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Apparent Thermal Conductivity of a Heterogeneous Ceramic Body Under Isothermal Conditions
Author(s) -
WHITMORE D. H.
Publication year - 1960
Publication title -
journal of the american ceramic society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.9
H-Index - 196
eISSN - 1551-2916
pISSN - 0002-7820
DOI - 10.1111/j.1151-2916.1960.tb14598.x
Subject(s) - thermal conductivity , thermodynamics , ceramic , isothermal process , volume fraction , materials science , heat transfer , dielectric , conductivity , thermal conduction , phase (matter) , chemistry , physics , composite material , optoelectronics , organic chemistry
USING statistical arguments, Brown 1 derived expressions for the apparent permittivity of a binary mixture of solid phases in terms of the volume fractions and the permittivitits of each phase. The purpose of the present note is to direct the attention of experimentalists working on heat‐transfer phenomena in ceramics to the fact that simple extensions of Brown's results will yield equations for the apparent thermal conductivity of a heterogeneow ceramic body at constant temperature, whether the heterogeneity arises from the existence of isometric pores in an otherwise homogeneous solid or as a result of two solid phases being present. It is demonstrated below that the averaging formula for the apparent thermal conductivity of a porous ceramic body derived by Loeb, 2 and employed by Francl and Kingery, 2 is a consequence of terminating series expansions for the thermal conductivity after the fist term. Brown's generalized result is given by where, for the dielectric case, KO is the ratio of the polarization to the Lorentz field intensity and K is the ratio of averaged values of these quantities, A is the shape factor for the particles of the minor phase in a binary mixture, and VA is the volume fraction of that phase.