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- W2095945072 abstract "We consider the problem of determining the effective thermal conductivity k ' of a composite that consists of spherical particles of thermal conductivity αk arranged on the lattice of a periodic array and surrounded by a matrix of conductivity k when a fraction f of the lattice sites is unoccupied by the particles. This may be regarded as a model of a composite medium in which the dispersed phase consists of relatively large aggregates. A method is developed to account for the long range multiparticle interactions and to determine k ' powers of a , where a is the ratio of the particle diameter to the lattice size. By using this method we determine k ' correct to O ( a 14 ) for all values of f and α . We also determine the ratio of effective conductivities k ' / k * , where k * is the conductivity at f = 0, for the case of when the particles are highly conducting ( α ⪢1) and are nearly touching their neighbours ( a → 1) via Monte-Carlo simulations including up to 3 x 10 4 particles. We then combine the two results to obtain estimates of k ' that are expected to be accurate for a wide range of α , a , and f ." @default.
- W2095945072 created "2016-06-24" @default.
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- W2095945072 date "1991-02-08" @default.
- W2095945072 modified "2023-09-27" @default.
- W2095945072 title "Conductivity of incompletely filled periodic arrays of spheres" @default.
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- W2095945072 doi "https://doi.org/10.1098/rspa.1991.0011" @default.
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