Shahbaz Hafiz Muhammad, Ahmad Iftikhar
Department of Mathematics, University of Gujrat, Gujrat, 50700, Pakistan.
Sci Rep. 2024 Dec 28;14(1):31214. doi: 10.1038/s41598-024-82569-3.
This study is the application of a recurrent neural networks with Bayesian regularization optimizer (RNNs-BRO) to analyze the effect of various physical parameters on fluid velocity, temperature, and mass concentration profiles in the Darcy-Forchheimer flow of propylene glycol mixed with carbon nanotubes model across a stretched cylinder. This model has significant applications in thermal systems such as in heat exchangers, chemical processing, and medical cooling devices. The data-set of the proposed model has been generated with variation of various parameters such as, curvature parameter, inertia coefficient, Hartmann number, porosity parameter, Eckert number, Prandtl number, radiation parameter, activation energy variable, Schmidt number and reaction rate parameter for different scenarios. The refinement of each data-set is processed through RNNs-BRO for attestation of the proposed scheme. The outcomes are provided through graphical interpretation. The increment of curvature parameter results in the acceleration of the velocity profile, while an opposite behavior is noticed for higher values of inertia coefficient, Hartmann number, porosity parameter for single wall carbon nanotubes (SWCNTs) as well as multi wall carbon nanotubes (MWCNTs). The temperature of fluid increases for both SWCNTs and MWCNTs as the curvature parameter, radiation parameter, Eckert number, and Hartmann number are increased. However, an opposite trend is noticed for Prandtl number. The concentration profile is enhanced for higher values of activation energy variable and curvature parameter for both SWCNTs and MWCNTs, whereas opposite trend is observed for reaction rate parameter, and Schmidt number. The effectiveness of scheme is endorsed through various statistical measures like regression index, error histograms, correlation analysis and convergence analysis showing a minimum level of mean square error (E-12 to E-04) for the comprehensive simulation of the proposed model.
本研究应用带有贝叶斯正则化优化器的递归神经网络（RNNs - BRO），来分析各种物理参数对丙二醇与碳纳米管混合模型在拉伸圆柱上的达西 - 福希海默流动中流体速度、温度和质量浓度分布的影响。该模型在热系统中具有重要应用，如热交换器、化学加工和医疗冷却设备等。所提出模型的数据集是针对不同场景，通过改变各种参数生成的，这些参数包括曲率参数、惯性系数、哈特曼数、孔隙率参数、埃克特数、普朗特数、辐射参数、活化能变量、施密特数和反应速率参数。每个数据集通过RNNs - BRO进行细化处理，以验证所提出的方案。结果通过图形解释呈现。曲率参数的增加导致速度分布加速，而对于单壁碳纳米管（SWCNTs）和多壁碳纳米管（MWCNTs），惯性系数、哈特曼数、孔隙率参数较高时则出现相反的情况。随着曲率参数、辐射参数、埃克特数和哈特曼数的增加，SWCNTs和MWCNTs的流体温度均升高。然而，普朗特数呈现相反的趋势。对于SWCNTs和MWCNTs，活化能变量和曲率参数较高时，浓度分布增强，而反应速率参数和施密特数则呈现相反趋势。通过各种统计量，如回归指数、误差直方图、相关性分析和收敛分析，证明了该方案的有效性，这些分析表明在所提出模型的综合模拟中，均方误差达到最低水平（E - 12至E - 04）。
