Determination of thermal diffusivity in a disk shaped sample using edge heating applications to Stainless Steel

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 cylinder heated on the outer surface and unique temperature measurement locations, the analytical solution for temperature at two specific radii can be approximated, after an initial transient, by a constant plus a single term that decreases exponentially with time. There are two special radii that fulfill the required condition. The data are analyzed by taking logarithms of the differences of the temperature versus time at these two radii, resulting in lines having slopes that are proportional to the thermal diffusivity. Surprisingly, other choices of the measurement locations lead to similar results, except with longer transients. Experimental results for type 304 stainless steel from room temperature to 450 °C agree with our numerical simulations and published data. This technique is applicable to solids and to liquids if heat transport due to convection is negligible.