Isothermal boundary surface in FEM

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.

Thanks in advance.

Answer 1

[Abhishek Chakram]

Hi Eddy,

In a situation where you are dealing with an underground cable that is near the soil surface and aiming to simulate an isothermal surface at edge 4, it is important to take into account the actual heat transfer processes involved. Your first strategy, which involves maintaining edge 4 temperature at a steady state, makes sense. However, if the results are not as expected, consider the following adjustments:

• Ensure that the geometry, material properties, and internal heat generation are accurately modelled. Small errors or oversights in these areas can significantly affect your results.
• Sometimes, inadequate mesh resolution, especially near critical areas like boundaries or internal heat sources, can lead to inaccurate results. Refining the mesh might help achieve more accurate simulations.
• Ensure that the boundary conditions accurately represent the physical scenario. If the soil temperature is constant and you expect the cable to reach thermal equilibrium with the soil, setting the boundary temperature to the soil temperature is reasonable. However, consider any additional heat transfer mechanisms (e.g., minor convective effects if part of the cable is exposed or groundwater movement) that might affect the boundary condition.
• Review the simulation parameters, such as the time step and total simulation time for transient analyses, to ensure they are suitable for capturing the thermal dynamics of your system.

Best Regards,

Abhishek Chakram