Thermal Conductivities of Unidirectional Materials

Abstract

In this paper the composite thermal conductivities of unidirectional composites are studied and expressions are obtained for predicting these conductivities in the directions along and normal to the filaments. In the direction along the filament an expression is presented based on the assumption that the filaments and matrix are connected in parallel. In the direction normal to the filaments composite thermal conductivity values are obtained first by utilizing the analogy between the response of a unidirectional composite to longitudinal shear loading and to transverse heat transfer; second by replacing the filament-matrix composite with an idealized thermal model. The results of the shear loading analogy agree reasonably well with the results of the thermal model particularly at filament contents below about 60%. These results were also compared to experimental data reported in the literature and good agreement was found between the data and those theoretical results that were derived for circular filaments arranged in a square packing array.

Thermal conductivity of engineered bamboo composites

“…The Halpin-Tsai equations [21], while commonly used to model transverse elastic moduli, may also be used to model transverse thermal conductivity. Springer and Tsai [22] and Zou et al [23] have also developed models for the transverse thermal conductivities of unidirectional composites, based on a thermal-shear loading analogy and a thermal-electrical analogy, respectively. The Springer and Tsai model is referred to as the C-S model as they assume circular cross section fibre reinforcements in a square-packing arrangement, while the model presented by Zou et al [23] is referred to as the E-S model as they assume elliptical cross section fibres in a square-packing arrangement.…”

The Thermal Conductivities of Periodic Fibrous Composites as Defined by a Mathematical Model

“…Figure 11 shows the variation of transverse thermal conductivity with respect to filler content according to four theoretical models. Here, one may observe that the values obtained from Springer and Tsai's formula [4] are well above those arising from Hashin's formula [3], the two-phase inverse mixture law and finally Equation (65). However, Springer and Tsai's approach has supposed matrix and fiber as parallel and series as in electrical circuits.…”

“…In continuation, Figure 10 illustrates the variation of c L Κ with respect to fiber volume fraction according to three different theoretical approaches. Here, one may observe that the proposed theoretical formula represented by Equation (63) definitely constitutes an improvement when compared with the classical expression introduced by Springer and Tsai [4]. Moreover, for low fiber contents, the theoretical values obtained from Rayleigh's formula are below those arising from Equation (63).…”

“…Besides, the theoretical values of the longitudinal thermal conductivity of the composite yielded by Equation (63) appear along with those arising from two other theoretical formulae derived from Rayleigh [2] and Springer and Tsai [4]. In continuation, Figure 10 illustrates the variation of c L Κ with respect to fiber volume fraction according to three different theoretical approaches.…”

“…In continuing, we should determine the radii of the three interphases 2 r , 4 r , 6 r along with the interphase volume fractions in the three regions separately. To this end, let us adopt the following notations:…”