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Vector Products in Anisotropic heat transfer

  1. Aug 21, 2011 #1

    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.


    - Mike
  2. jcsd
  3. Aug 22, 2011 #2


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    Science Advisor

    I don't see any direct mathematics here. Looks more like "Materials Science" so I am moving it to "Materials and Chemical Engineering".
  4. Aug 22, 2011 #3


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    Homework Helper

    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).
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