ABSTRACT

The purpose of this paper is to analyze the application of one-dimensional heat transfer models for estimating material properties from full-field temperature measurements, such as those obtained from thermography experiments. The forward problem is that of heat conduction in a fin; however, simple one-dimensional models are analyzed. The classical fin formulation considers no gradients across the fin cross section, which limits its application to problems that involve low Biot number values. This can become a problem in multi-phase systems that involve a notable amount of a low thermal conductivity phase, as occurs in gas-filled porous media. In such materials, an increase in the porosity reduces the effective thermal conductivity, easily increasing the Biot number to values above the classical 0.1 limit. Besides these cases, the same problem can be found in many composite materials as well. Hence, this paper studies the application of the so-called improved lumped-differential models for the estimation of the thermal conductivity and phase fractions of two-phase systems from a given temperature field. Synthetic data of the surface temperature are employed for assessing models obtained with different approximation levels. These data were generated from the analytical solution of a two-dimensional model of the problem, and in some cases included the addition of a Gaussian error. The results show that the improved-lumped models clearly outperform the classical lumped fin formulation, providing very reasonable estimates for the Biot number and volume fraction of two-phase systems for most cases, the exception being a few cases where the Biot number of the continuous phase alone is high.