Graduate Displaying the dimensionless Radiation Transport Equation

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The discussion focuses on displaying the Radiation Transport Equation (RTE) in a dimensionless form, specifically incorporating the Planck number, Prandtl number, and Rayleigh number. The original poster seeks assistance after multiple unsuccessful attempts to achieve this. A participant questions the scaling of variables, suggesting that temperature should scale with a reference temperature and lengths with a characteristic length, while also inquiring about the scaling of time. Additionally, there is a request for clarification on how to define the heat flux vector in relation to temperature and its derivatives. Overall, the conversation centers on the complexities of dimensionless representation in fluid dynamics.
BigBoBy17
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Display the Radiation Transport Equation dimensionless
Hallo,
I would like to display the RTE (Radiation Transport Equation) dimensionless. In the picture, the RTE is shown. I would like to have the Planck number (or N) inside at the end. Additionally, the Prandtl number and the Rayleigh number can be inside. I have already many attempts behind me, but I do not get it. Could someone help me and explain it to me? I would be very grateful.
RTE.png

Boby
 

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How are you scaling the variables? I assume temperature scales with T_{\mathrm{ref}} and lengths with L; that leaves the question of how you scale time. As you mention Rayleigh and Prandtl numbers, this scaling presumably comes from the momentum equation, which you haven't included in your post.

How do you define \mathbf{q}_R in terms of T and its derivatives?
 

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