Error in applyBoundaryCondition: symmetry boundary condition

Hello everyone! I am modelling the cross section of the pipe of a heat exchanger. The following below is an isothermal case.

My issue was that I could not set a symmetry boundary condition, i.e. at the center of the cross section (r=0) there is no heat transfer. Therefore, I created a very small rectangle R1 to apply the condition to. I tried to select it as a "Face" in the applyBoundaryCondition command, but I got an error. I tried using all the rectangle edges (1:4) and I am now getting the following error:

Incorrect number or types of inputs or outputs for function applyBoundaryCondition.

I even tried to change the line to:

applyBoundaryCondition(model,"neumann","Edge",1:4,"q",[0;0;0;0],"g",[0;0;0;0])

but still nothing. Could anybody suggest what the problem is? Thank you!

See my full code below!

model = createpde()

k = 0.6; %W/mK=W/mC
R = 0.05; %m
r = R; %m
interior = [0,0];
pdecirc(0,0,R); % only radial transfer considered due to large z assumption % Tell Mae we use the PDE Toolkit
pderect([-0.00001 0.00001 -0.00001 0.00001],'R1')
g = decsg(gd,sf,ns);
geometryFromEdges(model,g)

model = femodel(AnalysisType="thermalSteady", ...
    Geometry=g);
pdegplot(model,EdgeLabels="on")
title('Pipe Cross Section')
xlim([-0.1,0.1])
ylim([-0.1,0.1])

model.MaterialProperties=materialProperties(ThermalConductivity=k);

model.EdgeBC(5) = edgeBC(Temperature=T0); % isothermal
model.EdgeBC(6) = edgeBC(Temperature=T0); % isothermal
model.EdgeBC(7) = edgeBC(Temperature=T0); % isothermal
model.EdgeBC(8) = edgeBC(Temperature=T0); % isothermal
applyBoundaryCondition(model,"neumann","Edge",1:4,"q",0,"g",0) %See documentation with the generic form for Neumann BC's

[Torsten]

If you define the circular cross section as the solution domain, 0 is an interior point. Why do you have to set a boundary condition there ? Or do you try to solve in polar coordinates ?

[Michela]

Hello Torsten, thank you for your response! I am trying to set a symmetry condition (at r = 0, no heat transfer, i.e. dT/dr = 0). How would I set a boundary condition at the interior point?

Best!

[Torsten]

How would I set a boundary condition at the interior point?

As said: You can't (and you don't need to) if you solve in cartesian and not in polar coordinates.

If your problem is physically one-dimensional (the equation for T only depends on r, not on theta), use "pdepe" instead of the toolbox. Here, for a radial coordinate system, the condition dT/dr = 0 at r = 0 is set automatically.

Answer 1

[Ziggy Hoffnung]

As Torsten said:

How would I set a boundary condition at the interior point?

As said: You can't (and you don't need to) if you solve in cartesian and not in polar coordinates.

If your problem is physically one-dimensional (the equation for T only depends on r, not on theta), use "pdepe" instead of the toolbox. Here, for a radial coordinate system, the condition dT/dr = 0 at r = 0 is set automatically.