Modelling the effective thermal conductivity of compressing structures including contact resistance

A multi-physics simulation-based methodology for estimating the effective conductivity of single or repeated arrays of mechanically deforming structures being compressed between solid planer surfaces is detailed in this work. The proposed methodology utilises Finite Element (FE) simulations to determine the mechanical environment and resulting shape of the deforming structures together with its effective bulk thermal conductivity by simulating the heat transfer through the structure(s). Importantly, the FE model also incorporates the constriction thermal resistance as well as the contact thermal resistance associated with the contact region between the deforming structure(s) and the rigid planer surfaces. The latter is endemically problematic to predict and an approach is proposed which combines accurate multi-physics simulations with precision experiments to estimate the contact resistance in terms of contact pressure on the deforming structure(s). The thermal-mechanical simulation results are compared with experiments for one exemplar geometry verifying the efficacy of the approach. Although illustrated here for determining the effective thermal conductivity, the method is equally valid for determining effective electrical conductivity of deforming electrically conductive structures undergoing compression between rigid planer surfaces.