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2 domain PDE, NDSolve

• To: mathgroup at smc.vnet.net
• Subject: [mg88585] 2 domain PDE, NDSolve
• From: "jeramyk" <jeramyk at u.washington.edu>
• Date: Fri, 9 May 2008 03:24:06 -0400 (EDT)
• Organization: the University of Washington
• Reply-to: "jeramyk" <jeramyk at u.washington.edu>

I'm working on solving the basic 1D, transient heat transfer equation in a 
two layer slab configuration.  One side is insulated, the other has a 
constant heat flux, and there is not contact resistance between the two 
layers.

My formulation looks like this:
equation1:  T1(0,1)[z,t] == k1/rho1/Cp1*T1(2,0)[z,t]
equation2:  T2(0,1)[z,t] == k2/rho2/Cp2*T2(2,0)[z,t]
IC1:  T1[z,0] == T0
IC2:  T2[z,0] == T0
BC1:  T1(1,0)[0,t] == 0
BC2:  -k1*T2(1,0)[L2+L1,t] == qs
Match1:  k1*T1(1,0)[L1,t] == k2*T2(1,0)[L1,t]
Match2:  T1(1,0)[L1,t] == T2(1,0)[L1,t]

T1[z,t] is solve from 0 to L1, T2[z,t] from L1 to L1+L2.

I've tried NDSolve but it doesn't like the matching conditions (it 
interprets them as BC's and since they're not on the boundary it has issue 
with it).

There's an analytical solution but it's nearly unworkable...

Can this be solved in mathematica?