Use of the Laplace transformation for data reduction in the flash method of measuring thermal diffusivity

Abstract

This paper presents a new way to reduce data in the laser flash method of measuring thermal diffusivity. Experimental temperature vs time data are first transformed by using the Laplace transformation, and then they are fitted with an appropriate theoretical formula. The data reduction procedure is more efficient and enables the use of more realistic models of heat conduction in the sample, because the theoretical formulae for transformed temperatures have a simpler form than those for nontransformed ones. Some examples of the theoretical formulae of transformed temperatures are included here for one- and two-dimensional heat transfer, respectively. The models described take into account a finite pulse time and heat losses from the sample. Two fitting algorithms are proposed. Experimentally, the data reduction procedure has been tested for a correction of the finite pulse time effect in the flash method. The results show that the accuracy of our procedure is comparable with other data reduction methods. Provided that the shape and duration of the pulse are known, this procedure allows elimination of the finite pulse time effect on calculation of the thermal diffusivity for any transformable heat pulse time function, even in cases where the other specialized data reduction procedures have failed.