A theoretical upper limit for sensitivity coefficients in parameter estimation and complementary transient experiments

In the design of transient thermal experiments for estimating the thermal conductivity, k, and volumetric heat capacity, C, the scaled sensitivity coefficients are utilized. These coefficients should be large and uncorrelated. It is proven that they are the largest when the heated surface temperature of the sample is held at the maximum value. Hence, they can be assumed as ‘ideal reference sensitivities,’ which actual k- and C-sensitivity coefficients can refer to in order to evaluate their relative magnitude. In addition, by using two complementary experiments, the sensitivity coefficients can be made more uncorrelated than if a single experiment is used. The result of two combined experiments is that the above two parameters are found with the greatest accuracy. The parameters are also of equal accuracy, which is generally not the case.