We examined numerical and experimental use of a coupled-transducer system comprised of a thermocouple temperature measurements and time of flight acoustic measurements to determine the recession rate of a carbon material. A problem in the use of ultrasonic transducers for high temperature thickness measurements is that the temperature of the specimen is not always known. The variation of the speed of sound with temperature makes this a challenging problem and the use of a limited number of temperature measurements helps to construct a temperature profile on which the acoustic time of flight measurement can be characterized. In the problem of interest, a high heat flux is directed towards the surface of a carbon based material. A temperature profile is set up in the material. Initially the heated face simply increases in temperature with no mass loss. With increasing heating and oxygen transport to the surface, the hot face begins to oxidatively erode. Temperature measurements Y (xi) are made at xi locations within the material. At the same time a time of flight measurement is made in the material. We can assume that the time of flight measurement takes place over a time period that is small relative to the time for which the spatial temperature variation evolves. As such, the time of flight measurement primarily involves a weighted spatial integration of a function of temperature. Given the temperature measurements and the time of flight measurement, we seek the recession rate or equivalently, the sample length. We develop a simple thermal model with appropriate representation of oxidation kinetics to describe the process. A simple inversion analysis is developed and tested on synthetic data to best fit the experimental data.

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