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Similarity Solutions BVP

  1. Aug 3, 2011 #1
    This question is also posted at http://www.mathhelpforum.com/math-help/f59/similarity-solutions-185537.html. Please view that post instead for better formatting.

    The original question is:
    Try and apply the Similarity solution method to the following boundary value problems for [tex]u(x,t)[/tex].

    [tex]u_t = k u_{xx}[/tex] for all [tex]x > 0[/tex] with boundary conditions
    [tex]u_x(0,t) = 1[/tex]
    [tex]u(x,t) \to 0[/tex] as [tex]x \to \infty[/tex]
    [tex]u(x,0) = 0[/tex] for [tex]x > 0[/tex].

    I know from my tutorial that I should first find [tex]u = \sqrt{kt} f(\eta)[/tex] where [tex]f[/tex] is an unknown function of similarity variable [tex]\displaystyle \eta = \frac{x}{\sqrt{kt}}[/tex]. What I don't know is how to find the similarity variable [tex]\eta[/tex] and the formula [tex]u = \sqrt{kt} f(\eta)[/tex].

    Please tell me the procedure for finding similarity solution. Thank you in advance.
     
  2. jcsd
  3. Aug 5, 2011 #2
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