PINN-FFHT: A physics-informed neural network for solving fluid flow and heat transfer problems without simulation data

Abstract

In recent years, physics-informed neural networks (PINNs) have come to the foreground in many disciplines as a new way to solve partial differential equations. Compared with traditional discrete methods and data-driven surrogate models, PINNs can learn the solutions of partial differential equations without relying on tedious mesh generation and simulation data. In this paper, an original neural network structure PINN-FFHT based on PINNs is devised to solve the fluid flow and heat transfer problems. PINN-FFHT can simultaneously predict the flow field and take into consideration the influence of flow on the temperature field to solve the energy equation. A flexible and friendly boundary condition (BC) enforcement method and a dynamic strategy that can adaptively balance the loss term of velocity and that of temperature are proposed for training PINN-FFHT, serving to accelerate the convergence and improve the accuracy of predicted results. Three cases are predicted to validate the capabilities of the network, including the laminar flow with the Dirichlet BCs in heat transfer, respectively, under the Cartesian and the cylindrical coordinate systems, and the thermally fully developed flow with the Neumann BCs in heat transfer. Results show that PINN-FFHT is faster in convergence speed and higher in accuracy than traditional PINN methods.