New exact analytical formulas for the simultaneous estimation of thermal diffusivity and optical absorption depth from laser flash experiments

This paper develops new exact analytical formulas for the simultaneous estimation of thermal diffusivity and absorption depth in the one-dimensional adiabatic laser flash analysis with finite absorption depth. The analysis is based on the exact front-face and rear-face thermograms. Three closed-form identification routes are derived. We denote these routes by FRZM, RF01, and FF01.RF01, and FF01. In each case, explicit formulas are obtained for both thermal diffusivity and absorption depth. The proposed formulas are assessed by Monte Carlo simulations using synthetic front and rear thermograms corrupted by Gaussian noise. The results show a clear ranking between the estimators. For diffusivity, the FRZM formula gives nearly the same performance as Carr’s exact surface integral formula, while avoiding prior knowledge of the absorption depth. Its RMSE is 0.0742%, 0.3008%, and 0.7285% for noise levels σ = 0.005 , 0.02, and 0.05, compared with 0.0693%, 0.2812%, and 0.6814% for Carr’s formula. For absorption depth, the FRZM formula is the most stable of the three new approaches. Its bias remains close to 0.7% to 0.8%, and its RMSE increases from 1.3359% to 10.6437% over the same noise scale. By contrast, Parker’s half-rise-time formula shows a strong increase in bias, whereas the RF01 formula exhibits large dispersion. These results demonstrate that the developed low order integral formulas perform best in terms of balance between exact analytical structure and noise sensitivity. These results support the relevance of the FRZM estimator for the simultaneous estimation of thermal diffusivity and absorption depth under the stated one-dimensional adiabatic assumptions.