Sensitivity Coefficients for Thermal Properties Measurements Using a Boundary Condition of the Sixth Kind

In the parameter estimation the sensitivity analysis of the temperature to the unknown parameter (such as thermal conductivity, heat capacity) plays a fundamental role. In the current paper such a sensitivity analysis is carried out in the event that the imperfect thermal contact between the thin heater and the specimen is taken into account. In particular, in the experimental configuration for thermal properties measurements of solid materials, the thin heater, which is in imperfect contact with the specimen, may be modeled through an high conductivity thin layer at which an heat flux is applied. Thus, in the addressed conductive problem, the one dimensional finite rectangular body, representing the sample, is subject to a boundary condition of the sixth kind at the heated boundary. Once the thermal field is known, the scaled sensitivity coefficients are computed analytically for different locations: at the interface between the heater and the sample (heater side and sample side), and at the sample backside. The results show that the sensitivity to the thermal conductivity and to the heat capacity of the sample are uncorrelated and large in magnitude.