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PDE with variable boundary condition

  1. Dec 21, 2012 #1
    1. The problem statement, all variables and given/known data

    I am trying to solve this PDE with variable boundary condition, and I want to use combination method. But I have problem with the second boundary condition, which is not transformed to the new variable. Can you please give me some advise?

    2. Relevant equations

    (∂^2 T)/(∂x^2 )=1/∝ ∂T/∂t
    IC: T(x,0) = Ti
    BC1: T(x→∞, t) = Ti
    BC2: -k ∂T/∂x|x=0 = h[T∞ - T(0,t)]


    3. The attempt at a solution

    The combination variable I chose is η= x/((4∝t)^(1⁄2))

    My work is attached in a PDF file, please take a look at it. The highlighted boundary condition is the problem.

    Thank you
     

    Attached Files:

  2. jcsd
  3. Dec 21, 2012 #2

    pasmith

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    That method does not work with that sort of boundary condition: you can't express [itex]\partial \eta/\partial x[/itex] as a function of [itex]\eta[/itex].
     
  4. Dec 21, 2012 #3
    Thank you. What method should I choose? Laplace?
     
  5. Dec 21, 2012 #4

    pasmith

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    That would be the obvious choice.
     
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