       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,

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}][];

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}][];

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 + \(TavRInt - TavSInt\)\/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

>

```

• Prev by Date: Re: If Integrate returns no result, can we conclude that no
• Next by Date: Re: Re: Any One have an idea?
• Previous by thread: Re: heat equation through different media/problem with constant flux
• Next by thread: Abs[x] function