Sensitivity Coefficients in Heat Conduction for Short Times Using a Boundary Condition of the 6th Kind

An analytical approach for computing the transient temperature and related sensitivity coefficients in a onedimensional, two-layer Cartesian body is described. In particular, we refer to an experimental apparatus for thermal property measurements of solid materials where one layer is the thin heater while the other is the sample of interest that can exchange heat on the backside. Once the temperature of both layers is obtained [1], the so-called ‘scaled’ sensitivity coefficients are calculated using a finite difference scheme [2]. In the inverse problems such as parameter estimation, the sensitivity coefficients give a significant contribution to the optimal design of experimental apparatus [2,3]. Since the parameter estimation technique requires measured temperature values, the scaled sensitivity coefficients are desired to be large in magnitude (compared to the representative temperature). Moreover, in order to estimate multiple parameters simultaneously, the sensitivity coefficients need also to be linearly independent (having different shapes).