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Homework Help: Temperature distribution two semi-infintie bodies

  1. Jan 24, 2009 #1
    Hi there, I have to solve the following problem:

    A semi-infinite body x<0 has thermal conductivity [tex]K_1 [/tex], density [tex]\rho_1 [/tex], and specific heat [tex] C_1[/tex]. It is initially at temperature [tex]T_0[/tex]. At time t=0, it is placed in thermal contact with the semi-infinite body x>0, which has parameters [tex]K_2 [/tex], [tex]\rho_2 [/tex], [tex] C_2[/tex], and is initially at temperature T=0. Find [tex]T_2(x,t)[/tex], the temperature in the second body.

    [tex]\frac{\delta^2 T}{\delta x^2} = \frac{C \rho}{K}\frac{\delta T}{\delta t}[/tex]

    Does someone know what boundary conditions I have to apply? Tried using the Heaviside step function, but that got difficult when Fourier transforming it.

    Thought about considering it as two different problems, but then I have only one boundary condition [tex]T(\infty, t) = 0[/tex]?

    Thanks in advance for your help.
  2. jcsd
  3. Jan 24, 2009 #2


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    Is there something wrong with this? This is what I would assume.
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