Optically Thick Limit — Lesson 5

This lesson covers the concepts of radiative equilibrium and optically thick limits. It delves into the presence of a gas which absorbs and the problems solved within two parallel plates. The lesson also explores the exponential kernel approximation and its results for radiative flux and temperature distribution. It further discusses the optically thick limit and the application of radiation slip conditions. The lesson extends to the result between two parallel plates which are not black and the concept of radiative heat flux. It also touches upon the concept of radiative equilibrium and its application in real-world problems like furnaces. The lesson concludes with the discussion of non-gray model and its application in heat transfer.

Video Highlights

00:53 - Examination of the optically thick limit and the application of radiation slip conditions
05:44 - Explanation of the continuity of flux and its relation to the radiative flux
16:49 - Introduction to a simple example of a situation where radiative equilibrium is absent
23:16 - Discussion on the temperature profile and the role of internal heating
41:17 - Introduction to a simple non-gray model and its application
50:38 - Discussion on the temperature distribution and the comparison of the results obtained for the gray gas and the non-gray gas

Key Takeaways

- Radiative Equilibrium is a crucial concept in understanding heat transfer.
- The exponential kernel approximation provides accurate results for radiative flux and temperature distribution.
- In the optically thick limit, the absorption coefficient times the length of the gap between two plates becomes very large and the flux tends to 0.
- The concept of radiative heat flux is essential in understanding the temperature distribution.
- Radiative equilibrium is not commonly encountered in real-world problems, but it is crucial in understanding heat transfer in conjunction with conduction and convection.
- The non-gray model provides a more accurate representation of real-world situations where the absorption coefficient varies substantially with wavelength.