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Article

Application of Euler Neural Networks with Soft Computing Paradigm to Solve Nonlinear Problems Arising in Heat Transfer

1
Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, KP, Pakistan
2
Al-Nahrain Nanorenewable Energy Research Center Baghdad, Al-Nahrain University, Baghdad 10001, Iraq
3
COMBA R&D Laboratory, Faculty of Engineering, Universidad Santiago de Cali, Cali 76001, Colombia
4
Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Kuala Nerus 21300, Terengganu, Malaysia
*
Author to whom correspondence should be addressed.
Academic Editors: Florent Duchaine and Daniel Mira
Entropy 2021, 23(8), 1053; https://doi.org/10.3390/e23081053
Received: 17 June 2021 / Revised: 31 July 2021 / Accepted: 9 August 2021 / Published: 16 August 2021
(This article belongs to the Special Issue Computational Fluid Dynamics and Conjugate Heat Transfer)
In this study, a novel application of neurocomputing technique is presented for solving nonlinear heat transfer and natural convection porous fin problems arising in almost all areas of engineering and technology, especially in mechanical engineering. The mathematical models of the problems are exploited by the intelligent strength of Euler polynomials based Euler neural networks (ENN’s), optimized with a generalized normal distribution optimization (GNDO) algorithm and Interior point algorithm (IPA). In this scheme, ENN’s based differential equation models are constructed in an unsupervised manner, in which the neurons are trained by GNDO as an effective global search technique and IPA, which enhances the local search convergence. Moreover, a temperature distribution of heat transfer and natural convection porous fin are investigated by using an ENN-GNDO-IPA algorithm under the influence of variations in specific heat, thermal conductivity, internal heat generation, and heat transfer rate, respectively. A large number of executions are performed on the proposed technique for different cases to determine the reliability and effectiveness through various performance indicators including Nash–Sutcliffe efficiency (NSE), error in Nash–Sutcliffe efficiency (ENSE), mean absolute error (MAE), and Thiel’s inequality coefficient (TIC). Extensive graphical and statistical analysis shows the dominance of the proposed algorithm with state-of-the-art algorithms and numerical solver RK-4. View Full-Text
Keywords: heat transfer problems; nonlinear differential equations; variable specific heat coefficient; lumped system; Euler neural networks; hybrid soft computing; generalized normal distribution optimization; interior point algorithm heat transfer problems; nonlinear differential equations; variable specific heat coefficient; lumped system; Euler neural networks; hybrid soft computing; generalized normal distribution optimization; interior point algorithm
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MDPI and ACS Style

Khan, N.A.; Khalaf, O.I.; Romero, C.A.T.; Sulaiman, M.; Bakar, M.A. Application of Euler Neural Networks with Soft Computing Paradigm to Solve Nonlinear Problems Arising in Heat Transfer. Entropy 2021, 23, 1053. https://doi.org/10.3390/e23081053

AMA Style

Khan NA, Khalaf OI, Romero CAT, Sulaiman M, Bakar MA. Application of Euler Neural Networks with Soft Computing Paradigm to Solve Nonlinear Problems Arising in Heat Transfer. Entropy. 2021; 23(8):1053. https://doi.org/10.3390/e23081053

Chicago/Turabian Style

Khan, Naveed Ahmad, Osamah Ibrahim Khalaf, Carlos Andrés Tavera Romero, Muhammad Sulaiman, and Maharani A. Bakar. 2021. "Application of Euler Neural Networks with Soft Computing Paradigm to Solve Nonlinear Problems Arising in Heat Transfer" Entropy 23, no. 8: 1053. https://doi.org/10.3390/e23081053

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