Local similar solution and neural network optimization of EMHD Boger fluid flow around a horizontal cylinder with Wu’s slip condition and Joule heating

The main goal of this research is to develop and analyze a local similarity solution for the electromagnetic flow of a Boger liquid over a circular cylinder, incorporating the combined effects of transpiration and Wu’s slip boundary conditions, which have not been simultaneously examined for this geometry and fluid type. The temperature model further includes frictional and Joule heating, adding realistic thermal effects often neglected in previous studies. To get local similar solutions, partial differential equations (PDEs) are converted to ordinary differential equations (ODEs) by first-level truncation using local non-similarity transformations. BVP4C numerical technique is employed to obtain numerical results. Moreover, an artificial neural network (ANN) is implemented for the current model using the Levenberg-Marquardt technique (LMA), which trains the network to approximate the solution of the differential equations. The artificial neural network (ANN) model has one hidden layer with five neurons that approximate the velocity and temperature solution. In order to assess the effectiveness of the ANN-LMA technique, regression analysis, histogram tests, and mean squared error indices are performed. Furthermore, the LMA neural network is trained using 70% of the data, with 15% allocated for validation and 15% for testing. It demonstrates outstanding performance, achieving a perfect predictive accuracy (R = 1). Moreover, it is observed that higher values of the solvent fraction parameter lead to a significant enhancement in the velocity profile. Likewise, the temperature profile is found to increase noticeably with larger values of the electric parameter. ANN and numerical results obtained using the MATLAB software versus various parameters are displayed in graph form.