Real-time determination of thermal diffusivity in a disk-shaped sample: Applications to graphite and boron nitride

Abstract

We describe a methodology for determining thermal diffusivities in real time by using temperature measurements at only two locations in a cylindrical sample. The technique is based on an analytical solution of heat transfer in a circular cylinder. This methodology does not require knowing the initial temperature increase or any timing between the applied and measured response. Starting with a heated cylindrical region having a unique fraction of the sample radius, and unique temperature measurement locations, the analytical solution for temperature at three specific radii can be approximated, after an initial transient, by a constant plus a single term that decreases exponentially with time. There are three special radii that fulfill the required condition. The data are analyzed by taking logarithms of the differences of the temperature versus time at these three radii, resulting in lines having slopes at large times that are proportional to the thermal diffusivity. Surprisingly, other choices of the size of the heated region and the measurement locations lead to similar results, except with longer transients. Experimental results for graphite and boron nitride agree with our numerical simulations and with the manufacturer’s data. This technique is applicable to solids and to liquids if heat transport due to convection is negligible.