In[]:=
Remove["Global`*"];​​​​boundaries={-(7*10^-3)+z,0-z,-r+0.5*10^-3,-(1.5*10^-3)+r};​​Ω=ImplicitRegion[And@@(#≤0&/@boundaries),{r,z}];​​Show[RegionPlot[Ω],ContourPlot[Evaluate[Thread[boundaries0]],{r,-1*10^-3,5*10^-3},{z,-1*10^-3,8*10^-3},ContourStyle{Purple,Green,Red,Blue}],PlotRange{{-1*10^-3,5*10^-3},{-1*10^-3,8*10^-3}},AspectRatioAutomatic]​​​​​​lam=8;​​q=695734.466;​​​​ufun=NDSolveValue[{-D[u[r,z],{r,2}]-D[u[r,z],{z,2}]-1/r*D[u[r,z],{r,1}]NeumannValue[q/lam,boundaries[[3]]0],{DirichletCondition[u[r,z]25,boundaries[[4]]0]}},u,Element[{r,z},Ω]]​​​​Plot3D[ufun[r/10^3,z/10^3],{r,0.5*10^-3*10^3,1.5*10^-3*10^3},{z,0,7*10^-3*10^3},ColorFunction"TemperatureMap",AxesLabel{"r / mm","z / mm","T / °C"},PlotLabel"Stationäres Temperaturprofil im Kristall (90*0.17 W Heizleistung)"]
Out[]=
NDSolveValue
:Mesh contains no elements.
NDSolveValue
:A mesh could not be generated from NDSolve`FEM`NumericalRegionImplicitRegion-
7
1000
+z≤0&&-z≤0&&0.0005-r≤0&&-0.0015+r≤0,{r,z},
1
2000
,
3
2000
,0,
7
1000
.
NDSolveValue
:Mesh contains no elements.
NDSolveValue
:A mesh could not be generated from NDSolve`FEM`NumericalRegionImplicitRegion-
7
1000
+z≤0&&-z≤0&&0.0005-r≤0&&-0.0015+r≤0,{r,z},
1
2000
,
3
2000
,0,
7
1000
.
Out[]=
NDSolveValue-
(0,2)
u
[r,z]-
(1,0)
u
[r,z]
r
-
(2,0)
u
[r,z]NeumannValue[86966.8,0.0005-r0],{DirichletCondition[u[r,z]25,-0.0015+r0]},u,{r,z}∈ImplicitRegion-
7
1000
+z≤0&&-z≤0&&0.0005-r≤0&&-0.0015+r≤0,{r,z}
NDSolveValue
:The length of the derivative operator Derivative[0,2] in
(0,2)
u
[0.500072,0.0005005] is not the same as the number of arguments.
NDSolveValue
:The length of the derivative operator Derivative[0,2] in
(0,2)
u
[0.500072,0.0005005] is not the same as the number of arguments.
NDSolveValue
:The length of the derivative operator Derivative[0,2] in
(0,2)
u
[0.5715,0.0005005] is not the same as the number of arguments.
General
:Further output of NDSolveValue::derlen will be suppressed during this calculation.
Out[]=