The formalism developed by [Benveniste, (1987)] for describing the elastic behavior of fiber reinforced materials can be directly extended to diffusion problems (see also [Böhm, et al (2008)]). The thermal conductivity coefficients predicted by the Mori-Tanaka method then read

(3–13)

where the gradient concentration tensor is given by

(3–14)

with

(3–15)

You can find expressions of the Eshelby tensor for the diffusion problem for different type of inclusions in, for example, [Parnell, (2016)]. Material Designer supports ellipsoidal inclusion types.

The orientations averaging for a composite with misaligned fiber orientations is done similarly as for the stiffness tensor in the section above, Orientations Averaging. Assuming the inclusions to be transversely isotropic along and the matrix to be isotropic, the orientation average of the conductivity tensor is completely determined by the second-order orientation tensor and the underlying unidirectional conductivity tensor. See for example [Advani et al, (1987)].