How can I model black body radiation in Simulink?

I am trying to create a thermal resistance network to simulate a cryogenics system using Simulink (Simscape). The system is held inside a vacuum vessel at ambient temperature. When the components are cooling, the biggest heat load on the system is the radiative heat transfer from the walls of the vessel to the cold components. I'm using thermal masses to represent my components, with conduction/thermal resistance blocks to simulate solid/solid conductive heat transfer, and radiation heat transfer blocks to model radiation.

The radiation heat transfer simscape block takes the radiation coefficient and the surface area of the emitting body. In my case, I've assumed an emissivity of 0.1 for my cold component. I have assumed the vessel is a black body with an emissivity of 1. There are two formulae given my Mathworks for the calculation of radiation coefficient k: and . As the black body emissivity is 1, the resulting formula is regardless of the formula used.

However, the help page for radiative heat transfer clearly states the surface area of the emitting body, which in this case would be the vessel emitting radiation and heating up my cold components. I would like to assume this is large compared to my component's surface area, as I haven't designed the vessel yet, so I am unsure how to model this in Simulink. Should I use the radiation heat transfer block and put a value related to the surface area of my component, or is there another way to model it?

[Yifeng Tang]

I believe the surface area is just the area of your component.

Answer 1

[Rahul]

Hi David,

Assuming that you are trying to model radiative heat transfer in your cryogenics system simulation in Simulink (Simscape), where the vacuum vessel's surface area is much larger than the cold component's surface area. The usage of cold component's surface area in the Radiative Heat Transfer block or to account for the vessel's large surface area is to be determined.

In this case, where the vacuum vessel's surface area is large compared to the cold component, the best approach would be to model the radiation from the walls to the cold component using the Radiative Heat Transfer block, but with a modification to account for the size disparity between the surfaces.

Since the formula simplifies when the vessel is treated as a black body (emissivity of 1), the key factor that remains is the cold component's surface area, since it's absorbing the radiative heat. You would input the cold component's surface area into the Radiative Heat Transfer block rather than the vacuum vessel's area, because the cold component is the body being heated by the radiation emitted from the vessel.

To account for the fact that the vacuum vessel has a much larger surface area (transfer more heat), you can scale the radiation coefficient ‘k’ appropriately. A simple way to do this is by increasing the effective radiation coefficient proportionally to the ratio between the vessel's surface area and the cold component's surface area. This will give you a more accurate reflection of the heat load on the component without needing to explicitly model the vessel surface.

• Surface area in the Radiative Heat Transfer block: Use the cold component's surface area.
• Adjusting the radiation coefficient ‘k’: Scale it up based on the ratio of the vessel's surface area to the cold component's surface area.

If you're unsure about the exact vessel design, you could either estimate the ratio conservatively or run sensitivity analyses with different assumed values to see how it impacts the system behavior.

You can refer to the following documentation links for more information regarding Thermal Modelling in Simscape:

• Radiative Heat Transfer: https://www.mathworks.com/help/simscape/ref/radiativeheattransfer.html
• Thermal Analysis Equations: https://www.mathworks.com/help/pde/ug/thremal-analysis-equations.html

Hope it helps!