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Effective thermal conductivity of composites containing spheroidal inclusions
Author(s) -
Lu ShihYuan,
Kim Sangtae
Publication year - 1990
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690360614
Subject(s) - thermal conductivity , volume fraction , materials science , composite material , composite number , conductivity , particle (ecology) , range (aeronautics) , aspect ratio (aeronautics) , distribution (mathematics) , boundary value problem , spheroid , periodic boundary conditions , oblate spheroid , mathematical analysis , mathematics , physics , classical mechanics , chemistry , quantum mechanics , oceanography , biochemistry , in vitro , geology
The effective thermal conductivity of composite materials containing perfectly‐conducting, perfectly‐aligned, spheroidal inclusions has been computed to O ( c 2 ), where c is the volume fraction of the inclusions, by incorporating two‐particle interactions in a rigorous fashion. Relevant two‐particle problems were solved by boundary collocation and method of reflections in the near and far fields, respectively. Our results for the effective thermal conductivity are rigorous extensions of Maxwell's theory in the form of an expansion in small c ℓ α , where ℓ is the spheroid aspect ratio (α = 1 for oblate and α = 2 for prolate spheroids). The influence of microstructure was examined with two ad hoc model distribution functions: 1. a uniform distribution and 2. a stretched hard‐sphere pair distribution. The latter yielded superior results over a greater range of c , as judged by comparisons with Willis' (1977) bounds developed from variational methods.