Comparison of uniform and piecewise-uniform heatings when estimating thermal properties of high-conductivity materials

Abstract

A d-optimum criterion is applied to the three-layer apparatus used for simultaneously estimating thermal properties (for example, thermal conductivity and effusivity) through the plane source method. The objective is to perform a comparison between uniform heating and piecewise-uniform heating of high-conductivity solid samples. In particular, the latter case is modeled through a two-dimensional heat conduction problem in which a rectangular plate (i.e. the sample) is partially heated at the front boundary through a surface heat flux, while all the other boundaries are kept insulated. The optimal experiment is designed for different set-ups of the experimental apparatus (width of the heated region, number of sensors and their locations). The convergence and the computational efficiency of the estimation iterative procedure are the terms of the comparison, as well as the expected standard deviations of thermal conductivity and effusivity. The results indicate that the use of a piecewise-uniform heating is not completely beneficial for isotropic materials. In fact, if on one hand it may offer standard deviations reduced up to about 40%, on the other hand it would require an experiment about six times longer than that required by a uniform heating to ensure a good convergence of the estimation iterative procedure. Therefore, a major computational effort is required.