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A length factor artificial neural network method for the numerical solution of the advection dispersion equation characterizing the mass balance of fluid flow in a chemical reactor

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Abstract

In this article, a length factor artificial neural network (ANN) method is proposed for the numerical solution of the advection dispersion equation (ADE) in steady state that is used extensively in fluid dynamics and in the mass balance of a chemical reactor. An approximate trial solution of the ADE is constructed in terms of ANN using the concept of the length factor in a way that automatically satisfies the desired boundary conditions, regardless of the ANN output. The mathematical model of ADE is presented adopting a first-order reaction, and the steady-state case for the same is examined by estimating the numerical solution using the ANN technique. Numerical simulations are performed by choosing the best ANN ensemble, based on a combination of numerous design parameters, random starting weights, and biases. The solution obtained using the ANN method is compared to the existing finite difference method (FDM) to test the reliability and effectiveness of the proposed approach. Three cases of ADE are considered in this study for different values of advection and dispersion. The numerical results show that the ANN method exhibits a higher accuracy than the FDM, even for the smaller number of training points in the domain, and eliminates the instability issues for the case where advection dominates dispersion.

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Acknowledgements

This work was supported by National Research Foundation of Korea (NRF) Grant funded by the Korean government (MSIP) (NRF-2013R1A2A1A01013886) and the Brain Korea 21 (BK-21) fellowship from the Ministry of Education of Korea.

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Authors and Affiliations

  1. School of Civil Environmental and Architectural Engineering, Korea University, Seoul, 02841, South Korea

    Neha Yadav & Joong Hoon Kim

  2. Department of Mechatronics Engineering, Kennesaw State University, Kennesaw, GA, USA

    Kevin Stanley McFall

  3. Department of Mathematics, Motilal Nehru National Institute of Technology, Allahabad, U.P., 211004, India

    Manoj Kumar

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  1. Neha Yadav
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  2. Kevin Stanley McFall
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  3. Manoj Kumar
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  4. Joong Hoon Kim
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Correspondence to Joong Hoon Kim.

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Yadav, N., McFall, K.S., Kumar, M. et al. A length factor artificial neural network method for the numerical solution of the advection dispersion equation characterizing the mass balance of fluid flow in a chemical reactor. Neural Comput & Applic 30, 917–924 (2018). https://doi.org/10.1007/s00521-016-2722-9

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  • DOI: https://doi.org/10.1007/s00521-016-2722-9

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