Bayesian regularization-based intelligent computing for peristaltic propulsion of curvature-dependent channel walls
Authors: Iqbal Jamshaid , Akbar Yasir , Alam Mohammad Mahtab 
Published: February 2025

This study investigates the numerical analysis of curvature-dependent symmetric channel walls filled with porous media, focusing on various flow characteristics using Artificial Neural Networks optimized with the Levenberg–Marquardt Backpropagation Scheme (ANNs-BLMS). The analysis explores the Electrically Conducting Peristaltic Propulsion of Carreau–Yasuda Ternary Hybrid Nanofluids (ECPPCY-THNFs) propagating through sinusoidal wave trains within a curved conduit. To streamline the analysis, the governing equations have been simplified under specific assumptions of lubrication theory. The simplified governing equations are solved using Adam and three-stage Lobatto IIIa formula numerical techniques to generate a dataset spanning the curvature-dependent channel walls, covering four cases and nine scenarios of ECPPCY-THNFs. This dataset encompasses four cases and nine scenarios of ECPPCY-THNFs, with a step size of 0.02. As a result, the domain is divided into 131 grid points for velocity and temperature profiles and 71 grid points for rates of heat transfer analysis. The dataset is divided into three parts: 10% for training, 10% for testing, and 80% for validation. To apply the proposed methodology, the dataset is constructed by varying the Hartmann number, flow rate, Darcy number, curvature parameter, and radiation parameter. Subsequently, an artificial intelligence-based algorithm is employed to derive solution expressions for various flow fields and to analyze the dataset. The results are presented through detailed tabular and graphical illustrations. Heat transfer analysis is performed using the proposed model, and the findings are validated through multiple techniques, including error histograms, regression plots, mean square error (MSE), time series analysis, error autocorrelation, and state transition. A comparative study between two numerical methods and Artificial Intelligence (AI)-generated predictions is also undertaken. The results obtained using the AI-based ANN-BLMS framework confirm the reliability and accuracy of the proposed methodology in effectively solving the ECPPCY-THNFs. The results demonstrate that the curvature parameter has a considerable effect on the mechanical and thermal aspects of the flow, and therefore, it must be incorporated into the modeling of flows through curved channels. Additionally, the flow rate of 7.5 is the critical value, representing the minimum required to sustain fluid flow in a curved channel. When the curvature parameter is below this critical value, an increase in the curvature results in a decrease in the temperature profile. However, when the curvature parameter exceeds the critical value, the temperature profile shows the opposite trend. Furthermore, the velocity of ternary hybrid nanofluids show concave-up shapes for flow rates (Θ) values greater than 7.5 and concave-down shapes for flow rates values less than 7.5. The highest and lowest velocities occur near the center of the curved channel for Θ&gt;7.5 and Θ&lt;7.5, respectively. Moreover, the coefficient of determination values, used as performance indicators, are found to be unity (1.000) for the ANN model. The MSE values and error histogram values for the heat transfer rates are 2.8467 × 10−11 and −3.05 × 10−7, respectively.