A physics-informed neural networks approach for coupled flow and heat transfer problems

Physics-Informed Neural Networks (PINNs) have demonstrated their capability in solving highly nonlinear partial differential equations, such as the Navier-Stokes equations and energy conservation equations, with only known boundary conditions or limited data, leveraging the universal approximation ability of deep neural networks. As an emerging method, challenges remain when applying PINNs to solve flow and heat transfer problems at high Reynolds or Prandtl numbers. Vanilla PINNs often encounter significant errors when addressing these complex problems. Drawing inspiration from entropy viscosity stabilization techniques employed in direct numerical simulations to mitigate numerical oscillations in high Reynolds number in-compressible flows, we propose an enhanced PINN that incorporates entropy viscosity. This approach modifies the loss function in vanilla PINNs and is applied to solve forced convection heat transfer and mixed convection heat transfer problems in a lid-driven cavity. The results demonstrate that PINNs can accurately predict complex flow and heat transfer phenomena at high Reynolds and Prandtl numbers (Re = 2000, Pr = 7.1), significantly improving computational accuracy and solution stability.