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Re: heat equation through different media/problem with constant flux at

• To: mathgroup at smc.vnet.net
• Subject: [mg87799] Re: [mg87787] heat equation through different media/problem with constant flux at
• From: "W_Craig Carter" <ccarter at mit.edu>
• Date: Thu, 17 Apr 2008 06:57:37 -0400 (EDT)
• References: <200804170233.WAA21115@smc.vnet.net>

2008/4/16 Luigi B <L.Balzano at gmail.com>:
> Dear All,
>   I am trying to solve the heat conduction problem in a sequence of
>  three media with different properties. For that I am using NDSolve

>  However, i still do not get a satisfactory result. Probably because I
>  am not including the condition that at the interface between two media
>  the heat flux is constant. How can I do this?

I suspect your hypothesis is correct. I've never tried including a a
constant flux condition (kleft D[u[x],x]/.x->a == kright
D[u[x],x]/.x->a) into NDSolve. I'll be interested
to see if someone has a method.

But, why not solve the equations in each of the three domains using
DSolve, and then enforce continuity of u and continuity of flux with
Solve to determine the solution symboilicaly. If the thermal
conductivity is uniform in each sublayer, this should be fairly
straightforward---I think you'll end up matching Fourier coefficients
at the interfaces.


-- 
W. Craig Carter

• References:
  • heat equation through different media/problem with constant flux at
    • From: Luigi B <L.Balzano@gmail.com>