Thermocouple Data in the Inverse Heat Conduction Problem

The presence of thermocouples inside a heat-conducting body will distort the temperature field in the body and may lead to significant bias in the temperature measurement. If temperature histories obtained from thermocouples are used in the inverse heat conduction problem (IHCP), errors are propagated into the IHCP results. The bias in the thermocouple measurements can be removed through use of appropriate detailed thermocouple models to account for the dynamics of the sensor measurement. The results of these models can be used to generate correction kernels to eliminate bias in the thermocouple reading, or can be applied as sensitivity coefficients in the IHCP directly. Three-dimensional and axisymmetric models are compared and contrasted and a simple sensitivity study is conducted to evaluate the significance of thermal property selection on the temperature correction and subsequent heat flux estimation. In this paper, a high-fidelity thermocouple model is used to account for thermocouple bias in an experiment to measure heat fluxes from solidifying aluminum to a sand mold. Correction kernels are obtained that are used to demonstrate the magnitude of the temperature measurement bias created by the thermocouples. The corrected temperatures are used in the IHCP to compute the surface heat flux. A comparison to IHCP results using uncorrected temperatures shows the impact of the bias correction on the computed heat fluxes.