Application of Legendre polynomials based neural networks for the analysis of heat and mass transfer of a non-Newtonian fluid in a porous channel

In this paper, the mathematical models for flow and heat-transfer analysis of a non-Newtonian fluid with axisymmetric channels and porous walls are analyzed. The governing equations of the problem are derived by using the basic concepts of continuity and momentum equations. Furthermore, artificial i...

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Veröffentlicht in:Advances in continuous and discrete models Jg. 2022; H. 1
Hauptverfasser: Khan, Naveed Ahmad, Sulaiman, Muhammad, Kumam, Poom, Alarfaj, Fawaz Khaled
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 22.01.2022
Springer Nature B.V
Schlagworte:
Algorithms
Analysis
Artificial intelligence
Artificial neural networks
Difference and Functional Equations
Difference Equations
Fluid flow
Functional Analysis
Heat transfer
Mass transfer
Mathematical models
Mathematics
Mathematics and Statistics
Momentum
Neural networks
Newtonian fluids
Non Newtonian fluids
Normal distribution
Optimization
Ordinary Differential Equations
Partial Differential Equations
Polynomials
Porous walls
Quadratic programming
Reynolds number
Root-mean-square errors
Special Functions and Orthogonal Polynomials
Statistical analysis
Temperature profiles
Velocity distribution
Porous media
Hybrid soft computing
Sequential quadratic programming
Heat and mass transfer
Machine learning
Generalized normal-distribution optimization
Weighted Legendre neural networks
Non-Newtonian fluid
ISSN:2731-4235, 1687-1839, 2731-4235, 1687-1847
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Zusammenfassung:In this paper, the mathematical models for flow and heat-transfer analysis of a non-Newtonian fluid with axisymmetric channels and porous walls are analyzed. The governing equations of the problem are derived by using the basic concepts of continuity and momentum equations. Furthermore, artificial intelligence-based feedforward neural networks (ANNs) are utilized with hybridization of a generalized normal-distribution optimization (GNDO) algorithm and sequential quadratic programming (SQP) to study the heat-transfer equations and calculate the approximate solutions for the momentum of a non-Newtonian fluid. Legendre polynomials based Legendre neural networks (LNN) are used to develop a mathematical model for the governing equations, which are further exploited by the global search ability of GNDO and SQP for rapid localization convergence. The proposed technique is applied to study the effect of variations in Reynolds number Re on the velocity profile ( f ′ ) and the temperature profile ( q ) . The results obtained by the LeNN-GNDO-SQP algorithm are compared with the differential transformation method (DTM), which shows the stability of the results and the correctness of the technique. Extensive graphical and statistical analyses are conducted in terms of minimum, mean, and standard deviation based on fitness value, absolute errors, mean absolute deviation (MAD), error in the Nash–Sutcliffe efficiency (NSE), and root mean square error (RMSE).
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:2731-4235
1687-1839
2731-4235
1687-1847
DOI:10.1186/s13662-022-03676-x