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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

> 




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