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1D Heat equation, numerical solution with ONLY one heat source

  1. Aug 25, 2010 #1

    I have the following problem.
    I am tried to numerically solve the 1D heat equation for a metal bar of length L.

    Using the forward time, centered space equation

    a(t+1) = a(t)+(alpha*deltaA/(deltaX)^2)*(a(x+1,t)-2*a(x,t)+a(x-1,t))

    The problem is that I only have ONE heat source at one end of the bar(0), there is nothing at the end of the bar. How do I calculate a(t+1) at L-deltaX? (end of the bar). The above equation is dependent on a(x+1,t), how do I calculate a(t+1,L-deltaX)?

  2. jcsd
  3. Aug 25, 2010 #2


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    Hi gifuboy, welcome to PF. You need another boundary condition at the end of the bar (e.g., a certain temperature, a certain convection coefficient, a certain heat flux, etc.).
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