We report here on the use of the heat equation to simulate a thermal interrogation method for detecting damage in a heterogeneous porous material. We first use probability schemes to randomly generate pores in a sample material; then we simulate flash heating of the compartment along one of its boundaries. Temperature data along the source and back boundaries are recorded and then analyzed to distinguish differences between the undamaged and damaged materials. These results suggest that it is possible to detect damage of a certain size within a porous medium using thermal interrogation.

We discuss a mathematical model for the flash-heat experiment in homogeneous isotropic media. We then use this model to investigate the use of homogenization techniques in approximating models for interrogation via flash-heating in porous materials. We represent porous materials as both randomly perforated domains and periodically perforated domains.

In 1969, M.I. Mendelson published a paper in the Journal of the American Ceramic Society that introduced a proportionality constant of 1.558 for estimating the average 3D grain size from the mean 2D lineal intercept under the assumption of lognormally distributed grains. Recent simulations by the authors revealed that the lognormal parameterization in the original work actually calculates the median grain size instead of the mean. The relationship between the mean caliper diameter and mean lineal intercept was found to be 1.60 when using common parameterizations. In addition, it is demonstrated through simulations that the correct proportionality constant can range from 1.776 to below unity depending on a material's grain size dispersion, such that 1.60 should only be used as a crude approximation. K E Y W O R D Scharacterization, grain size distribution microstructure, particle size distribution, simulations, stereology

In this effort we investigate the behavior of a model derived from homogenization theory as the model solution in parameter estimation procedures for simulated data for heat flow in a porous medium. We consider data simulated from a model on a perforated domain with isotropic flow and data simulated from a model on a homogeneous domain with anisotropic flow. We consider both ordinary and generalized least squares parameter estimation procedures.

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