Sensitivity Coefficients for Thermal Properties Measurements Using a Boundary Condition of the 4th 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. Considering the experimental configuration for thermal properties measurements of solid materials, the heater in contact with the specimen can be modeled through an high conductivity thin layer at which an heat flux is applied. In such a case the one dimensional finite Cartesian body, representing the sample, is subject to a boundary condition of the 4th kind at the heated boundary. The transient temperature within the finite body, assuming the back side surface insulated, is derived by means of the Green’s Function Solution Equation. Then the scaled sensitivity coefficients are computed in part analytically and in part numerically, for two different location: at the interface between the heater and the sample, and at the sample back side. The results show that the sensitivity coefficients with respect to the thermal conductivity and to the heat capacity of the sample are uncorrelated.