Analytical developments and experimental validation of a thermocouple model through an experimentally acquired impulse response function

Abstract

This paper addresses the significance of and need for understanding the thermal impulse response function for (1) validating in-situ thermocouple models; and, (2) forming a “parameter free” inverse heat conduction methodology. The former application is the focus of the present study but it will be evident how to implement the findings of this presentation into the latter situation. The experimental component of this study utilizes a new small-sample, high-accuracy, electrical heating test facility for producing a quantifiable and accurate heat flux source. The impulse response kernel at the probe site is extracted and used for verifying the proposed in-depth thermocouple model. A linear, first-order thermocouple model is proposed based on the orientation of the probe and limited test temperature range. The location of the thermocouple and time constant are assumed known from some independent means or experiments. The impulse response function is determined and compared with the kernel of the resulting solution of the heat equation using the first-order model. Both kernels should nearly replicate if the model is not physically deficient. This preliminary investigation demonstrates a new means for (1) reconstructing the impulse response function and (2) validating a thermocouple model. Further, this experimentally generated impulse function can be used for resolving inverse heat conduction problems.