Displaying the dimensionless Radiation Transport Equation

[BigBoBy17]

TL;DR

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.

Boby

 

[pasmith]

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?