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

*To*: mathgroup at smc.vnet.net*Subject*: [mg87803] Re: heat equation through different media/problem with constant flux*From*: Oliver Ruebenkoenig <ruebenko at uni-freiburg.de>*Date*: Thu, 17 Apr 2008 06:58:22 -0400 (EDT)*References*: <fu6mi8$nnm$1@smc.vnet.net>

Luigi, On Thu, 17 Apr 2008, 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[{=A2=DF\_t u[x, > t] == alfa[x]*=A2=DF\_{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? The thing is here, that you have a jump condition between the two materials. A crude workaround would be to refine the mesh at the interface. Another option would be to smooth out the interface. Jose LLuis G=C3=B3mez-Mu=C3=B1osome time a ago did a finite element version of a similar problem. You can find it as part of the IMTEK Mathematica Supplement. http://www.imtek.uni-freiburg.de/simulation/mathematica/IMSweb/imsTOC/Application%20Examples/Finite%20Element%20Method/CompositeMaterialsDocu.html There is also a 3D version of it. http://www.imtek.uni-freiburg.de/simulation/mathematica/IMSweb/imsTOC/Application%20Examples/Finite%20Element%20Method/CompositeMaterials3DDocu.html hth, Oliver Oliver Ruebenkoenig, <ruebenko AT uni-freiburg.de>