Estimating thermal contact resistance using sensitivity analysis and regularization

Characterization of the thermal contact resistance is important in modeling of multi-component thermal systems which feature mechanically mated surfaces. Thermal resistance is phenomenologically quite complex and depends on many parameters including surface characteristics of the interfacial region and contact pressure. Although most studies seek a single value as a function of these parameters, in general, the contact resistance is non-uniform over the interface. In this paper, a technique is developed for extracting non-uniform contact resistance values from experiments in two-dimensional configurations. To begin, a two-dimensional model problem is formulated for a known contact resistance between two mated surfaces. An inverse problem is devised to estimate the variation of the contact resistance by using the BEM to determine sensitivity coefficients for specific temperature measurement points in the geometry. Temperature measured at these discrete locations can be processed to yield the contact resistance between the two mating surfaces using a simple matrix inversion technique. The inversion process is sensitive to noise and requires using a regularization technique to obtain physically possible results. The regularization technique is then extended to a genetic algorithm for performing the inverse analysis. Numerical simulations are carried out to demonstrate the approach. Random noise is used to simulate the effect of input uncertainties in measured temperatures at the sensors.