The inverse problem of thermal contact resistance between rough surfaces

When two solid surfaces are in contact, it leads to non-uniform contact because of surfaces roughness. This causes constriction of heat flux and forms thermal contact resistance. The theoretical research is mainly focused on the positive problem, but there are few studies on the inverse problem. The inverse problem of thermal contact resistance is to obtain thermal contact resistance by a part of the boundary temperature, heat flux and some of the measured point temperature. The research has been applied in many fields, such as aerospace, mechanical manufacturing, microelectronics and other fields. It is a fast and effective method to determine thermal contact resistance in engineering field. In this paper, the inverse problem of thermal contact resistance with 2-D coordinate variation was solved by the boundary element method (BEM) and the conjugate gradient method (CGM). In order to verify the accuracy and feasibility of the method, according to the measured point temperature and the assumed thermal contact resistance, the temperature and the heat flux of the interface could be obtained, and then calculated and compared with the value of actual thermal contact resistance. The results show that the actual thermal contact resistance can be accurately obtained by using the BEM and CGM without the measurement error. But there exists the measurement error, the calculated result will be extremely sensitive to the measurement error, and the error of inversion result will be amplified due to the measurement error. In order to deal with this ill-posed problem, the least-squares method (LSM) was used to correct the calculated results. The results show that it can avoid some points deviating from the actual value in the inverse problem, and obviously improve the accuracy of calculations. © 2018, Editorial Office of Chinese Journal of Theoretical and Applied Mechanics. All right reserved.