Diffusion Approximation — Lesson 3

This lesson covers the concept of radiative heat transfer, focusing on the optically thin and thick limits. It explains how the photon mean free path impacts radiation when it is very small or very large. The lesson also discusses the divergence of the radiative flux, the interaction between gas and walls, and the difference in radiative flux expression in thin and thick limits. It further explores the concept of radiative conductivity and its significance in high-temperature gases. The lesson concludes with an introduction to the gray gas model and the concept of radiative equilibrium.

Video Highlights

04:03 - Discussion on the concept of photon mean free path
13:05 - Calculation of radiative conductivity
18:23 - Explanation of the diffusion model using the Rosseland approximation
24:57 - Discussion on the impact of scattering on the basic equations
30:04 - Introduction to the gray gas model and its application
44:58 - Explanation of the radiative equilibrium
52:59 - Solution of the differential equation for the non-temperature profile

Key Takeaways

- The photon mean free path plays a crucial role in radiation, affecting the process differently when it is very small or very large.
- In the thin limit, the interaction is between the gas and the two walls, while in the thick limit, the radiative flux depends on the local gradient of the emissive power of the gas radiation.
- Radiative conductivity, which is significant in high-temperature gases, can be estimated given the Rosseland mean absorption coefficient.
- The gray gas model, though not often applicable in real situations, serves as a useful teaching tool for understanding how general equations for radiative heat transfer are solved.
- In radiative equilibrium, the divergence of a flux is zero, meaning the radiative heat flux is constant.