Optimal experiment design for thermal property estimation using a boundary condition of the fourth kind with a time-limited heating period

Abstract

An optimal design of a three-layer experimental apparatus where a thin heater is placed between two identical samples is proposed. It allows thermal conductivity and volumetric heat capacity of high-conductivity materials to be estimated when the heating period is finite and the heater heat capacity is not negligible. Once the thermal field within the sample is known and the sensitivity coefficients are computed, a D-optimum criterion is applied in order to minimize the area of the confidence region of the estimates. Three experimental variables (experiment duration, heating duration and sensor location) are investigated for different values of the heater heat capacity. For instance, when it is 5% of the sample heat capacity, the optimal experiment duration is of about 4% longer than that occurring when the heater is neglected. However, the heater heat capacity does not affect the optimal heating duration and the optimal sensor locations.