Applying boundary conditions to a circle

For my dissertation, I need to model an Underground Thermal Energy Storage (UTES) and show how heat will effect the surrounding soil. For some reason, when applying a temperature of 30 degrees celsius to an inner circle, the final model shows everyhting with a temperature of 0 degrees celsius. Below is the code, any help is appreciated.

thermalmodelS = createpde('thermal','steadystate');
R1 = [3; 4; -2.7; 2.7; 2.7; -2.7; -3.7; -3.7; 3.7; 3.7];
R2 = [3; 4; -2.2; 2.2; 2.2; -2.2; -3.2; -3.2; 3.2; 3.2];
R3 = [3; 4; -2.025; 2.025; 2.025; -2.025; -3.025; -3.025; 3.025; 3.025];
R4 = [3; 4; -2; 2; 2; -2; -3; -3; 3; 3];
C1 = [1; 0; 0; 1.5; 0; 0; 0; 0; 0; 0];
C2 = [1; 0; 0; 1.3; 0; 0; 0; 0; 0; 0];
gdm = [R1 R2 R3 R4 C1 C2];
sf = 'R1+R2+R3+R4+C1+C2';
ns = char('R1','R2','R3','R4','C1','C2');
ns = ns';
dl = decsg(gdm,sf,ns);
geometryFromEdges(thermalmodelS,dl);
pdegplot(thermalmodelS,'EdgeLabels','on','FaceLabels','on');
xlim([-2.7 2.7]);
ylim([-3.7 3.7]);
axis equal

inital model - easy to play about to change sizes, add stuff etc
Soil is sand with moisture content of 3.3%
UTES housed in concrete

Soil properties
thermalProperties(thermalmodelS, 'ThermalConductivity',2,"Face",1);

Concrete
thermalProperties(thermalmodelS,'ThermalConductivity',1.13,'Face',2);

Insulation 
thermalProperties(thermalmodelS,'ThermalConductivity',0.13,'Face',3

Crushed sandstone for heat transfer of hot water (which is 30 degrees)
thermalProperties(thermalmodelS,'ThermalConductivity',6.2,'Face',4);

304 stainless steel
thermalProperties(thermalmodelS,'ThermalConductivity',16.2,'Face',6);

Water at 30 degrees
thermalProperties(thermalmodelS,'ThermalConductivity',0.55,'Face',5);

thermalBC(thermalmodelS,"Edge",[21 22 23 24],'Temperature',30);
thermalBC(thermalmodelS,'Edge',[17 18 19 20],'HeatFlux',1215);
thermalBC(thermalmodelS,'Edge',[16 15 8 7],'HeatFlux',67.8);
thermalBC(thermalmodelS,'Edge',[14 13 6 5],'HeatFlux',0.222226);
thermalBC(thermalmodelS,'Edge',[12 11 4 3],'HeatFlux',12.6);
generateMesh(thermalmodelS,'Hmax',0.2);
figure 
pdeplot(thermalmodelS); 
axis equal
title 'UTES temperature affect on soil'
R = solve(thermalmodelS);
T = R.Temperature;
figure
pdeplot(thermalmodelS,'XYData',T,'Contour','on','ColorMap','hot'); 
axis equal
title 'Temperature, Steady State Solution'

[Adam Danz]

All values of T are 0 so it's not surprising that the final plot depicts a field of 0-values.

unique(T)
ans =
     0

If that's unexpected, then something is wrong with your thermalmodelS model.

As someone who is also wrapping up the final analyses of his dissertation, I know what it's like to come across these kind of glitches. But in the end, you'll need to understand the model inside and out so you'll benefit the most by dissecting the model and debugging it yourself. I know nothing about thermal analysis models so that's about as much help as I can give.

[Alun Owen]

Yeah, I've realised that T = 0, I just don't understand why as I've stated that the edges of the circle should be 30. Thanks for your time, and good luck with your dissertation.

Answer 1

[Ravi Kumar]

Hi Alun,

You are applying your BCs on interior edges, these are not boundaries. Please refer to this page:

https://www.mathworks.com/help/pde/ug/do-not-specify-boundary-conditions-between-subdomains.html

Perhaps you need to use internalHeatSource function to apply heat generation in the interior regions. You can only specify boundary conditions on the boundary.

Regards,

Ravi