Application of an improved three-phase model to calculate effective characteristics for a composite with cylindrical inclusions

Abstract

A modified three-phase composite model yielding reliable effective characteristics of composite structures has been proposed. In particular, the problem of effective heat transfer coefficient of the composite structure with periodically located inclusions of circular cross-sections located on a square net is solved. Advantages of the proposed model in comparison to the classical three-phase model are illustrated and discussed.

Effective Conductivity and Critical Properties of a Hexagonal Array of Superconducting Cylinders

“…When expressed in terms of volume fraction of inclusions (103), coincides with Keller's formula (3). The first (constant) correction term to the formulae (102), can be also obtained, leading to "shifted" expression for the conductivity in the critical region, σ 1 ≃ σ 0 − 5.10217.…”

“…where index s is considered as another unknown. All unknowns can be obtained from the three starting non-trivial terms of (6), namely σ ≃ 1 + 2x + 2x 2 + 2x 3 . Thus the parameters equal α 1 = 2.24674, α 2 = −1.43401, α 3 = 0.0847261, s = 0.832629.…”

“…Formula (102) becomes invalid for x ≤ 0.3023. In the case of a square lattice of inclusions, Lubrication theory gives the following asymptotic result [3],…”

Refinement of the Maxwell formula for a composite reinforced by circular cross-section fibres. Part II: using Padé approximants

“…In Table 1, for average and large sizes of inclusions, the values of the effective heat transfer parameter are reported based on the carried out computations given in [11][12][13][14][15][16] for the case of absolutely conductive inclusions (λ → ∞). Further, they are compared with results of SAM-PA computations based on formulas (2.5), (2.6).…”

“…Further, they are compared with results of SAM-PA computations based on formulas (2.5), (2.6). Table 2 reports the values of the averaged coefficient computed with a help of SAM-PA in contrast to the asymptotic solutions obtained in [11,12,15,16] for inclusions of large sizes close to the limiting ones (a → 1) and for large conductivity λ >> 1 (including the limiting case λ → ∞).…”