4.4 Radiation in participating media

Radiation in participating media is a crucial aspect of heat transfer. It involves the absorption, emission, and scattering of thermal radiation by gases and particles as it passes through a medium.

Understanding this process is key for many engineering applications. From combustion systems to solar receivers, the interaction between radiation and participating media significantly impacts overall heat transfer and system efficiency.

Thermal Radiation in Participating Media

Interaction of Thermal Radiation with Participating Media

Top images from around the web for Interaction of Thermal Radiation with Participating Media

• 

  1.6 Mechanisms of Heat Transfer – University Physics Volume 2 View original

  Is this image relevant?

• 

  Heat Transfer in the Atmosphere | Physical Geography View original

  Is this image relevant?

• 

  Atmospheric Gasses | Physical Geography View original

  Is this image relevant?

• 

  1.6 Mechanisms of Heat Transfer – University Physics Volume 2 View original

  Is this image relevant?

• 

  Heat Transfer in the Atmosphere | Physical Geography View original

  Is this image relevant?

1 of 3

Top images from around the web for Interaction of Thermal Radiation with Participating Media

• 

  1.6 Mechanisms of Heat Transfer – University Physics Volume 2 View original

  Is this image relevant?

• 

  Heat Transfer in the Atmosphere | Physical Geography View original

  Is this image relevant?

• 

  Atmospheric Gasses | Physical Geography View original

  Is this image relevant?

• 

  1.6 Mechanisms of Heat Transfer – University Physics Volume 2 View original

  Is this image relevant?

• 

  Heat Transfer in the Atmosphere | Physical Geography View original

  Is this image relevant?

1 of 3

• Participating media (gases and particles) can absorb, emit, and scatter thermal radiation as it passes through the medium
• Absorption converts a portion of the incident radiation into internal energy, increasing the temperature of the medium (CO2 in combustion systems)
• Emission releases energy in the form of thermal radiation due to the temperature of the participating medium (hot gases in a furnace)
• Scattering redirects radiation by the participating medium
  • Can be elastic with no change in wavelength (Rayleigh scattering by air molecules)
  • Can be inelastic with a change in wavelength (Raman scattering in gases)
• The interaction of thermal radiation with participating media depends on factors such as composition, density, temperature of the medium, and wavelength of the radiation (water vapor in air affects solar radiation)

Factors Influencing Radiation Interaction with Participating Media

• Composition of the medium determines the absorption and scattering properties (soot particles in flames)
• Density of the medium affects the number of particles available for interaction (dense smoke in a fire)
• Temperature of the medium influences the emission of thermal radiation (hot exhaust gases from an engine)
• Wavelength of the radiation determines the specific absorption and scattering behavior (ultraviolet radiation scattered by atmospheric particles)

Absorption, Emission, and Scattering

Absorption Coefficient

• Absorption coefficient (κ) quantifies the ability of a medium to absorb radiation per unit length
• Depends on the composition and density of the medium, as well as the wavelength of the radiation (water vapor absorbs infrared radiation)
• Higher absorption coefficients indicate stronger absorption of radiation by the medium (soot particles in a flame)

Emission Coefficient

• Emission coefficient (ε) describes the ability of a medium to emit thermal radiation per unit length
• Depends on the temperature and composition of the medium, as well as the wavelength of the radiation (hot CO2 emits infrared radiation)
• Higher emission coefficients indicate stronger emission of thermal radiation by the medium (glowing embers in a fire)

Scattering Coefficient and Extinction Coefficient

• Scattering coefficient (σ) represents the ability of a medium to scatter radiation per unit length
• Depends on the size, shape, and composition of the particles in the medium, as well as the wavelength of the radiation (dust particles scatter visible light)
• The sum of the absorption and scattering coefficients is called the extinction coefficient (β)
  • Represents the total attenuation of radiation per unit length in the participating medium
  • Higher extinction coefficients indicate stronger overall attenuation of radiation (dense fog attenuates visible light)
• The single scattering albedo (ω) is the ratio of the scattering coefficient to the extinction coefficient
  • Indicates the relative importance of scattering compared to absorption
  • A single scattering albedo of 1 means the medium only scatters radiation, while a value of 0 means it only absorbs radiation (pure scattering by air molecules vs. pure absorption by black soot)

Radiative Transfer Equation

General Form and Assumptions

• The equation of radiative transfer (ERT) describes the change in radiative intensity along a path through a participating medium
• Accounts for absorption, emission, and scattering (radiative intensity changes due to interaction with the medium)
• The general form of the ERT is an integro-differential equation that accounts for spatial, directional, and spectral dependencies of radiative intensity (complex mathematical description)
• The ERT can be simplified under certain assumptions
  • Local thermodynamic equilibrium (LTE) assumes the medium is in thermal equilibrium with its surroundings (valid for optically thick media)
  • Gray medium assumption considers the radiative properties to be independent of wavelength (simplifies the spectral dependence)
  • Isotropic scattering assumes the scattering is uniform in all directions (simplifies the directional dependence)

Boundary Conditions and Numerical Methods

• Boundary conditions must be specified to solve the ERT for a given problem
  • Surface emission accounts for the thermal radiation emitted by the boundaries of the medium (hot walls of a furnace)
  • Surface reflection considers the reflection of incident radiation at the boundaries (reflective insulation materials)
• Numerical methods are often used to solve the ERT for complex geometries and participating media
  • Discrete ordinates method (DOM) discretizes the angular and spatial domains to solve the ERT (used in computational fluid dynamics)
  • Monte Carlo method simulates the random propagation and interaction of photons in the medium (used for complex geometries and scattering media)

Participating Media Effects on Heat Transfer

Impact on Engineering Applications

• Participating media can significantly impact the overall heat transfer in various engineering applications
• In combustion systems, the presence of gases and particles (CO2, H2O, and soot) can enhance or attenuate radiative heat transfer
  • Affects the temperature distribution and efficiency of the system (flame temperature and heat transfer to surroundings)
• In solar receivers, participating media (air, water vapor, and dust) can absorb and scatter solar radiation
  • Influences the performance of the receiver and the overall efficiency of the solar energy system (reduced solar energy reaching the receiver)

Design Considerations for Participating Media

• Thermal insulation materials often contain participating media (fibers and foams) that scatter and absorb thermal radiation
  • Reduces the effective thermal conductivity and improves the insulation performance (fiberglass and foam insulation in buildings)
• The choice of materials and the design of systems involving participating media must consider the radiative properties and the effects of absorption, emission, and scattering
  • Optimize heat transfer and overall performance (selecting materials with desired radiative properties for specific applications)
• Understanding the interaction of thermal radiation with participating media is crucial for the design and analysis of efficient and effective heat transfer systems (combustion chambers, solar collectors, and insulation materials)