Physics-informed neural networks for heat transfer in non-Newtonian Casson fluid flow around a horizontal cylinder

In the field of artificial intelligence and machine learning, physics-informed neural networks (PINNs) have received considerable attention because of their extensive applications in flow problems. PINN is a highly effective tool for discovering the intrinsic physics behind transport phenomena by incorporating governing equations into the training procedure of the neural network. The system of nonlinear partial differential equations is developed using non-Newtonian Casson fluid over a cylinder under the effect of a magnetic field in a porous medium. TensorFlow was employed to create and train the models, and the predicted results were compared with the reference solutions using the bvp4c method. This study compared the numerical and predicted solutions for parameter variation. The desired solutions were obtained by extending the parameter values, which required more neurons and hidden layers. To examine the prediction with PINNs, we used four number of hidden layer and three two number of neurons in the PINN design. In addition, the infinite boundary condition requires a suitable number of layers and neurons to be accounted for when the faraway boundary is set at a larger distance from the origin. The variations of various parameters are analyzed on flow output, i.e. velocity and temperature profiles. The interesting of Lorentz force is examined on fluid velocity and heat transfer analysis. It is noted Lorentz force have opposing effects on velocity. It is also noted that with the growing value of thermal radiation results in the increment of heat transfer.