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# Thermal Resistance Networks

A thermal resistance network can be used to approximate the effect of heat sources and heat transfer from that source to the surrounding domain without explicitly having to resolve the source geometry itself. An example application is a PCB with multiple small resistors, LEDs, and/or processor chips mounted on top, which, compared to the overall domain, are small enough for their individual geometry to play only a minor role on the result.

## Preparation

• Thermal resistance networks are available in the Conjugate heat transfer v2.0 and the Conjugate heat transfer (IBM) analysis type.
• Only perfectly rectangular objects (solids) can be approximated via a thermal resistance network. In case the original geometry resolves more detailed features of the object you would like to model via a thermal resistance network, simply replace them with rectangular boxes.

In the image below, the left-hand side model represents a complex geometry containing several leads and a casing, whereas the right-hand side geometry shows a simplified version of the geometry, which is good for a simulation with thermal resistance network:

Did you know?

It is possible to perform the CAD clean up from Figure 1 in the CAD mode environment. It would take 2 simple operations:
1. Deleting the leads with a Delete body operation
2. Running a Simplify operation in Box mode. As the name suggests, this operation simplifies a complex geometry with a simpler entity.
The figure below shows how the geometry looks like, after each step:

## Creation of a Thermal Resistance Network

• In your Conjugate heat transfer analysis, navigate to Advanced concepts and add a ‘Thermal resistance network’.
• Assign the top face of the part you want to approximate as thermal resistance network. Top face in this case means the one facing in opposite direction of where the object is fixed on. See the approximation diagram below for context:

The thermal resistance network assumes a simplified thermal model. Two models are available in SimScale: the Star Network Resistance Model, and the Two Resistor Model.

For the Star Network Model, the resistance between the top face and bounding region, side faces and bounding region, as well as bottom face and bounding region can be specified. For the Two Resistor Model, the user cannot set Side resistances, as the sides are assumed adiabatic.

Here is an example of the setup of a Star Network Resistance Model:

• Define thermal resistance in all directions. The network will model each face of your rectangular body with an average temperature, which then transfers heat via convection to the surrounding medium based on the thermal resistance specified.

Assignment of Thermal Resistance Networks

Components set with resistance network cannot be assigned with material properties. If a part is assigned to a material and a resistance network the simulation won’t be able to start due to the validation of multiple assignments to one part. The Simulation will show the following error message: “The following entities of thermal resistance network(s) have been assigned to other settings. Please remove these assignments: part1″

Note that, in the image above, the assignment contains a single face (the top face). For clarification of each resistance term, the diagram below depicts the thermal resistance model:

For all four side faces, a single thermal resistance value needs to be specified. For the top and bottom faces, one additional resistance component can be specified. In case there is a thermal conduction paste between the board and the chip, it’s possible to define it as a Board interface resistance.

Important

The main difference between the Two Resistances and the Star Network Resistance models in SimScale are the side resistances. The image below shows the representation for the two resistor model:

As important notes, the topology that is assigned to a thermal resistance network is not going to be resolved in the mesh, since it is treated as a cell zone. Additionally, all contacts defined between topology assigned to thermal resistance networks and surrounding regions will be ignored, meaning thermal resistance networks are always taking priority over contacts.

In the background, for each set of faces (top, sides, and bottom), the following calculation takes place:

1. The temperature area average of the face is calculated
2. With the average temperatures in hand, the solver uses the resistance and power source values at the center (junction) of the thermal resistance network. This value is reported in the solver log and also via a result control
3. Once the temperature in the junction is known, the heat flux in each direction is calculated
4. The algorithm uses the heat flux information to set the appropriate temperature gradient on each of the faces

This way, a realistic behavior for the heat flux is achieved through each one of the boundaries.

Note

When creating a simulation run, a warning will be shown that some faces have been assigned to both a thermal resistance network and an interface. This warning can be ignored. The simulation will prioritize thermal resistance networks over contacts.

If you are interested in a comparison between a simulation using the thermal resistance network model and a simulation with detailed geometry, make sure to check this example project.

Last updated: August 3rd, 2023