The thermal conductivity of particulate composites by the use of a polyhedral model

The Thermal Conductivity of Periodic partIculate Composites as Obtained from a Crystallographic Mode of Particle Packing

“…In addition, theoretical values derived from two and three phase inverse law of mixtures and other formulae also appear [see Appendix Section]. Venetis and Sideridis [20] Also, in the above equation the symbol "k" is used to denote thermal conductivity, "n" to denote viscosity, "E" for the elastic modulus, and "G" for the shear modulus. On the other hand, a shear loading analogy method was proposed by Springer and Tsai [25], to estimate thermal conductivity of a composite.…”

“…(63) constitutes a slight improvement of Agari and Uno formula; whilst for medium contents up to 0.4 this improvement seems to be more considerable. On the other hand, it is evident that the proposed formula for thermal conductivity yields much better theoretical predictions when compared with inverse mixing laws for two and three phases and the three other theoretical formulae [13,19,20] which were derived on the basis of multiphase forms of inverse law of mixtures given that the application of standard rule of mixtures cannot take place to evaluate this bulk property of a particulate composite. The latter is attributed to the fact that in particulate composites the component phases are interconnected through consecutive spherical phases of filler and matrix [21].…”

“…Moreover, since we have already considered that in the 4 -phase model occurring in Fig. 3 the circle of radius 20 w , lies in the middle of the circular section denoting the third phase, eqn. (7) Here, one may pinpoint that 20 inclusions occupy the centroids of all faces whereas 30 inclusions occupy the midpoints of the edges.…”

“…Yet, one may suppose the maximum influence of interphase both on the thermal conductivity of this intermediate zone and the overall material by supposing that this indicator equals unity [19,20] Now, to estimate the terms A , B and C which depend on the radii as well as the thermal conductivities of constituents of the composite, one may apply the previous boundary conditions and in addition, may suppose that all the parabolas which represent graphically this aforementioned variation should have global minima at the critical values i r . The corresponding mathematical expression of this requirement, can be formulated as follows…”

“…Moreover, in Ref. [20] a more advanced polyhedral model was introduced to simulate the paricle arrangement and then to evaluate the thermal conductivity of periodic particulates. In the present work, we examine a periodic particulate composite in the frame of an icosahedral non body centered model yielding three different variations.…”