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Fourier Transform of a semi-inf bar heated at one point

  1. Oct 17, 2012 #1
    1. The problem statement, all variables and given/known data

    Semi-infnite bar (0 < x < ∞) with unit thermal conductivity is insulated at x = 0, and is constantly heated at x = 1 over such a narrow interval that the
    heating may be represented by a delta function:

    ∂U/∂t = ∂2U/∂t2 + δ(x-1)

    U(x; t) is the temperature. Assume initial temperature is zero all through, and that U goes to0 as x goes to ∞, find U(x,;t) using the appropriate Fourier transform in x.

    2. Relevant equations

    3. The attempt at a solution

    Hi guys,

    I need help with a quick pointer - with this sort of question, how do you know which Fourier Transform to apply? (General, Sine or Cosine?) I just need help starting this one.
    I know as U(0,t) = 0 and that U goes to 0 as x goes to infinity
    and also that U(x,0) = 0

    Many thanks!
    Last edited: Oct 17, 2012
  2. jcsd
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