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Upper and lower reciprocal variational principles have been used to estimate the effective conductivity (or diflusivity)across beds of randomly dispersed fibers with orientations distributed in two and three dimensions. Estimated thermal conductivities of fiber glass insulation, graphite-epoxy fiber reinforced composite materials, as well as the diffusivities of several fibrous materials agree well with measured values.
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Tsai et al. (1986) studied this question.
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