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

Abstract

In this paper, we analyzed the mass transfer model with chemical reactions during the absorption of carbon dioxide (CO2) into phenyl glycidyl ether (PGE) solution. The mathematical model of the phenomenon is governed by a coupled nonlinear differential equation that corresponds to the reaction kinetics and diffusion. The system of differential equations is subjected to Dirichlet boundary conditions and a mixed set of Neumann and Dirichlet boundary conditions. Further, to calculate the concentration of CO2, PGE, and the flux in terms of reaction rate constants, we adopt the supervised learning strategy of a nonlinear autoregressive exogenous (NARX) neural network model with two activation functions (Log-sigmoid and Hyperbolic tangent). The reference data set for the possible outcomes of different scenarios based on variations in normalized parameters (α1,α2,β1,β2,k) are obtained using the MATLAB solver “pdex4”. The dataset is further interpreted by the Levenberg–Marquardt (LM) backpropagation algorithm for validation, testing, and training. The results obtained by the NARX-LM algorithm are compared with the Adomian decomposition method and residual method. The rapid convergence of solutions, smooth implementation, computational complexity, absolute errors, and statistics of the mean square error further validate the design scheme’s worth and efficiency.

Heat Transfer Analysis of Nanofluid Flow in a Rotating System with Magnetic Field Using an Intelligent Strength Stochastic-Driven Approach

“…In this section, the proposed FFNN-BLM algorithm is employed to study the influence of variations in the magnetic parameter, Prandtl number, rotation parameter, thermophoresis, and Brownian motion parameter on heat transfer, velocity, gravitational acceleration, and concentration profiles of the nanofluid, governed by Equations ( 9)- (12). To demonstrate the accuracy and efficiency of the design algorithm, the results obtained by the FFNN-BLM algorithm are compared with the Runge-Kutta-Fehlberg method, the least square method [55], and a machine learning algorithm (NARX-BLM) [56], as detailed in Tables 1 and 2. The statistics demonstrate the validity of the FFNN-BLM algorithm, and it is observed that the solutions overlap the numerical results with minimal absolute errors that lie around 10 −5 to 10 −9 .…”

Investigation of Three-Dimensional Condensation Film Problem over an Inclined Rotating Disk Using a Nonlinear Autoregressive Exogenous Model

“…To overcome these drawbacks, artificial intelligence-based supervised learning techniques are designed that are free of gradient and only require the essential initial parameter and terminal conditions for execution. Some recent applications of the stochastic techniques include the solutions for the saturation of water and oil [ 20 ], absorption of carbon dioxide [ 21 ], the corneal model for eye surgery [ 22 ], and the temperature distribution of conductive-convective and radiative fins [ 23 ]. These facts inspire authors to explore and incorporate the intelligent strength of artificial neural networks to solve the problem formed by the condensation of 3D-fluid flow on a rotating disk.…”

On the Computational Study of a Fully Wetted Longitudinal Porous Heat Exchanger Using a Machine Learning Approach

“…In this paper, numerical solutions for fully wetted longitudinal porous heat exchangers with different thermal conductivities are calculated based on the simple concept of artificial intelligence (AI), implemented through the application of neural networks and optimization procedures of meta-heuristic techniques [ 35 , 36 , 37 , 38 , 39 ]. Recently, artificial intelligence-based stochastic techniques have been successfully implemented for various problems in different domains of reaction kinematics [ 40 , 41 ], marine engineering [ 42 ], wireless communication [ 43 ], and fluid dynamics [ 44 , 45 , 46 ]. These applications motivated the authors to design a novel unsupervised technique using the computational approximation ability of layer structure feed-forward ANNs, the global and local optimization of the Tiki-Taka algorithm (TTA), and sequential quadratic programming (SQP).…”