Finite pulse time effects in flash diffusivity measurements

Abstract

Analytical short-time solutions of one-dimensional heat conduction problems associated with flash thermal diffusivity measurements are given for the case of triangular pulse shape. The heat conduction problem is solved by the use of Laplace transforms taking advantage of the fact that the convolution of the temperature response curve at the back face of the sample with a triangular pulse function reduces to a simple multiplication in the Laplace domain. Instead of using the usual inversion, an expansion of the transform, followed by a term-by-term inversion, yields the solution in the time domain. This leads to a rapidly converging series for short times. Even using only one term, the relative error from the exact solution does not exeed 0.1 % at the double half-rise time. The given solutions describe the rear-face temperature response after illumination of the front surface of a mono-layer slab with a triangular shape pulse for the case of heat losses from the sample faces as well as for adiabatic conditions. Numerical approximations are given for less common higher functions appearing in the analytical solutions.