{"title":"利用机器学习范式研究威廉姆森在带有辐射能和热源的分层介质中的热流体传输问题","authors":"","doi":"10.1016/j.ijft.2024.100818","DOIUrl":null,"url":null,"abstract":"<div><p>This study investigates Williamson fluid with stratification aspects through an inclined medium with radiative effects and with consideration of transversally applied magnetic field. Additionally, the study involves novel contribution of thermal generating source and chemically reactive species. Modelling is conceded by incorporating conservation laws in view of ordinary differential setup after employing similar variables. Afterwards, numerical simulations through shooting and Rk-4 procedures are executed to inspect the behavior of flow and thermosolutal distributions versus variation in key parameters. Subsequently, the collected data is evaluated by utilizing a multilayer perceptron-based ANN model. The input data for the heat flux, corresponding to different fluid model parameters, is trained by employing Levenberg-Marquardt paradigm and validated against numerical experiment results. The precision of the predicted data is assessed by calculating the mean squared error, determination coefficient and error rating scale. The magnitude of heat flux coefficient elevates up to 15 % in the existence of radiation effect, while depreciates up to 6 % in the presence of stratification effect. The implementation of ANN model depicts a mean square error value 1.36×10<sup>−3</sup> when no heat source, which rises to 1.41×10<sup>−2</sup> when a heat source is present. From small values of mean squared error for testing, training and validation estimated for Nusselt number ensures the performance of developed ANN network.</p></div>","PeriodicalId":36341,"journal":{"name":"International Journal of Thermofluids","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666202724002593/pdfft?md5=1d4d48b8ca34de61deb5bc9c410e2aa6&pid=1-s2.0-S2666202724002593-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Thermofluidic transport of Williamson flow in stratified medium with radiative energy and heat source aspects by machine learning paradigm\",\"authors\":\"\",\"doi\":\"10.1016/j.ijft.2024.100818\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This study investigates Williamson fluid with stratification aspects through an inclined medium with radiative effects and with consideration of transversally applied magnetic field. Additionally, the study involves novel contribution of thermal generating source and chemically reactive species. Modelling is conceded by incorporating conservation laws in view of ordinary differential setup after employing similar variables. Afterwards, numerical simulations through shooting and Rk-4 procedures are executed to inspect the behavior of flow and thermosolutal distributions versus variation in key parameters. Subsequently, the collected data is evaluated by utilizing a multilayer perceptron-based ANN model. The input data for the heat flux, corresponding to different fluid model parameters, is trained by employing Levenberg-Marquardt paradigm and validated against numerical experiment results. The precision of the predicted data is assessed by calculating the mean squared error, determination coefficient and error rating scale. The magnitude of heat flux coefficient elevates up to 15 % in the existence of radiation effect, while depreciates up to 6 % in the presence of stratification effect. The implementation of ANN model depicts a mean square error value 1.36×10<sup>−3</sup> when no heat source, which rises to 1.41×10<sup>−2</sup> when a heat source is present. From small values of mean squared error for testing, training and validation estimated for Nusselt number ensures the performance of developed ANN network.</p></div>\",\"PeriodicalId\":36341,\"journal\":{\"name\":\"International Journal of Thermofluids\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S2666202724002593/pdfft?md5=1d4d48b8ca34de61deb5bc9c410e2aa6&pid=1-s2.0-S2666202724002593-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Thermofluids\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2666202724002593\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Chemical Engineering\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Thermofluids","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2666202724002593","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Chemical Engineering","Score":null,"Total":0}
引用次数: 0
摘要
本研究探讨了威廉姆森流体通过具有辐射效应的倾斜介质的分层问题,并考虑了横向施加的磁场。此外,研究还涉及热生成源和化学反应物种的新贡献。在采用类似变量后,通过结合常微分设置的守恒定律进行建模。随后,通过射击和 Rk-4 程序执行数值模拟,以检查流动和热固性分布与关键参数变化的关系。随后,利用基于多层感知器的 ANN 模型对收集到的数据进行评估。采用 Levenberg-Marquardt 范式训练不同流体模型参数对应的热通量输入数据,并根据数值实验结果进行验证。通过计算均方误差、确定系数和误差分级,对预测数据的精度进行了评估。在存在辐射效应的情况下,热通量系数的幅度最多可提高 15%,而在存在分层效应的情况下,热通量系数的幅度最多可降低 6%。在没有热源的情况下,ANN 模型的均方误差值为 1.36×10-3,而在有热源的情况下,均方误差值上升到 1.41×10-2。努塞尔特数的测试、训练和验证估计均方误差值较小,确保了所开发的 ANN 网络的性能。
Thermofluidic transport of Williamson flow in stratified medium with radiative energy and heat source aspects by machine learning paradigm
This study investigates Williamson fluid with stratification aspects through an inclined medium with radiative effects and with consideration of transversally applied magnetic field. Additionally, the study involves novel contribution of thermal generating source and chemically reactive species. Modelling is conceded by incorporating conservation laws in view of ordinary differential setup after employing similar variables. Afterwards, numerical simulations through shooting and Rk-4 procedures are executed to inspect the behavior of flow and thermosolutal distributions versus variation in key parameters. Subsequently, the collected data is evaluated by utilizing a multilayer perceptron-based ANN model. The input data for the heat flux, corresponding to different fluid model parameters, is trained by employing Levenberg-Marquardt paradigm and validated against numerical experiment results. The precision of the predicted data is assessed by calculating the mean squared error, determination coefficient and error rating scale. The magnitude of heat flux coefficient elevates up to 15 % in the existence of radiation effect, while depreciates up to 6 % in the presence of stratification effect. The implementation of ANN model depicts a mean square error value 1.36×10−3 when no heat source, which rises to 1.41×10−2 when a heat source is present. From small values of mean squared error for testing, training and validation estimated for Nusselt number ensures the performance of developed ANN network.