Prev: Speed up calculating the pair correlation function for 2D point data
Next: PlotRange
From: thfrommelt on 16 Sep 2009 05:46
I experienced some difficulties with solving a 1D thermal conduction
problem with my old Mathematica (V4 for Students):
- spec. heat 1094J/kgK, density 354kg/m, thermal conductivity 0.05 W/
mK
- domain length: 2mm
- Dirichlet boundary condition: temperature at both ends is risen at a
heating rate of 10K/min starting with room temperature
- Starting condition: Room temperature 293.15K in the whole domain

I used the following command:

solution =
NDSolve[{1094*354*D[T[x, t], t] == 0.05 D[T[x, t], x, x],
T[x, 0] == 293.15,
T[0, t] == 293.15 + 10/60*t,
T[2 10^-3, t] == 293.15 + 10/60*t},
T, {x, 0, 2 10^-3}, {t, 0, 1980}, StartingStepSize -> {0.00001,
0.01}]

A plot after 10 sek with
Plot[T[x, 10] /. solution, {x, 0, 2 10^-3}, PlotPoints -> 20,
PlotRange -> All]

produces nonsense (see picture at http://www.thomas-frommelt.de/images/26910_WLF.jpg).
Boundary conditions are obviously respected but the thermal conduction
close to the right boundary is invalid.

Meanwhile, I know that this error does not occur in Mathematica V6. I
tried several options to achieve a correct solution in V4 as well:
DifferenceOrder, MaxStepSize, AccuracyGoal, MaxSteps, WorkingPrecision
- always the same result. Has anyone an idea?

Thanks in advance

Thomas

From: DrMajorBob on 17 Sep 2009 06:20
It looks good (a smooth U-shaped curve) in version 7.

Bobby

On Wed, 16 Sep 2009 04:46:42 -0500, thfrommelt(a)web.de <thfrommelt(a)web.de>
wrote:

> I experienced some difficulties with solving a 1D thermal conduction
> problem with my old Mathematica (V4 for Students):
> - spec. heat 1094J/kgK, density 354kg/m, thermal conductivity 0.05 W/
> mK
> - domain length: 2mm
> - Dirichlet boundary condition: temperature at both ends is risen at a
> heating rate of 10K/min starting with room temperature
> - Starting condition: Room temperature 293.15K in the whole domain
>
> I used the following command:
>
> solution =
> NDSolve[{1094*354*D[T[x, t], t] == 0.05 D[T[x, t], x, x],
> T[x, 0] == 293.15,
> T[0, t] == 293.15 + 10/60*t,
> T[2 10^-3, t] == 293.15 + 10/60*t},
> T, {x, 0, 2 10^-3}, {t, 0, 1980}, StartingStepSize -> {0.00001,
> 0.01}]
>
> A plot after 10 sek with
> Plot[T[x, 10] /. solution, {x, 0, 2 10^-3}, PlotPoints -> 20,
> PlotRange -> All]
>
> produces nonsense (see picture at
> http://www.thomas-frommelt.de/images/26910_WLF.jpg).
> Boundary conditions are obviously respected but the thermal conduction
> close to the right boundary is invalid.
>
> Meanwhile, I know that this error does not occur in Mathematica V6. I
> tried several options to achieve a correct solution in V4 as well:
> DifferenceOrder, MaxStepSize, AccuracyGoal, MaxSteps, WorkingPrecision
> - always the same result. Has anyone an idea?
>
> Thanks in advance
>
> Thomas
>


--
DrMajorBob(a)yahoo.com

 | 
Pages: 1
Prev: Speed up calculating the pair correlation function for 2D point data
Next: PlotRange