Parameter estimation for high-conductivity materials using boundary conditions of high even kind

A three-layer apparatus for thermal property measurements (thermal conductivity k and volumetric heat capacity C) of high-conductivity materials where a thin electrical heater is sandwiched between two identical samples is investigated. In particular, the thin heater is modeled as a lumped body so that the heat conduction transient problem concerns a one-dimensional (1-D) finite single-layer rectangular body (sample) subject to a boundary condition of the fourth or sixth kind at the heated surface and insulated at the backside. Specifically, a boundary condition of the fourth kind accounts for the heater heat capacity, while the one of the sixth kind considers also the imperfect contact between heater and sample. Once the thermal field within the sample is known and the sensitivity coefficients are computed, an optimal experiment is designed by applying the D-optimum criterion [1] in order to estimate accurately and simultaneously k and C. Then the standard deviations of the estimates are also computed.