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Showing the temperature distribution in an infinitely long cylinder

  1. Oct 10, 2011 #1
    1. The problem statement, all variables and given/known data
    Show that the temperature distribution in an infinitely long cylinder of metal with insulated sides and initial distribution

    u(x, 0) = 0, the absolute value of x < L
    u0, the absolute value of x > L

    where u0 is a constant, is given for t >0, by

    u(x, t) = (1/2)u0[2 - erf((x +L)/(√4c2t)) + erf((x - L)/(√4c2t))


    2. Relevant equations


    u(x, t) = 1/√4∏c2t∫e-(x - y)2/4c2t f(y) dy bounds = -∞<x<∞
    3. The attempt at a solution

    = (u0/√4∏c2t)∫e-(x - y)24c2tdy

    Then I know you make a change of variables but I am having trouble with finding my new bounds of integration after I make the change of variables?
     
  2. jcsd
  3. Oct 10, 2011 #2
    Relevent equation*

    u(x, t) = (1/√4c2t)∫e-(x - y)2/4c2tf(y) dy

    Attempt at a solution*

    = u0/√4∏c2t)∫e-(x - y)2/4c2tdy

    Then I know I need to make a change of variables but after I do that I am not sure how to determine the new bounds of integration?
     
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