Infrared thermography-based estimation of Biot number in 2D polymeric fins using Levenberg–Marquardt and Gradient Boosting

This study combines experimental and theoretical approaches to investigate steady-state, multi-dimensional heat conduction in polymeric fins. Surface temperature fields are measured using infrared thermography, while a normalized two-dimensional heat conduction model is developed and solved via integral transform techniques. Two base boundary conditions — prescribed temperature (Dirichlet) and prescribed heat flux (Neumann) — are analyzed to evaluate their impact on thermal behavior and parameter estimation. The Biot number is estimated using two approaches: (1) an inverse problem solved with the Levenberg–Marquardt (LM) algorithm and (2) a machine learning model based on Gradient Boosted Trees (GBT). Synthetic data generated from the forward model serve as the training set for the GBT approach, aligning with Problem-Informed Machine Learning (PIML) methodologies. Both approaches are then employed to estimate the convective heat transfer coefficient, while the material’s thermal conductivity is experimentally measured using a Heat Flow Meter (FOX 50). Results indicate that the LM method provides interpretability and strong performance when sensitivity is adequate and regularization is applied, while the GBT demonstrates greater robustness in nonlinear regimes and with ample training data. • Biot number estimation in polymeric fins via inverse problem and machine learning. • Synthetic temperature data from the 2D heat model trained ML for fast Bi prediction. • GBT achieved the best overall performance; Levenberg–Marquardt remained stable. • Infrared imaging experiments confirmed model validity and boundary assumptions. • Both methods achieved < 10 % average Biot error, validating the proposed approach.