使用 Levenberg-Marquardt 算法计算磁场、辐射和焦耳热对威廉姆森流体在垂直通道中自然对流的影响

IF 2.3 4区 工程技术 Q2 ENGINEERING, MECHANICAL
Subham Jangid, Kaladhar Kolla
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引用次数: 0

摘要

研究探讨了威廉姆森流体在磁场、辐射和焦耳热效应影响下通过垂直通道的自然对流。利用适当的变换将支配偏微分方程转化为常微分方程,并使用谱准线性化方法(SQLM)进行求解。研究解释了一种使用 Levenberg-Marquardt 技术(BPFF-LMT)的前馈反向传播神经网络算法。此外,还为几个参数创建了参考数据集,包括磁参数、霍尔参数、辐射参数、魏森伯格数、比奥特数和焦耳热参数。该数据集包括采用 SQLM 的不同情况下的速度和温度曲线。BPFF-LMT 方法的准确性通过涉及训练、验证和测试阶段的综合分析,以及均方误差、误差直方图、性能和回归图进行了评估。人工神经网络的结果与 SQLM 数值解决方案相比,显示出良好的准确性。结果通过图形直观呈现,并进一步对数学公式中的有效参数进行了定量分析。结果表明,磁参数值的增加会导致速度和温度曲线的下降。此外,左通道的热传导率也有所增加。辐射参数和韦森伯格数都会导致速度和温度曲线升高,从而增加左通道的表皮摩擦。BPFF-LMT 方法的准确性通过图表加以说明,图表显示了[公式:见正文]至[公式:见正文]范围内的绝对误差。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Magnetic field, radiation, and Joule heating effects on natural convection Williamson fluid flow through a vertical channel using Levenberg–Marquardt algorithm
The study examined the natural convection flow of Williamson fluid through a vertical channel under the influence of the magnetic field, radiation, and joule heating effects. The governing partial differential equations are turned into ordinary differential equations using suitable transformations and solved by using the spectral quasi-linearization method (SQLM). The study explained a neural network algorithm called feed-forward back-propagation using the Levenberg–Marquardt technique (BPFF-LMT). Furthermore, a reference dataset is created for several parameters, including the magnetic parameter, Hall parameter, radiation parameter, Weissenberg number, Biot number, and Joule heating parameter. This dataset encompasses velocity and temperature profiles for different scenarios, employing the SQLM. The BPFF-LMT method’s accuracy was evaluated through a comprehensive analysis involving training, validation, and testing phases, along with mean squared error, error histograms, and performance and regression graphs. The artificial neural network’s result shows good accuracy when compared to the SQLM solution numerically. The results are presented visually through graphical representation and further analyzed quantitatively concerning the active parameters featured in the mathematical formulations. The result indicates that increasing values of the magnetic parameter result in decreased velocity and temperature profiles. Additionally, the heat transfer rate increases in the left channel. Both the radiation parameter and Weissenberg number contribute to higher velocity and temperature profiles, leading to increased skin friction in the left channel. The accuracy of the BPFF-LMT method is illustrated through graphs displaying the absolute error falling within the range of [Formula: see text] to [Formula: see text].
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来源期刊
CiteScore
3.80
自引率
16.70%
发文量
370
审稿时长
6 months
期刊介绍: The Journal of Process Mechanical Engineering publishes high-quality, peer-reviewed papers covering a broad area of mechanical engineering activities associated with the design and operation of process equipment.
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