Vector Products in Anisotropic heat transfer

[Mike_In_Plano]

Hello,

I'm brushing up on my heat transfer / vector calculus, when I realized that my notes were all for isotropic heat transfer. i.e.

q(vector) = k(scaler) del(u)

However, there are cases, such as pyrolytic graphite where the thermal conductivity, k, cannot be described as a scaler. Furthermore, I'm not even certain that k can adequately be described as a simple vector since the material generally transfers at least some measure of heat through any orientation (i.e. there is not a direction that pyrolitic graphite will not transfer heat, it simply has prefferential orientations.)

Anyway, if anyone would like to take up this topic, I'd certainly like to explore it - in a simply academic fashion.

Thanks,

- Mike

[HallsofIvy]

I don't see any direct mathematics here. Looks more like "Materials Science" so I am moving it to "Materials and Chemical Engineering".

[lurflurf]

The first natural generalization is
q(vector) = k(tensor rank 2). del(u)
In other words to take assume q varies linearly with del(u).