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Dissipation due to heat conduction

  1. Nov 25, 2008 #1
    What is the dissipation due to heat conduction?

    [tex] D = -k \frac{\vec q\cdot\nabla T}{T} [/tex]

    where q is the heat flux, k is the
    coefficient of heat conduction and T is the absolut temperature.

    What is the physical meaning of this?
    Last edited by a moderator: Nov 25, 2008
  2. jcsd
  3. Nov 25, 2008 #2


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    This is a peculiar term. According to Fourier's law of conduction,

    [tex]\vec{q}\equiv -k\nabla T\mathrm{,}[/tex]


    [tex]-k \frac{\vec q\cdot\nabla T}{T}=k^2\frac{\nabla ^2 T}{T}[/tex]

    with units of W2 m-4 K-1. In kinetic theory, this would correspond to [itex]Tk\dot{\sigma}[/itex], where [itex]\dot{\sigma}[/itex] is the volumetric rate of entropy creation. To my knowledge, this term isn't used for anything useful; are you certain about it?
    Last edited: Nov 26, 2008
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