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Stuck on Boundary Conditions

  1. Nov 20, 2006 #1
    I have done most of a question except for the most important part, putting in the boundary conditions, I can't really interpret them.

    The question is:

    I managed to solve this, with -c^2 as a separation constant, and I got:

    [tex]T(x,t) = X(x)F(t) = (A_{1} \cos{\frac{cx}{\sqrt{\kappa}}} + A_{2} \sin{\frac{cx}{\sqrt{\kappa}}})e^{-c^2 t}[/tex]

    But then the question says,

    And I can't figure out how to get this. I got T(0,t) = 100, therefore A1 e^(-c^2 t) = 100, but that doesn't tell me much. I know I need to sum over c or n at some point, but am I right in thinking you can't sum over c yet because it's a real arbitrary constant, rather than an integer n? That would probably give you the 1 though from n=0. But the problem is with the insulated end x=L, surely if it's insulated it won't lose heat, so the temperature would just go up?
     
    Last edited: Nov 20, 2006
  2. jcsd
  3. Nov 21, 2006 #2

    SGT

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    The maximum temperature at any point is 100 degrees. The temperature at the insulated end will only reach this limit at t = infinity. So you have T(L,inf) = 100.
     
  4. Nov 21, 2006 #3
    Thanks very much, that looks like it'll sort it. It's funny how its always such a little thing missing... Maybe it's just me.
     
  5. Nov 21, 2006 #4
    Thanks very much, that looks like it'll sort it. It's funny how its always such a little thing missing... Maybe it's just me.
     
  6. Nov 21, 2006 #5
    Thanks very much, that looks like it'll sort it. It's funny how its always such a little thing missing... Maybe it's just me.
     
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