The reciprocity function approach applied to the non-intrusive estimation of spatially varying internal heat transfer coefficients in ducts: numerical and experimental results

International Journal of Heat and Mass Transfer, 90 (2015), 1221-1231
http://www.sciencedirect.com/science/article/pii/S0017931015007371

This paper presents a methodology to estimate internal convective heat transfer coefficients in ducts, using only data available at an exterior boundary. The methodology is based on the reciprocity function approach, which does not require any intrusive measurements and it needs low computational resources because it avoids the use of iterative techniques. The unknown function can be estimated by solving a linear system, where the solution vector is composed of integrals of the boundary data. Numerical results are presented, where the stability of the method is tested against different functions, with high levels of noise. In the final part of the paper, for a real test case, using measurements taken by an infrared camera, the method is analyzed and compared with a traditional technique, showing very good results. The estimate can be performed in less than 3 s, using an inexpensive Raspberry Pi computer (less than US$28), equipped with a Broadcom BCM2835 system on a chip (SoC) processor.