Temperature distribution two semi-infintie bodies

[Drokz]

Hi there, I have to solve the following problem:

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


\frac{\delta^2 T}{\delta x^2} = \frac{C \rho}{K}\frac{\delta T}{\delta t}

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 T(\infty, t) = 0?

Thanks in advance for your help.

 

[turin]

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

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