## Thermal Diffusivity and Coefficient of Thermal Expansion of Composites

The thermal diffusivity of an isotropic composite can be determined from the knowledge of thermal conductivity, density, and heat capacity of the composite. The thermal conductivity of the composite can be estimated from the models discussed in the previous chapters. Assuming composite to be a pseudo-homogeneous mixture of dispersed phase and matrix, the density and heat capacity of the composite could be estimated from the following relations [1]:

1 1 ρ ρ ρ

= + −x x

(19.3)

or

ρ = ϕρd + (1 − ϕ)ρm (19.4)

Cp = (ρdCp,d ϕ + ρm(1 − ϕ)Cp,m)/ρ (19.5)

or

Cp = xCp,d + (1 − x)Cp,m (19.6)

where subscript “d” refers to dispersed phase property and “m” refers to matrix property, ϕ is the volume fraction of filler, and x is the mass fraction of filler. Note that ϕ and x are related as follows:

x d= ρ ρ

φ (19.7)

Figure 19.1 shows the plot of experimental values of thermal diffusivity of composites of copper spheres and copper whiskers [1]. The data are plotted as a function of filler volume fraction. The estimated values of thermal diffusivity, using the above equations in conjunction with the Maxwell-Eucken equation (Equation 16.24 of Chapter 16), are also shown as a solid curve. Clearly there is a good agreement between the experimental and estimated values.