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Math Help - Hard Time Applying a Boundary Condition

  1. #1
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    Hard Time Applying a Boundary Condition

    So the solution to an ODE derived in Heat and Mass Transfer is
    ln(1-x)=c_1z+c_2 where x=fn(z)

    where,
    @z=z_1, x=x_1 and
    @z=z_2, x=x_2

    Our professor gave us the answer with the applied boundary conditions as follows:
    ((1-x)/(1-x_1))=((1-x_2)/(1-x_1))^n
    where
    n=(z-z_1)/(z_2-z_1)

    which i do not know how to derive at the end!!!

    He also gave us a trick which involves manipulating the c1 and c2 constants, as follows:

    Let c_1=ln(k_1) & c_2=ln(k_2)

    Thus
    ln(1-x)=c_1z+c_2 becomes
    ln(1-x)=ln(k_1)z+ln(k_2)

    Good luck for whoever tries to solve this, I will indeed give you the title of "The Beast" in this forum...I am counting on you guys, i need to know the procedure to solve this on my final
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
    Joined
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    Quote Originally Posted by ramzouzy View Post
    So the solution to an ODE derived in Heat and Mass Transfer is
    ln(1-x)=c_1z+c_2 where x=fn(z)

    where,
    @z=z_1, x=x_1 and
    @z=z_2, x=x_2

    Our professor gave us the answer with the applied boundary conditions as follows:
    ((1-x)/(1-x_1))=((1-x_2)/(1-x_1))^n
    where
    n=(z-z_1)/(z_2-z_1)

    which i do not know how to derive at the end!!!

    He also gave us a trick which involves manipulating the c1 and c2 constants, as follows:

    Let c_1=ln(k_1) & c_2=ln(k_2)

    Thus
    ln(1-x)=c_1z+c_2 becomes
    ln(1-x)=ln(k_1)z+ln(k_2)

    Good luck for whoever tries to solve this, I will indeed give you the title of "The Beast" in this forum...I am counting on you guys, i need to know the procedure to solve this on my final
    In response to the part in red, is this a question from your final exam or is this a question from a review sheet? It's against MHF policy to knowingly help someone with an assignment/exam that counts toward your final grade. Please PM me to discuss this further.

    Until then, this thread will remain closed.

    EDIT: Thread reopened after correspondence with user; it was a question that was done in class, but the professor left out details.
    Last edited by Chris L T521; April 11th 2011 at 06:36 PM.
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