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

Abstract

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.

Numerical Analysis of Electrohydrodynamic Flow in a Circular Cylindrical Conduit by Using Neuro Evolutionary Technique

“…The performance operators were fitness functions, Theil's inequality coefficient (TIC), mean absolute deviations (MAD), Nash Sutcliffe efficiency (NSE), and error in Nash Sutcliffe efficiency (ENSE). A mathematical formulation of these indices is defined as in [45].…”

“…An overview of the working procedure of GNDO is provided in pseudocode as Algorithm 1. Recently, the GNDO algorithm has been applied to study the parameter extraction photovoltaic models [44] and heat transfer in temperature fins [45].…”

Mathematical Analysis of Reaction–Diffusion Equations Modeling the Michaelis–Menten Kinetics in a Micro-Disk Biosensor

“…Such stochastic computing techniques use artificial neural networks to model approximate solutions. These numerical solvers have wide applications in various fields including petroleum engineering [ 23 ], wireless communication [ 24 ], heat transfer [ 25 , 26 , 27 ], fuzzy systems [ 28 ], plasma system [ 29 ], civil engineering [ 30 , 31 ], wire coating dynamics [ 32 ] and Diabetic retinopathy classification [ 33 ]. The techniques mentioned earlier inspire the authors to explore and incorporate the soft computing architectures as an alternative, precise and feasible way for solving the mathematical model of micro-disk biosensors.…”

Theoretical Analysis on Absorption of Carbon Dioxide (CO2) into Solutions of Phenyl Glycidyl Ether (PGE) Using Nonlinear Autoregressive Exogenous Neural Networks

“…In recent times, stochastic computing paradigms based on artificial intelligence have been used extensively to find numerical solutions for different problems arising in various fields, such as fuzzy systems [ 16 , 17 , 18 ], petroleum engineering [ 19 ], carbon capture process [ 20 , 21 , 22 ], wire coating dynamics [ 23 ], biological systems [ 24 , 25 ], civil engineering [ 26 , 27 ], coal-fired power plant retrofitted [ 28 ], and electrical and thermal engineering [ 29 , 30 , 31 ]. These contributions motivated the authors to investigate the absorption of carbon dioxide (CO ) into solutions of phenyl glycidyl ether (PGE) by strengthening the computational ability of neural networks.…”