On the application of physics informed neural networks (PINN) to solve boundary layer thermal-fluid problems

Deep neural network is a powerful technique in discovering the hidden physics behind the transport phenomena through big-data training. In this study, the application of physic-informed neural networks is extended to solve viscous and thermal boundary layer problems. Three benchmark problems including Blasius-Pohlhausen, Falkner-Skan, and Natural convection are selected to investigate the effects of nonlinearity of the equations and unbounded boundary conditions on adjusting the network structure's width and depth, leading to reasonable solutions. TensorFlow is used to build and train the models, and the resulted predictions are compared with those obtained by finite difference technique with Richardson extrapolation. The results reveal that the Prandtl number in the heat equation is a key factor which its value drastically changes the required number of neurons and layers to achieve the desired solutions. Also, setting the unbounded boundary at a higher distance from the origin demands an adequate number of layers and correspondingly neurons to deal with the infinity boundary condition. Finally, trained models are successfully applied to unseen data to evaluate the boundary layer thicknesses.