Isotropic / anisotropic materials

Introduction

The studied materials can be isotropic or anisotropic. In other words, the thermal conductivity is:

• independent of the direction of the applied temperature gradient (isotropic material)

• dependent on the direction of the applied temperature gradient (anisotropic material)

These two cases are presented in the following sections.

Isotropic materials

Isotropic materials are characterized by a thermal conductivity, which is independent of the direction of the applied temperature gradient.

The and vectors are always collinear.

The dependence between and is a scalar relationship,

which is written as:

Anisotropic materials

Anisotropic materials are characterized by a thermal conductivity, which is dependent on the direction of the applied temperature gradient.

The and vectors are not collinear.

The dependence between and is a vector relationship,

which is written as:

with k conductivity tensor:

… in Flux

The model provided in Flux is a simplified model.

The vector dependence between and which is written as:

can therefore be expressed in the form of three curves:

, ,

The conductivity tensor is written: