Mathematical Models for Pulse-Heating Experiments

Accurate measurements of thermophysical properties at high temperatures (above 1000 K) have been obtained with millisecond pulse-heating techniques using tubular specimens with a blackbody hole. In the recent trend toward applications, simpler specimens in the form of rods or strips have been used, with simultaneous measurement of the normal spectral emissivity using either laser polarimetry or integrating sphere reflectometry. In these experiments the estimation of the heat capacity and of the hemispherical total emissivity is based on various computational methods that were derived assuming that the temperature was uniform in the central part of the specimen (long thin-rod approximation). The validity of this approach when using specimens with large cross sections (rods, strips) and when measuring temperature on the specimen surface must be verified. The application of the long thin-rod approximation to pulse-heating experiments is reconsidered, and an analytical solution of the heat equation that takes into account the temperature dependence of thermophysical properties is presented. A numerical model that takes into account the temperature variations across the specimen has been developed. This model can be used in simulated experiments to assess the magnitude of specific phenomena due to the temperature gradient inside the specimen, in relation to the specimen geometry and to the specific thermophysical properties of different materials.