Development of an algorithm to extract thermal diffusivity for the radial converging wave technique

The usual equation for the converging wave method [P. Cielo, L.A. Utracki, M. Lamontagne, Thermal diffusivity measurements by the converging thermal-wave technique, Canad. J. Phys. 64 (1986) 1172-1177] for thermal diffusivity measurements assumes idealised conditions that are difficult to achieve in a real experimental situation and this hinders the extraction of diffusivity values. A model for thermal transport is described here that takes into account errors due to heat losses and is relatively insensitive to detection position inaccuracy. A simple polynomial equation is derived from the model and it is used to generate initial guesses for the Levenberg-Marquardt algorithm, which uses these initial guesses to avoid a local minimum problem and ultimately produces a value for radial thermal diffusivity.