Effects of contact resistance on thermal conductivity of composite media with a periodic structure

Abstract

Abstract. The thermal conductivity of periodic composite media with spherical or cylindrical inclusions embedded in a homogeneous matrix is discussed. Using Green functions, we show that the Rayleigh identity can be generalized to deal with thermal properties of these systems. A new calculating method for effective conductivity of composite media is proposed. Uselul formulae for effective thermal conductivity are derived, and meanings of contact resistance in engineering problems are explained. volume fraction of inclusion for two-dimensional and three-dimensional system Ql,, VI, definite integrals, defined in (22) and (23) S , , T, definite integrals, defined in (28) and (29)

An eigenfunction expansion–variational method in prediction of the transverse thermal conductivity of fiber reinforced composites considering interfacial characteristics

“…At the same time, the so-called composite design is generally a design of periodically distributed unit cells of a composite [10]. Gu and Liu [11] discussed the thermal conductivity of periodic composite media with contact resistance by applying a generalized Rayleigh identity. Lu and Lin [12] studied the effect of interfacial characteristics on the effective thermal conductivity of two-dimensional periodic composites by using a boundary collocation scheme.…”

Effective thermal conductivity of composite spheres in a continuous medium with contact resistance

“…Apart from the large number of results which are based on either highly approximated micromodels or ad hoc mixing rules, several approaches based on reasonable physical models have also been established and refined to include the effects of various particle shapes plus imperfect thermal contact between the particle surface and the continuous medium. Such studies include: exact mathematical analysis of dilute systems in which bounds are established on the effective properties, and asymptotic behavior is determined (see, for example, Beasley and Torquato [2], and Thovert and Acrivos [3]); exact mathematical analysis of various regular arrays of particles (see, for example, McKenzie et al [4], Gu and Tao [5], Gu and Liu [6], Torquato and Rintoul [7], and Cheng and Torquato [8]); numerical simulation of Brownian diffusion of pulsed sources through particle arrays (see, for example, Torquato and Kim [9], and Kim and Torquato [10]); the self-consistent field concept for analyzing non-dilute, non-regularly spaced particles (see, for example, Hashin [11], Benveniste and Miloh [12], and Benveniste [13]); and the technique of Ôsuccessive embedding of effective media' to treat multi-coated cylinders or spheres (see, for example, Schulgasser [14], and Milgrom and Shtrikman [15]). …”

An Innovative High Thermal Conductivity Fuel Design

“…It can be seen that the boundary resistance will increase with a decrease in the size of the filler material, when the volume fraction is held constant, and this was shown experimentally in the 1990s [18], [19], [20]. Swartz and Pohl [21] in 1989 have compiled the most exhaustive literature on Thermal Boundary Resistance, which marked the culmination of significant research into the concept.…”