Rear-surface integral method for calculating thermal diffusivity from laser flash experiments

Abstract

The laser flash method for measuring thermal diffusivity of solids involves subjecting the front face of a small sample to a heat pulse of radiant energy and recording the resulting temperature rise on the opposite (rear) surface. For the adiabatic case, the widely-used standard approach estimates the thermal diffusivity from the rear-surface temperature rise history by calculating the half rise time: the time required for the temperature rise to reach one half of its maximum value. In this article, we develop a novel alternative approach by expressing the thermal diffusivity exactly in terms of the area enclosed by the rear-surface temperature rise curve and the steady-state temperature over time. Approximating this integral numerically leads to a simple formula for the thermal diffusivity involving the rear-surface temperature rise history. Numerical experiments demonstrate that our new formula produces estimates of the thermal diffusivity -for a typical test case -that are more accurate and less variable than the standard approach. The article concludes by briefly commenting on extension of the new method to account for heat losses from the sample.

Rear-surface integral method for calculating thermal diffusivity: Finite pulse time correction and two-layer samples

“…To identify the integration constants, c 0 and c 1 , we combine the form of du/dx with the boundary conditions (5) [11] yielding: du dx…”

“…In the discrete case, provided t N is large enough (see, e.g. [20,21], for how to estimate steady state times), the integral I T appearing in the thermal diffusivity formulas, Eqs (17)- (19) and (44)-(47), can be approximated using the trapezoidal rule [11]. For example, for the homogeneous sample:…”

“…We now investigate the accuracy of the thermal diffusivity formulas when applied to noisy rear-surface temperature data. To mimic the data arising from the laser flash experiment, we follow Carr [11] and add Gaussian noise to the sampled values from the previous section: T i = Tn(t i ) + z i , where z i is a random number generated from a normal distribution with mean zero and standard deviation σ. Repeatedly generating synthetic rear-surface temperature rise datasets in this manner and calculating the corresponding thermal diffusivities allows distributions of the signed relative error to be constructed.…”

Advection improves homogenized models of continuum diffusion in one-dimensional heterogeneous media

“…These quantities can be thought of as characterising the timescale of the heterogeneous and homogenized models [17,18], respectively, since their values will tend to be small (at a given location x) if the transition from initial to steady state is rapid. Attractively, w(x) and W (x) can be calculated without explicit calculation of u(x, t) and U (x, t) appearing in the definitions [19]. Following previous work [17,19,20], applying the linear operator…”

“…Attractively, w(x) and W (x) can be calculated without explicit calculation of u(x, t) and U (x, t) appearing in the definitions [19]. Following previous work [17,19,20], applying the linear operator…”