Wall heat transfer reconstruction in laminar and unsteady convective flows using physics-informed neural networks with coordinate transformations

Accurate reconstruction of convective wall heat transfer from known velocity fields remains challenging for physics-informed neural networks (PINNs), because thin near-wall thermal boundary layers and complex geometries often cause large errors in wall-normal temperature gradients. To address this challenge, this study evaluates a coordinate-transformation strategy within a PINN framework, where the physical domain is mapped to a computational domain that regularizes geometry and enhances near-wall resolution. Two representative convective flows are considered: laminar forced convection in a U-shaped channel and an unsteady Rayleigh-Bénard convection (RBC) flow. In the U-shaped channel, the standard PINN, even with near-wall refined sampling, exhibits a pronounced wall-adjacent error band, whereas the transformed formulation recovers the local Nusselt number distribution along the curved heated wall, with an error below 5%. In the RBC case, symmetric wall-normal stretching improves the representation of the top and bottom thermal boundary layers, leading to more accurate mean temperature profiles, clearer plume structures, and lower errors in time-resolved Nusselt number (around 4%). Velocity-noise tests further indicate reasonable robustness under moderate input uncertainty. These results demonstrate that the present strategy extends PINN-based reconstruction from bulk temperature prediction to reliable near-wall heat transfer estimation across geometrical complexity and unsteady convection.