Various heat flux quantities can be used to output the heat flux to walls and surfaces in Fire Dynamics Simulator (FDS). This post will explain the difference between various heat flux output quantities.

The options for outputting heat fluxes (kW/m^{2}) at a point location (on a surface) or boundary (along a wall or surface) are as follows:

- Radiative heat flux – \(\dot q_{rad}”\)
- Convective heat flux – \(\dot q_{conv}”\)
- Net heat flux – \(\dot q_{net}”\)
- Incident heat flux – \(\dot q_{inc}”\)
- Gauge heat flux – \(\dot q_{gauge}”\)
- Radiometer – \(\dot q_{radiometer}”\)
- Radiative heat flux gas – \(\dot q_{rad}”\)

## Radiative Heat Flux

Consider an energy balance on a surface or wall. The net radiative heat flux \(\dot q_{rad}”\) is given by the sum of the incoming (or absorbed) \(\dot q_{rad,in}”\) and outgoing (or reflected) \(\dot q_{rad,out}”\) radiation:

\(\dot q_{rad}” = \dot q_{rad,in}” – \dot q_{rad,out}”\)

where \(\dot q_{rad,out}”\) can be decomposed into

\(\dot q_{rad,out}” = \dot q_{rad,in}” – \varepsilon \sigma T_w^4\)

where \(\varepsilon\) is the emissivity, \(\sigma\) is the Stefan-Boltzmann constant, and \(T_w\) is the wall temperature.

The ‘RADIATIVE HEAT FLUX’ quantity can be used to output the net radiative heat flux to a surface.

## Convective Heat Flux

The convective heat flux \(\dot q_{conv}”\) is given by

\(\dot q_{conv}” = h (T_g – T_w)\)

where \(h\) is the heat transfer coefficient, and \(T_g\) is the local gas temperature.

The ‘CONVECTIVE HEAT FLUX’ quantity can be used to output the convective heat flux to a surface.

## Net Heat Flux

The net heat flux is the sum of the radiative heat flux and convective heat flux and is given by

\(\dot q_{net}” = \dot q_{rad}” + \dot q_{conv}”\)

The ‘NET HEAT FLUX’ quantity can be used to output the combined radiative and convective heat fluxes to a surface.

## Incident Heat Flux

The incident heat flux is a diagnostic output and is the sum of the incoming radiation and convection. It does not include outgoing radiation and is given by

\(\dot q_{inc}” = \dot q_{rad}”/\varepsilon + \sigma T_w^4 + \dot q_{conv}”\)

Substituting in the definition of the net radiative heat flux results in

\(\dot q_{inc}” = (\dot q_{rad,in}” – \dot q_{rad,out}”)/\varepsilon + \sigma T_w^4 + \dot q_{conv}”\)

Expanding the \(\dot q_{rad,out}”\) term results in

\(\dot q_{inc}” = (\dot q_{rad,in}” – \varepsilon \sigma T_w^4)/\varepsilon – \sigma T_w^4 + \sigma T_w^4 + \dot q_{conv}”\)

Expanding the first term and simplifying results in

\(\dot q_{inc}” = \dot q_{rad,in}”/\varepsilon – \sigma T_w^4 + \sigma T_w^4 + \dot q_{conv}”\)

Further simplification results in

\(\dot q_{inc}” = \dot q_{rad,in}”/\varepsilon + \dot q_{conv}”\)

The ‘INCIDENT HEAT FLUX’ quantity can be used as a diagnostic to output the convective and incoming radiative heat fluxes to a surface.

## Gauge Heat Flux

The gauge heat flux can be used when comparing experimentally measured heat fluxes for a gauge that is held at a fixed temperature. The gauge heat flux accounts for the incoming and outgoing radiation and convection and adjusts the heat fluxes based on a fixed (specified) wall temperature. The gauge heat flux is given by

\(\dot q_{gauge}” = \dot q_{rad}”/\varepsilon + \dot q_{conv}” + \sigma(T_w^4 – T_G^4) + h(T_w – T_G)\)

You must specify the gauge temperature \(T_G\) for this output.

The ‘GAUGE HEAT FLUX’ quantity can be used when comparing heat flux predictions to experimentally measured heat fluxes for a gauge at a fixed temperature.

## Radiometer

The radiometer output quantity is similar to the gauge heat flux output quantity, but convection is neglected, which is given by

\(\dot q_{gauge}” = \dot q_{rad}”/\varepsilon + \sigma(T_w^4 – T_\infty^4)\)

The ‘RADIOMETER’ quantity can be used when comparing heat flux predictions to experimentally measured heat fluxes from a radiometer.

## Radiative Heat Flux Gas

The ‘RADIATIVE HEAT FLUX GAS’ quantity is the same as the radiative heat flux \(\dot q_{rad}”\) except this device can be placed away from a solid surface to output the radiative heat flux if a surface was present at the specified location.

## Example

An example case can be used to demonstrate the different heat flux output quantities in FDS. The source code for this example can be found on the fire-tools repository.

In this example, a 200 kW propane fire measuring 0.4 m by 0.4 m is placed 0.3 m from a single wall in a domain measuring 1 m by 1 m by 2 m. The grid cells are 10 cm on each side. The wall is divided vertically into two halves: one with thermal properties of gypsum (and an emissivity of 0.5 to exaggerate the results), and another specified as an ‘INERT’ surface with a fixed temperature of 20 °C. The other walls are open to ambient air. Two measurement locations are located on the wall at a height of 0.5 m: one located on the gypsum portion of wall, and one located on the INERT portion of the wall. The following snapshot from Smokeview shows the fire in front of the gypsum wall (left) and inert wall (right).

Six heat flux output quantities were placed at the two measurement locations as follows: net heat flux, convective heat flux, radiative heat flux, incident heat flux, gauge heat flux, and radiometer.

The following snapshot shows the convective heat flux on the wall. If the radiative, net, or convective heat flux quantities are visualized via a boundary file, there is a difference between the heat flux values on the two materials because the gypsum material is warmer than ambient air, which results in a negative convective heat flux (heat transfer from the wall to the air), whereas the inert (cold) wall does not heat up, which results in a positive convective heat flux (heat transfer from the air to the wall):

The following snapshot shows the gauge heat flux on the wall. Note that the incident heat flux and gauge heat flux do not depend on the emissivity or properties of the materials, so the two different wall materials show no difference in the incident and radiative heat flux quantities. In other words, this is the heat flux “incident” upon the material and does not depend on the properties of the material (a similar effect is observed for the ‘WALL TEMPERATURE’ vs. the ‘ADIABATIC SURFACE TEMPERATURE’ output quantities):

The following plot shows the different heat fluxes on the inert wall:

The highest heat fluxes are the incident and gauge heat flux, which are between 10 kW/m^{2} and 15 kW/m^{2}, followed closely by the radiometer. This is expected because the incident and gauge heat fluxes do not account for radiative losses, the gauge heat flux is the heat flux to an inert (cold) wall, and the wall and gauge temperatures for the inert wall are fixed at 20 °C. The radiative and net heat fluxes are the next highest heat fluxes between 8 kW/m^{2} and 14 kW/m^{2}, and they are overlapping because the convective heat flux is close to 0 kW/m^{2}.

The following plot shows the different heat fluxes on the gypsum wall:

The various heat flux quantities are in the same order as the inert wall. The incident heat flux, gauge heat flux, and radiometer are overlapping from 10 kW/m^{2} to 15 kW/m^{2}. Because the gypsum material has an emissivity of 0.5, the radiative heat flux is lower (approximately 5 kW/m^{2}) because half of the radiation is reflected away. As the gypsum wall heats up, it begins to transfer heat outwards via convection, hence the negative convective heat flux of approximately -1 kW/m^{2}. Because of the reduced radiative heat flux and the negative heat flux, the net heat flux (sum of the radiative and convective heat fluxes) is less than the inert wall and is approximately 5 kW/m^{2}.

## Conclusion

Use the ‘RADIATIVE HEAT FLUX’, ‘CONVECTIVE HEAT FLUX’, or ‘NET HEAT FLUX’ output quantities to obtain the heat flux to a surface that accounts for both incoming and outgoing radiative and convective heat transfer and uses the actual wall temperature in the heat transfer calculations.

Use the ‘GAUGE HEAT FLUX’ or ‘RADIOMETER’ output quantities when comparing to experimental measurements. Specify a gauge temperature when using the gauge heat flux output quantity.

Use the ‘INCIDENT HEAT FLUX’ output quantity as a diagnostic output to check the heat flux value (neglecting radiative losses).

Walls with the default ‘INERT’ boundary condition should not be used in a realistic scenario because they remain at a fixed temperature. They should only be used for diagnostic purposes.

The source code for this heat flux example can be found on the fire-tools repository, including the FDS input file and the Python script to generate the plots.