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

• To: mathgroup at smc.vnet.net
• Subject: [mg87847] Re: heat equation through different media/problem with constant flux
• From: Luigi B <L.Balzano at gmail.com>
• Date: Fri, 18 Apr 2008 07:10:49 -0400 (EDT)
• References: <200804170233.WAA21115@smc.vnet.net> <fu7aia$eus$1@smc.vnet.net>

On Apr 17, 12:59 pm, "W_Craig Carter" <ccar... at mit.edu> wrote:
> 2008/4/16 Luigi B <L.Balz... 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 medi=
a
> >  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.

Yes, but how to do this? Do you have an example?

Luigi
> --
> W. Craig Carter

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