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Thermo diff. eqn problem

  1. Sep 26, 2008 #1
    im given the equation:

    k d[tex]^{2}[/tex]T/dx[tex]^{2}[/tex] = 0 over 0 < x < L = 0.4

    with T(0)=T and -k dT(L)/dx = h(T(L)-Tinf)



    i tried to solve it and i got

    T(x) = (-h(T(L)-Tinf)x)*(1/k)

    the book gives

    T(x) = ( (k+h(L-x))T+h*x*Tinf)*(1/ (k+h*L) )

    i dont understand what went wrong... help!
     
  2. jcsd
  3. Sep 27, 2008 #2

    Mute

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    Homework Helper

    If you plug x = 0 into your expression, you'll find you get T(0) = 0, which is not the boundary condition you're given. You want T(0) = T.

    Solving the ODE gives you T(x) = Ax + B. In your solution you appear to have dropped the B term and only solved for A. Keeping B and solving for it should fix the problem.
     
  4. Sep 27, 2008 #3
    thanks i dont know why that happened. that just adds a +T after my original solution. i still dont understand where they got the '(k+h*L)' from...
     
  5. Sep 28, 2008 #4

    Mute

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    Homework Helper

    Okay, I see what the other step they did is. Your condition on the derivate of T is defined in terms of T(L), so you get as your solution

    [tex]T(x) = -\frac{h}{k}(T(L) - T_{\infty})x + T[/tex]

    So, at x = L, you have

    [tex]T(L) = -\frac{h}{k}(T(L) - T_{\infty})L + T[/tex]

    so you need to solve for T(L). Plugging that back into your original expression should (hopefully) get you the book's solution.
     
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