Transient non-intrusive method for estimating spatial thermal contact conductance by means of the reciprocity functional approach and the method of fundamental solutions

Inverse Problems in Science and Engineering, 23(4) (2015), 688-717
http://dx.doi.org/10.1080/17415977.2014.933830

Thermal contact resistance/conductance is very important in many heat transfer applications, such as electronic packaging, nuclear reactors, aerospace and biomedicine, among others. The determination of the thermal contact resistance/conductance is often a very difficult task. Previously, the authors presented a computationally fast inverse problem methodology to estimate thermal contact conductance without intrusive measurements, in steady-state heat conduction problems. This paper is an extension of such methodology, applied to transient problems. The methodology presented is formulated in terms of a reciprocity functional approach, together with the method of fundamental solutions. The solution is composed of two steps. In the first step, two steady-state auxiliary problems, which do not depend on the thermal conductance, are solved. With the results of the first step, different thermal conductances can then be recovered through an integration process of the boundary data. Thus, the methodology is fast and can be used to detect contact flaws in different materials with small computational effort. Test cases with simulated measurements containing measurement errors are presented in order to illustrate the robustness of the proposed technique.