Modeling Heat Diffusion in a Laser Calorimetry Experiment

This report is about mathematical modeling of the time-dependent temperature distribution in a typical Laser Absorption Calorimetry Experiment (figure 1). Basically it is a boundary value problem of heat diffusion in cylindrical coordinates, with an inner circular region (glass sample) and an outer annular region (metal holder, not shown in the figure) with very different properties, a thermal contact resistance at the interface between them, a gaussian heat source distribution at the centre of the sample, and radiation losses from all the surfaces (the system is thermally isolated in a vacuum chamber). The first paragraph defines some mathematical tools (method of the Green’s function). A simplified model without the holder is discussed in the second paragraph. The general model is discussed in the third paragraph.