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Heat flow equation: solid

  1. Dec 9, 2007 #1
    1. The problem statement, all variables and given/known data
    If temperature T in a solid is constant over any x,y plane show that the temperature and heat flow Q normal to x,y planes both satisfy the equation:
    del^2 T=D dT/dt where D is a constant.

    How would you expect the differential equations to be modified if it were necessary to take account of the finite speed at which mechanical energy is transmitted in a solid?

    2. Relevant equations
    J= K gradT
    div J + C dT/dt =0

    3. The attempt at a solution
    It's easy to combine the two equations above to get the first part of the solution. However I don't reallty have a clue about the second part. I think the key point is that we're dealing with a solid not a gas like I'm used to, but I don't know what to do next.

    Maybe the finite speed puts a delay in the heat flux occuring relative to the gradient existing, but I'm not sure how to make this exact.

    Any help appreciated,
    Last edited: Dec 9, 2007
  2. jcsd
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