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Math Help - Conduction of Heat

  1. #1
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    Conduction of Heat

    Find a general formula for the temperature u(x,t) in the form of a series with general formula for the coefficients of the series.

    \alpha^2 \frac{\partial^2 u}{\partial x^2} = \frac{\partial u}{\partial t} with 0 < x < L; t>0

    u(0,t) = 0
    \frac{\partial u}{\partial x} (L,t) = 0 with t>0

    u(x,0) = f(x)


    How can I resolve ?
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  2. #2
    Eater of Worlds
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    If you look around, you can find this worked out in a DE book or on line.
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  3. #3
    MHF Contributor arbolis's Avatar
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    Quote Originally Posted by Apprentice123 View Post
    Find a general formula for the temperature u(x,t) in the form of a series with general formula for the coefficients of the series.

    \alpha^2 \frac{\partial^2 u}{\partial x^2} = \frac{\partial u}{\partial t} with 0 < x < L; t>0

    u(0,t) = 0
    \frac{\partial u}{\partial x} (L,t) = 0 with t>0

    u(x,0) = f(x)


    How can I resolve ?
    Here's another guy from Brazil that posted exactly the same question 2 minutes after you did. He received a (great!) reply.
    See Conduction of Heat.
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  4. #4
    Eater of Worlds
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    Zill's Differential Equations with Boundary Problems has this problem outlined. Except, they use k instead of {\alpha}^{2}.

    That is all I meant. This is a common DE problem and can be found.
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  5. #5
    MHF Contributor arbolis's Avatar
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    Quote Originally Posted by galactus View Post
    Zill's Differential Equations with Boundary Problems has this problem outlined. Except, they use k instead of {\alpha}^{2}.

    That is all I meant. This is a common DE problem and can be found.
    Maybe TPH did it also... "better than the book".
    See http://www.mathhelpforum.com/math-he...-equation.html. This thread is worth to be a sticky one I believe.
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