Physics-Informed Neural Networks for Heat Transfer and Fluid Flow in a Channel with Isothermal Staggered Wall-Mounted Squares

Physics-informed neural networks (PINNs) have been increasingly used for thermal-fluid problems. This study evaluates the performance of the PINN approach for reconstructing a laminar forced flow field inside a rectangular channel with four staggered wall-mounted squares. Air is used as the working fluid, at a Reynolds number of Re = 100 and a Prandtl number of Pr = 0.71. The four squares are isothermal at 80 °C while the inlet fluid temperature is 20 °C. The PINN is used to predict velocity, pressure and temperature fields, as well as local and average Nusselt numbers. The PINN solutions are verified against the reference finite volume solution with 262,400 control volumes. The finite volume method is validated against exact solutions for laminar flow between isothermal plates (Poiseuille flow and Graetz problem). The PINN was trained on 100, 250, 1000 and 4000 velocity and temperature sample points. Each case was trained five times with different random seeds. Without samples the PINN fails, with streamwise velocity and temperature errors equal to 49% and 137%, respectively. With 1000 uniformly placed samples throughout the domain, the streamwise and cross-stream velocity errors are 0.5% and 2.9%, respectively. The error of the pressure predicted by the network is 0.9% while the error in the temperature field is 1.6%. The average Nusselt number is underpredicted by 11% and increasing the sample count to 4000 points does not reduce this error. A significant improvement is obtained by placing sample points inside the thermal boundary layer of the isothermal squares. When 35% of the 1000 sample points are placed in the thermal boundary layer, the error in the average Nusselt number decreases to 8% and its scatter between the training runs is reduced by four times. The reconstructed fields are more accurate than linear, radial basis function and Kriging interpolation of the same samples.