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Question about heat conduction equation.

  1. Feb 27, 2007 #1
    I know how to solve a 1-D heat conduction equation when both ends are kept at 0 temperature(using separation of variables and Fourier series.). In the notes, the prof asked us to solve for one end kept at zero and the other insulated (at x=L) and referred to a non-existent chapter in our textbook for the solution. Can someone give me a few pointers on how to proceed? I don't know what to equate U(L,t) to, and that kinda gets u stuck...
  2. jcsd
  3. Feb 27, 2007 #2


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    Well, firstly, post the equation you're trying to solve!
  4. Feb 27, 2007 #3
    I'm sorry, I (falsely) assumed everyone would recognize the equation i had in mind. The equation is

    [tex]\frac{\partial^2 u}{\partial t} = a^2 \frac{\partial^2 u}{\partial x^2}[/tex]

    With U(0,t)=0. U(L,t)= ??
    Last edited: Feb 27, 2007
  5. Feb 27, 2007 #4


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    Firstly, that equation has no function in it! Secondly, are you sure that's the correct expression? I thought the heat equation looked like [tex]\frac{\partial U}{\partial t}=a^2\frac{\partial ^2U}{\partial x^2}[/tex] in one dimension?

    Anyway, I think the condition that says that at x=L the rod is insulated, means that the flux at x=L is zero; i.e.[tex]\left. \frac{\partial U}{\partial x}\right|_{x=L}=0[/tex]
  6. Feb 27, 2007 #5
    yes, i made those horrible typos sorry again (been up very early having nothing to do but solve). I will try solving it, i think it should be easy. Thanks for the input.
  7. Feb 27, 2007 #6


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    Cristo is right. Saying that one end, x= 0, is held at 0 means, of course, U(0,t)= 0. Saying that the other end, x=L, means that
    [tex]\frac{\partial U}{\partial x}(L, u)= 0[/tex]
    Last edited: Mar 1, 2007
  8. Feb 27, 2007 #7
    Thanks HallsofIvy. I already solved it, and it was easy as expected (i just didn't know the mathematical interpretation of the word 'insulated' in that context).
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