Computational Evaluation of Heat and Mass Transfer in Cylindrical Flow of Unsteady Fractional Maxwell Fluid Using Backpropagation Neural Networks and LMS

Waqar Ul Hassan, Khurram Shabbir (), Muhammad Imran Khan and Liliana Guran ()
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Waqar Ul Hassan: Department of Mathematics, Government College University, Katchery Road, Lahore 54000, Pakistan
Khurram Shabbir: Department of Mathematics, Government College University, Katchery Road, Lahore 54000, Pakistan
Muhammad Imran Khan: Department of Mathematics and Statistics, Faculty of Basic and Applied Sciences, International Islamic University Islamabad, H-10, Islamabad 44000, Pakistan
Liliana Guran: Department of Hospitality Services, Babes-Bolyai University, 7 Horea St., 400174 Cluj-Napoca, Romania

Mathematics, 2024, vol. 12, issue 23, 1-31

Abstract: Fractional calculus plays a pivotal role in modern scientific and engineering disciplines, providing more accurate solutions for complex fluid dynamics phenomena due to its non-locality and inherent memory characteristics. In this study, Caputo’s time fractional derivative operator approach is employed for heat and mass transfer modeling in unsteady Maxwell fluid within a cylinder. Governing equations within a cylinder involve a system of coupled, nonlinear fractional partial differential equations (PDEs). A machine learning technique based on the Levenberg–Marquardt scheme with a backpropagation neural network (LMS-BPNN) is employed to evaluate the predicted solution of governing flow equations up to the required level of accuracy. The numerical data sheet is obtained using series solution approach Homotopy perturbation methods. The data sheet is divided into three portions i.e., 80 % is used for training, 10 % for validation, and 10 % for testing. The mean-squared error (MSE), error histograms, correlation coefficient (R), and function fitting are computed to examine the effectiveness and consistency of the proposed machine learning technique i.e., LMS-BPNN. Moreover, additional error metrics, such as R-squared, residual plots, and confidence intervals, are incorporated to provide a more comprehensive evaluation of model accuracy. The comparison of predicted solutions with LMS-BPNN and an approximate series solution are compared and the goodness of fit is found. The momentum boundary layer became higher and higher as there was an enhancement in the value of Caputo, fractional order α = 0.5 to α = 0.9. Higher thermal boundary layer (TBL) profiles were observed with the rising value of the heat source.

Keywords: machine learning; ANN; LMS-BPNN; fractional order Maxwell fluid model; Caputo’s time fractional derivatives; heat and mass transfer; cylinder (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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