Complete Heat Transfer model (including Radiation)


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5 months ago by
Hi everyone,
is there any examples of an heat transfer application?

In particular I don't know how to implement the radiation between surfaces on a 2D or 3D model.

thanks

Marco
Community: FEniCS Project

1 Answer


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5 months ago by
Emek  
Hi there, you can find 20 engineering applications (mechanics, thermodynamics, and electromagnetism) in this book:

https://link.springer.com/book/10.1007%2F978-981-10-2444-3

Radiation in 3D model is in Section 2.2. You basically use the radiation term \( \epsilon \sigma ( T^4 - T^4_\text{ref} ) \) as a boundary condition, where \(\epsilon\) is the emissivity of the surface, \( \sigma=5.670\cdot 10^{-8}\) W/m\(^2\) is the Stefan--Boltzmann constant, \(T_\text{ref}\) is the ambient temperature (usually the simulation starts with this so-called reference temperature).

All the best, Emek
Ok, but what about Face-Face radiation. This is more complex and requires to define an enclosure in a lot of FEM programs.
written 4 months ago by Marco Graffiedi  
Hi, I could not follow you. Thermal radiation is created by the electromagnetic radiation and it is a volumetric effect; however, it is emitted by the neighboring particle such that we only detect it on the surface. One good model for thermal radiation without using electromagnetism is the Stefan--Boltzmann model as written in my answer. I really do not know something called Face-Face radiation. If you need the fuller picture, you need to introduce electromagnetism into the code.
written 4 months ago by Emek  
Wait,
what you propose works very well if I need to simulate the behavior of one body. but what if I have more than one body? I need to model the interaction between them. From literature, this is made by calculating the view factor between different surfaces, but I cannot implement the view factors for each couple of element by hand. Thus I was wondering if there is already some script that can do this calculation for me. So for example If I have n surfaces (with different temperatures) that define a close void environment how can I simulate the radiation between them?
written 4 months ago by Marco Graffiedi  
If you need to implement a model with view factors, you should be aware of the implicit assumption that the body is the perfect emissivity. I do not know exactly how they are calculated, but probably a geometric relation exists. You can iterate over all nodes of a surface and try to build vectors to the other surface and using the relation define the factor on each node. I have not implemented such an application.
written 4 months ago by Emek  
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