Heat experiment design to estimate temperature dependent thermal properties

Experimental conditions are studied to optimize transient experiments for estimating temperature dependent thermal conductivity and volumetric heat capacity. A mathematical model of a specimen is the one-dimensional heat equation with boundary conditions of the second kind. Thermal properties are assumed to vary nonlinearly with temperature. Experimental conditions refer to the thermal loading scheme, sampling times and sensor location. A numerical model of experimental configurations is studied to elicit the optimal conditions. The numerical solution of the design problem is formulated on a regularization scheme with a stabilizer minimization without a regularization parameter. An explicit design criterion is used to reveal the optimal sensor location, heating duration and flux magnitude. Results obtained indicate that even the strongly nonlinear experimental design problem admits the aggregation of its solution and has a strictly defined optimal measurement scheme. Additional region of temperature measurements with allowable identification error is revealed.