta \left( \xi \right)\) :

Temperature profile

\(f^{\prime}\left( \xi \right)\) :

Velocity profile

References:

  1. S.U.S. Choi, J.A. Eastman, Enhancing thermal conductivity of fluids with nanoparticles: the proceedings of the 1995 ASME international mechanical engineering congress and exposition, San Francisco, USA, ASME, FED 231/MD, 66 (1995) 99–105

  2. Ali, B.; Raju, C.S.K.; Ali, L.; Hussain, S.; Kamran, T.: G-Jitter impact on magnetohydrodynamic non-Newtonian fluid over an inclined surface: finite element simulation. Chin. J. Phys. 71, 479–491 (2021)

    Article  MathSciNet  Google Scholar 

  3. Awais, M.; Awan, S.E.; Raja, M.A.Z.; Parveen, N.; Khan, W.U.; Malik, M.Y.; He, Y.: Effects of variable transport properties on heat and mass transfer in MHD bioconvective nanofluid rheology with gyrotactic microorganisms: numerical approach. Coatings 11(2), 231 (2021)

    Article  Google Scholar 

  4. Upadhya, S.M.; Devi, R.R.; Raju, C.S.K.; Ali, H.M.: Magnetohydrodynamic nonlinear thermal convection nanofluid flow over a radiated porous rotating disk with internal heating. J. Therm. Anal. Calorim. 143(3), 1973–1984 (2021)

    Article  Google Scholar 

  5. Awais, M.; Raja, M.A.Z.; Awan, S.E.; Shoaib, M.; Ali, H.M.: Heat and mass transfer phenomenon for the dynamics of Casson fluid through porous medium over shrinking wall subject to Lorentz force and heat source/sink. Alex. Eng. J. 60(1), 1355–1363 (2021)

    Article  Google Scholar 

  6. Abdelmalek, Z.; Hussain, A.; Bilal, S.; Sherif, E.S.M.; Thounthong, P.: Brownian motion and thermophoretic diffusion influence on thermophysical aspects of electrically conducting viscoinelastic nanofluid flow over a stretched surface. J. Market. Res. 9(5), 11948–11957 (2020)

    Google Scholar 

  7. Ge-JiLe, H.; Shah, N.A.; Mahrous, Y.M.; Sharma, P.; Raju, C.S.K.; Upddhya, S.M.: Radiated magnetic flow in a suspension of ferrous nanoparticles over a cone with brownian motion and thermophoresis. Case Stud. Therm. Eng. 25, 100915 (2021)

    Article  Google Scholar 

  8. Irfan, M.: Study of Brownian motion and thermophoretic diffusion on non-linear mixed convection flow of Carreau nanofluid subject to variable properties. Surf. Interfaces 23, 100926 (2021)

    Article  Google Scholar 

  9. Irfan, M.; Farooq, M.A.: Thermophoretic MHD free stream flow with variable internal heat generation/absorption and variable liquid characteristics in a permeable medium over a radiative exponentially stretching sheet. J. Mater. Res. Technol. 9(3), 4855–4866 (2020)

    Article  Google Scholar 

  10. Chu, Y.M.; Hashmi, M.S.; Khan, N.; Khan, S.U.; Khan, M.I.; Kadry, S.; Abdelmalek, Z.: Thermophoretic particles deposition features in thermally developed flow of Maxwell fluid between two infinite stretched disks. J. Market. Res. 9(6), 12889–12898 (2020)

    Google Scholar 

  11. Awan, S.E.; Khan, Z.A.; Awais, M.; Rehman, S.U.; Raja, M.A.Z.: Numerical treatment for hydro-magnetic unsteady channel flow of nanofluid with heat transfer. Res. Phys. 9, 1543–1554 (2018)

    Google Scholar 

  12. Qureshi, I.H.; Awais, M.; Awan, S.E.; Abrar, M.N.; Raja, M.A.Z.; Alharbi, S.O.; Khan, I.: Influence of radially magnetic field properties in a peristaltic flow with internal heat generation: numerical treatment. Case Stud. Therm. Eng. 26, 101019 (2021)

    Article  Google Scholar 

  13. Ahmad, I.; Cheema, T.N.; Raja, M.A.Z.; Awan, S.E.; Alias, N.B.; Iqbal, S.; Shoaib, M.: A novel application of Lobatto IIIA solver for numerical treatment of mixed convection nanofluidic model. Sci. Rep. 11(1), 1–16 (2021)

    Google Scholar 

  14. Sharma, R.; Raju, C.S.; Animasaun, I.L.; Santhosh, H.B.; Mishra, M.K.: Insight into the significance of Joule dissipation, thermal jump and partial slip: dynamics of unsteady ethelene glycol conveying graphene nanoparticles through porous medium. Nonlinear Eng. 10(1), 16–27 (2021)

    Article  Google Scholar 

  15. Parveen, N.; Awais, M.; Awan, S.E.; Khan, W.U.; He, Y.; Malik, M.Y.: Entropy generation analysis and radiated heat transfer in MHD (Al2O3-Cu/Water) hybrid nanofluid flow. Micromachines 12(8), 887 (2021)

    Article  Google Scholar 

  16. Awan, S.E.; Awais, M.; Raja, M.A.Z.; Parveen, N.; Ali, H.M.; Khan, W.U.; He, Y.: Numerical treatment for dynamics of second law analysis and magnetic induction effects on ciliary induced peristaltic transport of hybrid nanomaterial. Front. Phys. 9, 68 (2021)

    Article  Google Scholar 

  17. Raju, S.S.K.; Babu, M.J.; Raju, C.S.K.: Irreversibility analysis in hybrid nanofluid flow between two rotating disks with activation energy and cross-diffusion effects. Chin. J. Phys. 72, 499–529 (2021)

    Article  MathSciNet  Google Scholar 

  18. Marzougui, S.; Mebarek-Oudina, F.; Assia, A.; Magherbi, M.; Shah, Z.; Ramesh, K.: Entropy generation on magneto-convective flow of copper–water nanofluid in a cavity with chamfers. J. Therm. Anal. Calorim. 143(3), 2203–2214 (2021)

    Article  Google Scholar 

  19. Afrand, M.; Pordanjani, A.H.; Aghakhani, S.; Oztop, H.F.; Abu-Hamdeh, N.: Free convection and entropy generation of a nanofluid in a tilted triangular cavity exposed to a magnetic field with sinusoidal wall temperature distribution considering radiation effects. Int. Commun. Heat Mass Transf. 112, 104507 (2020)

    Article  Google Scholar 

  20. Zhang, K.; Liu, M.; Zhao, Y.; Wang, C.; Yan, J.: Entropy generation versus transition time of heat exchanger during transient processes. Energy 200, 117490 (2020)

    Article  Google Scholar 

  21. Basir, M.F.M.; Mabood, F.; Narayana, P.S.; Venkateswarlu, B.; Ismail, A.I.M.: Significance of viscous dissipation on the dynamics of ethylene glycol conveying diamond and silica nanoparticles through a diverging and converging channel. J. Therm. Anal. Calorim. 147(1), 661–674 (2020)

    Article  Google Scholar 

  22. Wang, J.; Muhammad, R.; Khan, M.I.; Khan, W.A.; Abbas, S.Z.: Entropy optimized MHD nanomaterial flow subject to variable thicked surface. Comput. Methods Progr. Biomed. 189, 1053 (2020)

    Article  Google Scholar 

  23. Rasool, G.; Zhang, T.; Chamkha, A.J.; Shafiq, A.; Tlili, I.; Shahzadi, G.: Entropy generation and consequences of binary chemical reaction on MHD Darcy-Forchheimer Williamson nanofluid flow over non-linearly stretching surface. Entropy 22(1), 18 (2020)

    Article  MathSciNet  Google Scholar 

  24. Shoaib, M.; Raja, M.A.Z.; Khan, M.A.R.; Farhat, I.; Awan, S.E.: Neuro-computing networks for entropy generation under the influence of MHD and thermal radiation. Surf. Interfaces 25, 101243 (2021)

    Article  Google Scholar 

  25. Das, R.; Singh, K.; Akay, B.; Gogoi, T.K.: Application of artificial bee colony algorithm for maximizing heat transfer in a perforated fin. Proc. Inst. Mech. Eng. Part E J. Process Mech. Eng. 232(1), 38–48 (2018)

    Article  Google Scholar 

  26. Das, R.: A simulated annealing-based inverse computational fluid dynamics model for unknown parameter estimation in fluid flow problem. Int. J. Comput. Fluid Dyn. 26(9–10), 499–513 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  27. Debnath, B.K.; Das, R.: Prediction of performance coefficients of a three-bucket Savonius rotor using artificial neural network. J. Renew. Sustain. Energy 2(4), 043107 (2010)

    Article  Google Scholar 

  28. Sabir, Z., et al.: Novel design of Morlet wavelet neural network for solving second order Lane-Emden equation. Math. Comput. Simul. 172, 1–14 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  29. Ahmad, I., et al.: Integrated neuro-evolution-based computing solver for dynamics of nonlinear corneal shape model numerically. Neural Comput. Appl. 43(11), 5753–6759 (2020)

    Article  Google Scholar 

  30. Awais, M.; Bibi, M.; Raja, M.A.Z.; Awan, S.E.; Malik, M.Y.: Intelligent numerical computing paradigm for heat transfer effects in a Bodewadt flow. Surf. Interfaces 26, 101321 (2021)

    Article  Google Scholar 

  31. Siraj ul Islam, A., et al.: A new heuristic computational solver for nonlinear singular Thomas-Fermi system using evolutionary optimized cubic splines. Eur. Phys. J. Plus 135(1), 1–29 (2020)

    MathSciNet  Google Scholar 

  32. Umar, M., et al.: A stochastic computational intelligent solver for numerical treatment of mosquito dispersal model in a heterogeneous environment. The European Physical Journal Plus 135(7), 1–23 (2020)

    Article  Google Scholar 

  33. Raja, M.A.Z.; Shah, F.H.; Syam, M.I.: Intelligent computing approach to solve the nonlinear Van der Pol system for heartbeat model. Neural Comput. Appl. 30(12), 3651–3675 (2018)

    Article  Google Scholar 

  34. Nurmaini, S.; Darmawahyuni, A.; Sakti Mukti, A.N.; Rachmatullah, M.N.; Firdaus, F.; Tutuko, B.: Deep learning-based stacked denoising and autoencoder for ECG heartbeat classification. Electronics 9(1), 135 (2020)

    Article  Google Scholar 

  35. Mehmood, A.; Afsar, K.; Zameer, A.; Awan, S.E.; Raja, M.A.Z.: Integrated intelligent computing paradigm for the dynamics of micropolar fluid flow with heat transfer in a permeable walled channel. Appl. Soft Comput. 79, 139–162 (2019)

    Article  Google Scholar 

  36. Bukhari, A.H., et al.: Design of a hybrid NAR-RBFs neural network for nonlinear dusty plasma system. Alex. Eng. J. 59(5), 3325–3345 (2020)

    Article  Google Scholar 

  37. Maulik, R.; Garland, N.A.; Burby, J.W.; Tang, X.Z.; Balaprakash, P.: Neural network representability of fully ionized plasma fluid model closures. Phys. Plasmas 27(7), 072106 (2020)

    Article  Google Scholar 

  38. Li, L.; Lange, C.F.; Xu, Z.; Jiang, P.; Ma, Y.: Feature-based intelligent system for steam simulation using computational fluid dynamics. Adv. Eng. Inform. 38, 357–369 (2018)

    Article  Google Scholar 

  39. Abad, J.M.N.; Alizadeh, R.; Fattahi, A.; Doranehgard, M.H.; Alhajri, E.; Karimi, N.: Analysis of transport processes in a reacting flow of hybrid nanofluid around a bluff-body embedded in porous media using artificial neural network and particle swarm optimization. J. Mol. Liq. 313, 113492 (2020)

    Article  Google Scholar 

  40. Kotlyar, O.; Pankratova, M.; Kamalian-Kopae, M.; Vasylchenkova, A.; Prilepsky, J.E.; Turitsyn, S.K.: Combining nonlinear Fourier transform and neural network-based processing in optical communications. Opt. Lett. 45(13), 3462–3465 (2020)

    Article  Google Scholar 

  41. Hadian Rasanan, A.H.; Bajalan, N.; Parand, K.; Rad, J.A.: Simulation of nonlinear fractional dynamics arising in the modeling of cognitive decision making using a new fractional neural network. Math. Methods Appl. Sci. 43(3), 1437–1466 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  42. Yang, X.; Li, C.; Song, Q.; Chen, J.; Huang, J.: Global Mittag-Leffler stability and synchronization analysis of fractional-order quaternion-valued neural networks with linear threshold neurons. Neural Netw. 105, 88–103 (2018)

    Article  MATH  Google Scholar 

  43. Bukhari, A.H., et al.: Fractional neuro-sequential ARFIMA-LSTM for financial market forecasting. IEEE Access 8, 71326–71338 (2020)

    Article  Google Scholar 

  44. Soloviev, V.; Chernyshenko, V.; Feklin, V.; Zolotareva, E.; Titov, N.: Generative Adversarial neural networking of agents: avatars as tools for financial modelling. In: Mkrttchian, V.; Aleshina, E.; Gamidullaeva, L. (Eds.) Avatar-based control, estimation, communications, and development of neuron multi-functional technology platforms, pp. 107–120. IGI Global, Hershey (2020)

    Chapter  Google Scholar 

  45. Umar, M., et al.: A stochastic intelligent computing with neuro-evolution heuristics for nonlinear SITR system of novel COVID-19 dynamics. Symmetry 12(10), 1628 (2020)

    Article  Google Scholar 

  46. Wang, L.; You, Z.H.; Huang, Y.A.; Huang, D.S.; Chan, K.C.: An efficient approach based on multi-sources information to predict circRNA–disease associations using deep convolutional neural network. Bioinformatics 36(13), 4038–4046 (2020)

    Article  Google Scholar 

  47. Awais, M.; Ehsan Awan, S.; Raja, M.A.Z.; Nawaz, M.; Ullah Khan, W.; Yousaf Malik, M.; He, Y.: Heat transfer in nanomaterial suspension (CuO and Al2O3) using KKL model. Coatings 11(4), 417 (2021)

    Article  Google Scholar 

  48. Khan, W.A.; Pop, I.: Boundary-layer flow of a nanofluid past a stretching sheet. Int. J. Heat Mass Transf. 53(11–12), 2477–2483 (2010)

    Article  MATH  Google Scholar 

  49. Gorla, R.S.R.; Sidawi, I.: Free convection on a vertical stretching surface with suction and blowing. Appl. Sci. Res. 52(3), 247–257 (1994)

    Article  MATH  Google Scholar 

  50. Makinde, O.D.; Aziz, A.: Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition. Int. J. Therm. Sci. 50(7), 1326–1332 (2011)

    Article  Google Scholar 

  51. Das, R.; Mishra, S.C.; Ajith, M.; Uppaluri, R.: An inverse analysis of a transient 2-D conduction–radiation problem using the lattice Boltzmann method and the finite volume method coupled with the genetic algorithm. J. Quant. Spectrosc. Radiat. Transfer 109(11), 2060–2077 (2008)

    Article  Google Scholar 

  52. Mishra, S.C.; Kim, M.Y.; Das, R.; Ajith, M.; Uppaluri, R.: Lattice Boltzmann method applied to the analysis of transient conduction-radiation problems in a cylindrical medium. Numer. Heat Transf. Part A Appl. 56(1), 42–59 (2009)

    Article  Google Scholar 

  53. Das, R.: Inverse analysis of Navier-Stokes equations using simplex search method. Inverse Probl. Sci. Eng. 20(4), 445–462 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  54. Raju, C.S.K.; Upadhya, S.M.; Seth, D.: Thermal convective conditions on MHD radiated flow with suspended hybrid nanoparticles. Microsyst. Technol. 27(5), 1933–1942 (2021)

    Article  Google Scholar 

  55. Parveen, N.; Awais, M.; Awan, S.E.; Shah, S.A.; Yuan, A.; Nawaz, M.; Akhtar, R.; Malik, M.Y.: Thermophysical properties of chemotactic microorganisms in bio-convective peristaltic rheology of nano-liquid with slippage, Joule heating and viscous dissipation. Case Stud. Therm. Eng. 27, 101285 (2021)

    Article  Google Scholar 

  56. Zhang, H.; Nguyen, H.; Bui, X.N.; Pradhan, B.; Mai, N.L.; Vu, D.A.: Proposing two novel hybrid intelligence models for forecasting copper price based on extreme learning machine and meta-heuristic algorithms. Resour. Policy 73, 102195 (2021)

    Article  Google Scholar 

  57. Izadi, A.; Kashani, E.; Mohebbi, A.: Combining 10 meta-heuristic algorithms, CFD, DOE, MGGP and PROMETHEE II for optimizing Stairmand cyclone separator. Powder Technol. 382, 70–84 (2021)

    Article  Google Scholar 

  58. Mohammadpour, J.; Salehi, F.; Sheikholeslami, M.; Masoudi, M.; Lee, A.: Optimization of nanofluid heat transfer in a microchannel heat sink with multiple synthetic jets based on CFD-DPM and MLA. Int. J. Therm. Sci. 167, 1070 (2021)

    Article  Google Scholar 

  59. Kumar, M.S.; Raju, C.S.K.; Sherif, E.S.M.; Algehyne, E.A.; Bilal, S.; Junaedi, H.: A comprehensive physical insight about enhancement in thermo physical features of newtonian fluid flow by suspending of metallic oxides of single wall carbon nano tube structures. Surf. Interfaces 23, 100838 (2021)

    Article  Google Scholar 

  60. Ram, P.; Pop, I.; Joshi, V.K.; Raju, C.S.K.; Kumar, V.: Polarization force and geothermal viscosity driven unsteady Bödewadt transport phenomenon over a ferrofluid saturated disk. Physica Scripta 96(1), 015202 (2020)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, 64002, Yunlin, Taiwan

    Muhammad Asif Zahoor Raja

  2. Department of Electrical and Computer Engineering, COMSATS University Islamabad, Attock Campus, Attock, 43600, Pakistan

    Saeed Ehsan Awan

  3. Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock, 43600, Pakistan

    Muhammad Shoaib & Muhammad Awais

Authors
  1. Muhammad Asif Zahoor Raja
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Saeed Ehsan Awan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Muhammad Shoaib
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Muhammad Awais
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Muhammad Asif Zahoor Raja.

Ethics declarations

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Raja, M.A.Z., Awan, S.E., Shoaib, M. et al. Backpropagated Intelligent Networks for the Entropy Generation and Joule Heating in Hydromagnetic Nanomaterial Rheology Over Surface with Variable Thickness. Arab J Sci Eng 47, 7753–7777 (2022). https://doi.org/10.1007/s13369-022-06667-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-022-06667-y

Keywords

Search

Navigation