Estimation of spatially varying thermal contact resistance from finite element solutions of boundary inverse heat conduction problems split along material interface

Abstract

This paper presents a method for estimating spatially varying thermal contact resistance from a computational point of view. The method starts by splitting the computational domain along material interface to yield two boundary inverse heat conduction problems. Temperatures computed from analytical solutions are specified at only three interior points of each material instead of temperatures available from experiments. A number of equations constructed from modified cubic spline specified along the interface are incorporated into finite element equations during the solution process. After extracting temperatures and heat transfer rates from both finite element solutions, which are solved separately, thermal contact resistance at each pair of coincident nodes on the interface are calculated.Constant, sinusoidal, and triangle functions are selected as spatial functions of thermal contact resistance along material interface to test the method. Constant thermal contact resistance is estimated accurately. Shapes of sinusoidal and triangle functions are fairly captured, locations of their maximums are correctly predicted. Thermal load is suggested to be applied on the boundary of material that has lower thermal conductivity to let the method works properly. Quantifying the uncertainty of estimated thermal contact resistance is demonstrated by adding bias error based on accuracy of sensors to the temperatures specified on the interior points of both materials.