An Inverse Algorithm to Estimate Spatially Varying Thermal Contact Resistance

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. In general, the contact resistance varies as a function of pressure and is non-uniform along the interface. An inverse problem is formulated to estimate the variation of the contact resistance. A two-dimensional model is considered where the contact resistance is sought along the contact line at the interface between two regions. Temperature measured at discrete locations using embedded sensors placed in proximity to the interface provides the additional information required to solve the inverse problem. Given current estimates of the contact resistance as a function of position along the interface, a forward problem is solved, and a quadratic objective function is formulated to evaluate the difference between predicted temperatures at the sensors and those measured. A genetic algorithm is used to minimize the objective function and obtain the best estimate of the contact resistance. A boundary element method is used to solve the forward temperature field problem. 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.