Finite heating duration based-sensitivity analysis in transient heat conduction

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 experimental setup for thermal properties measurements of solid materials, the heater in contact with the specimen can be modelled through an high conductivity thin layer. In such a case the one dimensional finite rectangular body, representing the sample, is subject to a boundary condition of the 4th kind at the heated boundary. Also, a constant heat flux applied for a finite period of time is considered in the analysis and the sample backside is assumed insulated. The temperature field within the finite body is obtained by using the superposition principle. Then, the scaled sensitivity coefficients are computed analytically for two different locations: at the interface between the heater and the sample, and at the sample backside. The results show that the sensitivity coefficients with respect to the thermal conductivity and to the volumetric heat capacity of the sample are uncorrelated.