radiative transfer

Examples of radiative transfer in the following topics:

• Introduction

  • We are going to set the stage for a deeper look at astrophysical sources of radiation by defining the important concepts of radiative transfer, thermal radiation and radiative diffusion.
  • Upon these assumptions the field of radiative transfer is built.

• The Radiative Transfer Equation

  • Once we know $\alpha_\nu$ and $j_\nu$ for the system of interest, it is straightforward to solve the equations of radiative transfer.
  • The result for pure absorption inspires us to look at the radiative transfer equation again.
  • Using this definition we get the following equation of radiative transfer,
  • It allows a formal solution of the transfer equation.

• Eddington Approximation

  • The source function $S_\nu$ is isotropic, so let's average the radiative transfer equation over direction to yield
  • Let's also average the radiative transfer equation times $\mu$ over direction to yield
  • This is sometimes called the radiative diffusion equation.
  • If you know the temperature structure of the material you can solve the equation for the mean intensity $J_\nu$ and then you know the source function $S_\nu$ explicitly and you can use the formal solution to the radiative transfer equation to get the radiation field.

• Transformation of Radiative Transfer

  • The equations of radiative transfer follow the intensity of the radiation field.We would like to understand how this and other radiative transfer quantities transform relativistically.
  • Because the source function $S_\nu$ appears in the equations of radiative transfer as , must have the same transformation properties as , i.e.
  • These relations allow us to calculate the radiative transfer through a medium in whichever frame is convenient.
  • We could calculate the source function and absorption in the rest-frame of the material and the radiative transfer in the "lab'' frame.

• Greenhouse Gases and Global Warming

  • Radiation is a natural process of heat transfer; everything is constantly radiating heat.
  • The greenhouse effect is a phenomenon of radiative transfer, the process by which the energy of light waves is exchanged in matter.
  • Radiative transfer dictates what energy is reflected, absorbed, and emitted .
  • The radiative transfer properties of atmospheric chemicals depend on the energy of the radiation (both for absorption and emission), and those properties are unique to each chemical.

• Modelling the Stress

  • We can combine the $\alpha$-prescription with vertical radiative transfer to obtain an estimate of the central density and temperature of the disk.
  • By combining the previous equation with with vertical radiative transfer, we obtain

• Blackbody Radiation

  • Second if a material is emitting thermal radiation one can obtain a simple expression of the radiative transfer equation (see the problems).

• Thermodynamics

  • The brightness temperature has several nice properties.For one thing it has units of Kelvin rather than something clumsy.Second if a material is emitting thermal radiation one can obtain a simple expression of the radiative transfer equation (see the problems).

• Blackbody Temperatures

  • Second if a material is emitting thermal radiation one can obtain a simple expression of the radiative transfer equation (see the problems).

• Overview of Heat

  • This module defines and explores heat transfer, its effects, and the methods by which heat is transferred.
  • It is something which may be transferred from one body to another.
  • After defining and quantifying heat transfer and its effects on physical systems, we will discuss the methods by which heat is transferred.
  • So many processes involve heat transfer, so that it is hard to imagine a situation where no heat transfer occurs.
  • (a) The chilling effect of a clear breezy night is produced by the wind and by radiative heat transfer to cold outer space.