Engineering task and calculation objective
The K3 module calculates the thermal radiation of gases and gas mixtures according to the VDI Heat Atlas (VDI-Wärmeatlas), 12th edition 2019 — the standard German reference for heat transfer engineering. Unlike solids, gases do not radiate in a continuous spectrum but only in discrete bands: the technically relevant species are above all water vapor (H2O), carbon dioxide (CO2) and sulfur dioxide (SO2), while diatomic gases such as N2 and O2 are practically non-radiating. Anyone who wants to calculate the radiative heat flow from a hot flue gas to an enclosing wall needs the emissivity and the absorptivity of the gas mixture.
In practice, gas radiation becomes decisive wherever hot combustion gases meet walls or heating surfaces: in the furnaces of steam generators, process furnaces, heat-recovery boilers and flue-gas ducts. At gas temperatures above roughly 600–800 °C, radiation frequently provides the dominant contribution to heat transfer and must be taken into account alongside convection, for instance as a radiation-equivalent heat transfer coefficient.
The calculation method is based on the emissivity correlations of the VDI Heat Atlas: the emissivity of the gas is determined as a function of gas temperature, partial pressure of the radiating components and the mean beam length of the gas volume; for mixtures of H2O and CO2, the band overlap is corrected.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Define the gas composition and state: The inputs are total pressure, gas temperature and the partial pressures or volume fractions of the radiatively active components (water vapor, carbon dioxide and, where applicable, sulfur dioxide), plus the wall temperature of the enclosing surface.
- Determine the mean beam length: From the geometry of the gas volume, the equivalent (mean) beam length is calculated, approximately s ≈ 3.6·V/A from the volume and surface area of the gas space. It replaces the real, direction-dependent radiation path length with a single representative value.
- Evaluate the emissivities of the individual components: For each radiating component, the emissivity is determined from the correlations of the VDI Heat Atlas as a function of temperature and the product of partial pressure and beam length (p·s); pressure corrections account for deviations from the reference pressure.
- Form the mixture emissivity with overlap correction: The emissivities of H2O and CO2 are added and reduced by the overlap term Δε, because the radiation bands of the two gases partially coincide and the radiation would otherwise be counted twice.
- Calculate the absorptivity and net heat flow: The absorptivity of the gas with respect to the wall radiation is evaluated at the wall temperature — it is not equal to the emissivity, since emission occurs at the gas temperature and absorption at the wall temperature. From both quantities, the temperatures and the wall emissivity, the net radiative heat flow follows, which can also be expressed as a gas-radiation heat transfer coefficient.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Gas temperature | Tg | K |
| Wall temperature | Tw | K |
| Area | A | m² |
| Layer thickness | sgl | m |
| Partial pressure | pH2O | bar |
| Emissivity of the wall | εw | - |
| Total pressure | ptot | bar |
| Gas absorptance | av,H2O | - |
| Radiation heat flux between gas body and wall | Q̇gw | W |
| Emissivity at Tg | εH2O,g | - |
| Emissivita at p=1 bar and Tw | εH2O,Standard | - |
| Emissivity | εg | - |
| Pressure correction | CH2O | - |
| Emissivity at Tg | εCO2,g | - |
| Emissivita at p=1 bar and Tw | εCO2,standard | - |
| Partial pressure | pCO2 | bar |
| Pressure correction | CCO2 | - |
| Gas absorptance | av,CO2 | - |
| Gas absorptance | av | - |
| Mole fraction | H2O xH2O | - |
| Equivalent pressure | pe,H2O | bar |
| Product | (p∙sgl)H2O | bar·m |
| Equivalent pressure | pe,CO2 | bar |
| Product | (p∙sgl)CO2 | bar·m |
Calculation options
Selection of medium
1 · 2 · 3 · 4 · Mixture of H2O, CO2 and CO
Selection of calculation method
Band model with data in tabular form · Analytic calculation according "weighted sum of grey gas model"
Frequently asked questions
Why do nitrogen and oxygen radiate practically nothing?
Symmetric diatomic molecules such as N2 and O2 have no permanent dipole moment and do not change it during vibration either; they can therefore hardly emit or absorb radiation in the technically relevant infrared range. That is why the triatomic constituents such as H2O, CO2 and SO2 alone determine the radiation of a flue gas — for dry air, gas radiation is negligible.
Why is the absorptivity of the gas not equal to its emissivity?
Kirchhoff's law strictly applies only to radiation of identical spectral distribution. The gas emits according to its own temperature but absorbs radiation whose spectrum is shaped by the wall temperature. For large temperature differences between gas and wall, emissivity and absorptivity differ significantly; the method evaluates both separately.
What does the mean beam length mean, and what error does the approximation introduce?
The real radiation path length depends on direction; the mean beam length replaces it with a value for which a hemispherically radiating gas volume delivers the same heat flow to the wall. The approximation s ≈ 3.6·V/A is sufficiently accurate for most technical gas spaces; more precise values are tabulated for standard geometries such as spheres, cylinders or parallel-plate gaps.
From what point must I consider gas radiation in addition to convection?
Since radiative heat flow grows with the fourth power of the absolute temperature, gas radiation generally becomes the dominant transfer mechanism at flue-gas temperatures above roughly 600 °C. It governs furnaces and radiant passes of boilers; in downstream convective heating surfaces with cooler gas it still provides a relevant additional contribution, captured via a radiative heat transfer coefficient.