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 10 − 5 to 10 − 4 .