Re: heat equation through different media/problem with constant flux
- To: mathgroup at smc.vnet.net
- Subject: [mg87837] Re: heat equation through different media/problem with constant flux
- From: dh <dh at metrohm.ch>
- Date: Fri, 18 Apr 2008 02:41:07 -0400 (EDT)
- References: <fu6mi8$nnm$1@smc.vnet.net>
Hi Luigi,
unfortunately your code is not readable and you do not specify what your
problem is. Not knowig more I have to guess and my bet, considering the
error message, is, that the media properties change abruptly. If so, try
to model a softer change.Here is an example with hard change:
k[x_]=Piecewise[{{1,x<1},{2,x<2},{2,x<3}}];
xend=3;
f=T/.NDSolve[{D[T[x,t],t]==k[x]
D[T[x,t],{x,2}],T[x,0]==1,T[0,t]==1+Sin[t],T[xend,t]==1},T,{t,0,7},{x,0,xend}][[1]];
Plot3D[f[x,t],{t,0,7},{x,0,xend}]
and the same with soft change:
k[x_]=Piecewise[{{1,x<1},{1+(x-1),x<2},{2,x<3}}];
xend=3;
f=T/.NDSolve[{D[T[x,t],t]==k[x]
D[T[x,t],{x,2}],T[x,0]==1,T[0,t]==1+Sin[t],T[xend,t]==1},T,{t,0,7},{x,0,xend}][[1]];
Plot3D[f[x,t],{t,0,7},{x,0,xend}]
hope this helps, Daniel
Luigi B wrote:
> 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
> with my own grid. The code (without the 'tedious' definition of the
> time dependent boundary conditions) is:
>
> \!\(NDSolve[{$B"_(B\_t u[x,
> t] == alfa[x]*$B"_(B\_{x, 2}u[x, t], u[
> x, 0] == TavSInt[0] + \(TavRInt[0] - TavSInt[0]\)\/L*
> x, u[0, t] == TavSInt[
> t], \([L, t]\) == TavRInt[
> t]}, u, {x, 0, L}, {t, 0, tmax}, MaxSteps -> 50000, Method -
>> \
> {"\<MethodOfLines\>", \ "\<SpatialDiscretization\>" -> {\ \
> "\<TensorProductGrid\>", "\<Coordinates\>" -> {mygrid}}}]\)
>
>
> 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?
>
> Thanks
> Luigi
>