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

Journal article

Authors/Editors

POOM KUMAM

Strategic Research Themes

Other (Strategic Research Themes)

Publication Details

Author list: Khan N.A., Sulaiman M., Kumam P., Alarfaj F.K.

Publication year: 2022

Volume number: 2022

Issue number: 1

ISSN: 27314235

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85123480421&doi=10.1186%2fs13662-022-03676-x&partnerID=40&md5=23f9ff754632e33c05df8aea7ef39ce4

Languages: English-Great Britain (EN-GB)

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Abstract

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). © 2022, The Author(s).

Keywords

Generalized normal-distribution optimization, Non-Newtonian fluid, sequential quadratic programming