Filtered reciprocity functional approach to estimate internal heat transfer coefficients in 2D cylindrical domains using infrared thermography

Performance estimation of heat exchanger apparatuses requires a proper knowledge of the thermo-fluid dynamic interaction between fluid and device. One of the aspects to take into account is related to the estimation of the internal convective heat transfer coefficient. This requires the knowledge of the internal temperature and the internal wall heat flux, although these quantities are complicated to be measured. Therefore, the use of inverse problem techniques may be very useful for estimating these quantities. This approach deals with the estimation of the local internal properties, given some external temperature measurements, possibly by means of contactless experimental methodologies (i.e. infrared camera imaging). The solution strategy here presented, for a 2D model, is based on the Reciprocity Functional approach (RF), which requires the solution of two auxiliary problems that are solved, in this paper, by means of the Classical Integral Transform Technique (CITT). The RF approach coupled with CITT, presents some advantages over other techniques since its solution is completely analytical and therefore computationally fast, and it does not require any numerical simulation. Moreover, it deals with the noise content of the experimental data, filtering it and overcoming the documented limits of the classical RF approach. This original method, named Filtered Reciprocity Functional (FRF) approach, was applied to different test cases using simulated measurements, and the results were compared to both the exact and the reconstruct solutions obtained by the Truncated Singular Value Decomposition (TSVD) method, showing a good agreement. Finally, the FRF approach was applied to an experimental case in order to test its robustness when dealing with real data.