Skip to main content

Advertisement

SpringerLink
Log in

Implementation of Stochastic Optimization Method-Assisted Radial Basis Neural Network for Transport Phenomenon in Non-Newtonian Third-Grade Fluids: Assessment of Five Optimization Tools

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

Abstract

Implementation of radial basis neural network is demonstrated by considering a test case of non-Newtonian third-grade fluid flow and heat transfer through two parallel plates. Five commonly used stochastic optimization methods: genetic algorithm, global search algorithm, multiple starting point algorithm, simulated annealing algorithm, and pattern search algorithm, are employed to optimize the RBNN. Flow of a non-Newtonian third-grade fluid through two parallel plates, subjected to uniform heat flux, is considered. At first, governing equations, describing the flow and heat transfer problem, are solved by the least-square method, a semi-analytical tool. The velocity and the temperature profiles are obtained for different values of third-grade fluid parameter ‘A’, which are then used for training different stochastic optimization method-assisted RBNNs (SOMARBNNs). For proper functioning of RBNN, a suitable value for an important attribute called ‘spread’ is required. Deciding the value for ‘spread’ requires experience and knowledge of neural networks. The present approach makes the selection of proper value of ‘spread’ very easy, and beginners can use the RBNN for problem-solving. With the help of different stochastic optimization methods, the value of spread for the RBNN is determined. Once all SOMARBNNs are trained, the temperature profile and the corresponding third-grade fluid parameter ‘A’ are obtained as output, corresponding to any new velocity profile fed as input. Further, the data for training are perturbed by different levels of noise, and different SOMARBNNs are successfully employed to get the output. The performance evaluation of different SOMARBNNs is carried out in terms of CPU time and error in result. The results indicate that PSAARBNN is better than other SOMARBNNs, as it is able to generate results with high accuracy for both low noise data and high noise data. Moreover, the CPU time requirement by PSAARBNN is lowest.

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

Similar content being viewed by others

Abbreviations

\(A\) :

Third-grade fluid parameter

\(Ac\) :

Cross-sectional area [m2]

\(A_{1} ,\,A_{2} ,\,A_{3} ,...A_{n}\) :

Kinematic tensor

\(a_{0} ,\,a_{2} ,\,a_{4} ,\,a_{6} ,a_{8}\) :

Constants

\(an\) :

Layer output vector in RBNN

\(Br\) :

Brinkman number

\(\begin{gathered} b_{0} ,\,b_{2} ,\,b_{4} ,\, \hfill \\ b_{6} ,\,b_{8} ,\,b_{10} ,\,b_{12} \hfill \\ \end{gathered}\) :

Constants

bn:

Bias in RBNN

\(C_{P}\) :

Specific heat at constant pressure [J/kg.K]

\(c_{1} ,\,c_{2} ,...\,\) :

Constants

\(c_{i}\) :

Ith constant

\(D\) :

Differential operator

D/Dt :

Material derivative

\(f\) :

Body force per unit volume

\(g\) :

Function

\(h\) :

Half depth of channel [m]

\(IWn^{1}\) :

Hidden layer weight matrix in RBNN

\(k_{th}\) :

Thermal conductivity of the fluid [W/m K]

\(L\) :

Length of the channel [m]

\(LWn^{2}\) :

Output layer weight matrix in RBNN

\(l_{1} ,\,l_{2}\) :

Constants

\(N\) :

Non-dimensional pressure gradient

\(Nu\) :

Nusselt number

\(p^{*}\) :

Dimensional pressure [N/m2]

\(q\) :

Heat flux ratio

\(q_{1} ,\,q_{2}\) :

Heat fluxes at lower and upper walls [W/m2]

\(R\) :

Residual

\(Rn\) :

Number of observation points along y* direction (= 201)

\(S\) :

Sum of square of residual

\(sn\) :

Size of matrix in RANN

\(T^{*}\) :

Dimensional temperature [K]

\(T_{m}^{*}\) :

Bulk mean temperature [K]

\(T_{{w_{l} }}^{*}\) :

Temperature of the lower wall [K]

\(u\) :

Non-dimensional velocity along axial direction

\(u_{N}\) :

Non-dimensional velocity for Newtonian fluid

\(u^{*}\) :

Dimensional velocity along axial direction [m/s]

\(u_{0}\) :

Average velocity [m/s]

\(V^{*}\) :

Velocity vector [m/s]

\(v,\,\tilde{v}\) :

Functions [m/s]

\(x,\,y,\,z\) :

Non-dimensional coordinate

\(x*,\,y*,\,z*\) :

Dimensional coordinates [m]

\(Xn_{o} ,\;Xn_{1}\) :

Central point in PSA indifferent iterations

\(xn_{i}\) :

Neuron input

\(w_{i}\) :

Ith weight function

\(Wn_{i}\) :

Neuron weight

mse:

Mean squared error

ANN:

Artificial neural network

RBNN:

Radial basis neural network

GA:

Genetic algorithm

GAARBNN:

Genetic algorithm-assisted RBNN

GSA:

Global search algorithm

GSAARBNN:

Global search algorithm-assisted RBNN

MSPA:

Multiple starting point algorithm

MSPAARBNN:

Multiple starting point algorithm-assisted RBNN

OF :

Objective function

SAA:

Simulated annealing algorithm

SAAARBNN:

Simulated annealing algorithm-assisted RBNN

PSA:

Pattern search algorithm

PSAARBNN:

Pattern search algorithm-assisted RBNN

SOM:

Stochastic optimization method

SOMARBNN:

Stochastic optimization method-assisted radial basis neural network

TGF:

Third-grade fluid

\(\alpha_{1} ,\,\alpha_{2}\) :

Material constants

\(\beta\) :

Constant

\(\beta_{1,\,} \,\beta_{2,\,} \,\beta_{3,\,} ...\) :

Material constants

\(\rho\) :

Density of the fluid [kg/m3]

\(\mu\) :

Dynamic viscosity of the fluid [N s/m2]

\(\theta\) :

Non-dimensional temperature

\(\theta_{N}\) :

Non-dimensional temperature for Newtonian fluid

\(\tilde{\theta }\) :

Temperature obtained from SOMARBNNs

Φi:

Base function

τ:

Stress

1, 2:

Hidden layer and output layer variables

References

  1. Mai-Duy, N.; Tanner, R.I.: Computing non-Newtonian fluid flow with radial basis function networks. Int. J. Numer. Methods Fluids. 48, 1309–1336 (2005)

    Article  Google Scholar 

  2. Esfe, M.H.: Designing an artificial neural network using radial basis function (RBF-ANN) to model thermal conductivity of ethylene glycol–water-based TiO2 nanofluids. J Therm Anal Calorim. 127(3), 2125–2131 (2017)

    Article  MathSciNet  Google Scholar 

  3. Abualigah, L.; Diabat, A.: A novel hybrid antlion optimization algorithm for multi-objective task scheduling problems in cloud computing environments. Clust. Comput. 24, 205–223 (2021)

    Article  Google Scholar 

  4. Abualigah, L.; Diabat, A.; Mirjalili, S.; Elaziz, M.A.; Gandomi, A.H.: The arithmetic optimization algorithm. Comput. Methods Appl. Mech. Eng. (2021). https://doi.org/10.1016/j.cma.2020.113609

    Article  MathSciNet  MATH  Google Scholar 

  5. Karimi, H.; Yousefi, F.; Rahimi, M.R.: Correlation of viscosity in nanofluids using genetic algorithm-neural network (GA-NN). Heat Mass Transf. 47, 1417–1425 (2011)

    Article  Google Scholar 

  6. Li, S.J.; Liu, Y.X.; He, X.; Liu, Y.J.: Global search algorithm of minimum safety factor for slope stability analysis based on annealing simulation. Chinese J. Rock Mech. Eng. 22(2), 236–240 (2003)

    Google Scholar 

  7. Miri, T.; Tsoukalas, A.; Bakalis, S.; Pistikopoulos, E.N.; Rustem, B.; Fryer, P.J.: Global optimization of process conditions in batch thermal sterilization of food. J. Food Eng. 87, 485–494 (2008)

    Article  Google Scholar 

  8. Saruhan, H.: Designing optimum oil thickness in artificial human knee joint by simulated annealing. Math. and Comp. Applic. 14(12), 109–117 (2009)

    MathSciNet  Google Scholar 

  9. Torczon, V.: On the convergence of pattern search algorithms. SIAM J. Optim. 7, 1–25 (1997)

    Article  MathSciNet  Google Scholar 

  10. Mishra, V.K.; Mishra, S.C.; Basu, D.N.: Simultaneous estimation of four parameters in a combined mode heat transfer in a 2-D rectangular porous matrix with heat generation. Numerical Heat Transfer- A. 71(6), 677–692 (2017)

    Article  Google Scholar 

  11. Mishra, V.K.; Mishra, S.C.; Basu, D.N.: Simultaneous estimation of properties in a combined mode conduction-radiation heat transfer in a porous medium. Heat Transf. Asian Res 45(8), 699–713 (2016)

    Article  Google Scholar 

  12. Mulani, U.K.; Talukdar, P.; Das, A.; Alagirusamy, R.: Performance analysis and feasibility study of ant colony optimization, particle swarm optimization and cuckoo search algorithms for inverse heat transfer problems. Int. J. Heat Mass Transf. 89, 359–378 (2015)

    Article  Google Scholar 

  13. Inaba, H.; Zhang, Y.; Horibe, A.; Haruki, N.: Numerical simulation of natural convection of latent heat phasechange-material microcapsulate slurry packed in a horizontal rectangular enclosure heated from below and cooled from above. Heat Mass Transfer. 43, 459–470 (2017)

    Article  Google Scholar 

  14. Subba Rao, A.; Ramachandra Prasad, V.; Rajendra, P.; Sasikala, M.; Anwar Beg, O.: Numerical study of non-Newtonian polymeric boundary layer flow and heat transfer from a permeable horizontal isothermal cylinder. Front. Heat Mass Transfer. 9, 2 (2017)

    Google Scholar 

  15. Lim, H.; Back, S.M.; Hwang, M.H.; Lee, D.H.; Choi, H.; Nam, J.: Sheathless high-throughput circulating tumor cell separation using viscoelastic non-Newtonian fluid. Micromachines (Basel). 10, 462 (2019)

    Article  Google Scholar 

  16. Glinski, G.P.; Bailey, C.; Pericleous, K.A.: A non Newtonian of the stencil printing process. Proc. Inst. Mech. Eng. 215(C4), 437–446 (2001)

    Google Scholar 

  17. Chaudhuri, S.; Das, P.K.: Semi-analytical solution of the heat transfer including viscous dissipation in the steady flow of a Sisko fuid in cylindrical tubes. J. Heat Transf (ASME). 140, 071701 (2018)

    Article  Google Scholar 

  18. Kalani, H.; Sardarabadi, M.; Passandideh-Fard, M.: Using artificial neural network models and particle swarm optimization for manner prediction of a photovoltaic thermal nanofluid based collector. Appl. Therm. Eng. 113, 1170–1177 (2017)

    Article  Google Scholar 

  19. Esfe, M.H.: Designing a neural network for predicting the heat transfer and pressure drop characteristics of Ag/water nanofluids in a heat exchanger. Appl. Therm. Eng. 126, 559–565 (2017)

    Article  Google Scholar 

  20. Daneshfar, R.; Bemani, A.; Hadipoor, M.; Sharifpur, M.; Ali, H.M.; Mahariq, I.; Abdeljawad, T.: Estimating the heat capacity of non-Newtonian ionanofluid systems using ANN, ANFIS, and SGB tree algorithms. Appl. Sci. 10, 6432 (2020)

    Article  Google Scholar 

  21. Esfe, M.H.: Designing an artificial neural network using radial basis function (RBF-ANN) to model thermal conductivity of ethylene glycol–water-based TiO2 nanofluids. J. Therm. Anal. Calorim. 127, 2125–2131 (2017). https://doi.org/10.1007/s10973-016-5725-y

    Article  Google Scholar 

  22. Chhantyal, K.; Viumdal, H.; Mylvaganam, S.; Elseth, G.: Ultrasonic level sensors for flowmetering of non-Newtonian fluids in open Venturi channels: using data fusion based on artificial neural network and support vector machines. IEEE Sensors Applications Symposium (SAS), Catania. 1–6 (2016), https://doi.org/10.1109/SAS.2016.7479829

  23. Eshgarf, H.; Sina, N.; Esfe, M.H., et al.: Prediction of rheological behavior of MWCNTs–SiO2/EG–water non-Newtonian hybrid nanofluid by designing new correlations and optimal artificial neural networks. J Therm Anal Calorim. 132, 1029–1038 (2018). https://doi.org/10.1007/s10973-017-6895-y

    Article  Google Scholar 

  24. Wu, H.; Bagherzadeh, S.A.; D’Orazio, A.; Habibollahi, N.; Karimipour, A.; Goodarzi, M.; Bach, Q.-V.: Present a new multi objective optimization statistical Pareto frontier method composed of artificial neural network and multi objective genetic algorithm to improve the pipe flow hydrodynamic and thermal properties such as pressure drop and heat transfer coefficient for non-Newtonian binary fluids. Phys. Stat. Mech. Appl. 535, 122409 (2019)

    Article  Google Scholar 

  25. Zhang, S.; Ge, Z.; Fan, X., et al.: Prediction method of thermal conductivity of nanofluids based on radial basis function. J. Therm. Anal. Calorim. 141, 859–880 (2020). https://doi.org/10.1007/s10973-019-09067-x

    Article  Google Scholar 

  26. Mishra, V.K.; Chaudhuri, S.: Genetic algorithm-assisted artificial neural network for retrieval of a parameter in a third grade fluid flow through two parallel and heated plates. Heat Transfer (Wiley). (2020). https://doi.org/10.1002/htj.21970

    Article  Google Scholar 

  27. Amani, M.; Amani, P.; Bahiraei, M., et al.: Prediction of hydrothermal behavior of a non-Newtonian nanofluid in a square channel by modeling of thermophysical properties using neural network. J Therm Anal Calorim. 135, 901–910 (2019). https://doi.org/10.1007/s10973-018-7303-y

    Article  Google Scholar 

  28. Danish, M.; Kumar, S.; Kumar, S.: Exact analytical solutions for the Poiseuille and Couette-Poiseuille flow of third grade fluid between parallel plates. Commun. Non Linear Sci. 17, 1089–1097 (2012)

    Article  MathSciNet  Google Scholar 

  29. Balaji, C.: Thermal system design and optimization, 2nd edn. Ane Books Pvt. Ltd., New Delhi (2019)

    Google Scholar 

  30. Zsolt, U.; Lasdon, L.; Plummer, J.; Glover, F.; Kelly, J.; Martí, R.: Scatter Search and Local NLP Solvers: a Multistart Framework for Global Optimization. INFORMS J. Comput. 19(3), 328–340 (2007)

    Article  MathSciNet  Google Scholar 

  31. Glover, F.: A template for scatter search and path relinking. In: Hao, J.K.; Lutton, E.; Ronald, E.; Schoenauer, M.; Snyers, D. (Eds.) Artificial Evolution. AE 1997. Lecture Notes in Computer Science. Springer Berlin, Heidelberg (1998). https://doi.org/10.1007/BFb0026589

    Chapter  Google Scholar 

  32. Zhou, H.; Jiang, Z.; Li, W.; Wang, G.; Tu, Y.: Optimal design for an extruder head runner based on response surface method and simulated annealing algorithm. Int. J. Polym. Sci. 7239618, 10 (2018). https://doi.org/10.1155/2018/7239618

    Article  Google Scholar 

  33. Wu, C.; Wang, S.-S.; Jiang, X.; Li, J.: Thermodynamic analysis and performance optimization of transcritical power cycles using CO2-based binary zeotropic mixtures as working fluids for geothermal power plants. Appl. Therm. Eng. 115, 292–304 (2017)

    Article  Google Scholar 

  34. Bar, N.; Bandyopadhyay, T.K.; Biswas, M.N.; Das, S.K.: Prediction of pressure drop using artificial neural network for non-Newtonian liquid flow through piping components. J. Pet. Sci. E. 71, 187–194 (2010)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Kalinga Institute of Industrial Technology (KIIT) DU, Bhubaneswar, 751024, India

    Vijay K. Mishra & Sumanta Chaudhuri

Authors
  1. Vijay K. Mishra
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sumanta Chaudhuri
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vijay K. Mishra.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mishra, V.K., Chaudhuri, S. Implementation of Stochastic Optimization Method-Assisted Radial Basis Neural Network for Transport Phenomenon in Non-Newtonian Third-Grade Fluids: Assessment of Five Optimization Tools. Arab J Sci Eng 46, 11797–11818 (2021). https://doi.org/10.1007/s13369-021-05702-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-021-05702-8

Keywords

Search

Navigation