What are inverse heat transfer problems and how are they solved?

Inverse heat transfer problems determine unknown boundary conditions, heat sources, or material properties from measured temperature data - opposite of the direct problem. Examples: determining surface heat flux from internal temperature measurements, identifying heat source location from thermal images. Challenges: ill-posed nature (small measurement errors cause large solution oscillations), non-uniqueness, instability. Solution methods: Regularization techniques (Tikhonov adding smoothness constraints, truncated SVD), Iterative methods (conjugate gradient minimizing objective function J=Σ(T_measured-T_computed)² + regularization term), Bayesian approaches quantifying uncertainty, Neural networks for real-time applications. Applications include: estimating heat transfer coefficients in quenching, determining weld pool thermal history, identifying defects via thermal NDT, and estimating metabolic heat generation in medical imaging. Proper sensor placement and uncertainty quantification are critical for reliable solutions.