New In Situ Method for Estimating Thermal Diffusivity Using Rate-Based Temperature Sensors

This paper proposes an experimental methodology for estimating the thermal diffusivity alpha in a one-dimensional half-space geometry based on two in situ positioned probes that can acquire temperature and the first- and second-time derivatives of temperature. The thermal diffusivity is estimated at each sampled time by solving an nth-degree polynomial in the thermal diffusivity. The degree of the alpha polynomial and the required order of the time-derivative sensors depend on the chosen spatial truncation of the Taylor series. This approach does not require the specification of the imposed surface boundary condition. Additionally, a novel sensitivity analysis is proposed for guiding sensor placement that ensures a maximum, absolute sensitivity between the two probes, and it illustrates that a single point in time can be identified whereby the thermal diffusivity can be accurately approximated in an analogous manner to the determination of the time constant of a first-order system. Finally, the method is demonstrated with a numerical simulation.