Measuring thermal diffusivity when the principal axes are unknown a priori

Abstract

The thermal diffusivity of polymers may develop anisotropy due material possessing or mechanical loading. The orientation of the anisotropy may not be visually apparent. An analytical study has been performed where the four non-zero components of the diffusivity tensor are estimated for a specimen with in-plane anisotropy. Sensitivity coefficients were calculated for each of the non-zero components of the diffusivity tensor at the four measurement locations. The amplitude of the sensitivity coefficients suggest that the signal received at each sensor is sufficient for estimating the parameters, while the character of the coefficients over time suggests that the parameters are independent. Small values of in-plane anisotropy lead to negligible errors (< 0.4%) in the estimated parameters when the off-diagonal diffusivity is neglected. Larger differences in anisotropy require the estimation of the off-axis terms, which is possible with the addition of a fourth sensor to the extended flash diffusivity method. This additional measurement may be used to verify assumptions of thermally orthotropic behavior in materials.