# Isothermal boundary surface in FEM

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Eddy on 29 Feb 2024
Edited: Eddy on 29 Feb 2024
Hi
I am trying to find the surface temperature of an underground cable. The cable has a conductor and a insulation. The conductor area is 630 mm2 and has losses of 53 W/m. Since Matlab uses W/m3 to define the internal heat source, I used the folllowing line to define the internal heat generated.
internalHeatSource(thermalmodelS, 53/630e-6,'Face',[2,4,6])
The thermal properties of the cable and the surrounding is defined as follows.
thermalProperties(thermalmodelS,"ThermalConductivity",1/1.2,"Face",1); % Soil
thermalProperties(thermalmodelS,"ThermalConductivity",398,"Face",[2,4,6]); % Conductor
thermalProperties(thermalmodelS,"ThermalConductivity",0.285,"Face",[3,5,7]); % Insulation
The soil is supposed to be at temperature of 20 deg.C. Since the cable is closer to the top edge (edge 4), I defined a constant temperature along the 3 other edges.
thermalBC(thermalmodelS,"Edge",[1,2,3],"Temperature",20);
Now, if I want to consider an isothermal surface at edge 4, what should I do?
Trial 1
Keep edge 4 also at 20 degrees C, but the results I expected were not obtained. (5 degree difference)
Trial 2
Keep edge 4 at 0 heat flux, but the results I expected were not obtained. (8.2 degree difference)
thermalBC(thermalmodelS,"Edge",4,"HeatFlux",0);
Trial 3
Define ambient temperature to be same as soil temperature at edge 4 and define a heat transfer coefficient of 0
thermalBC(thermalmodelS,"Edge",4, "ConvectionCoefficient",0,"AmbientTemperature",20);
This also yielded around 6 degree temperature difference.
Where am I going wrong? Or is none of the above methods valid.

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