25.1. Fluxes Through Boundaries

This section describes the quantities that you can compute for boundaries. For more information about generating flux reports, see Generating a Flux Report in the User's Guide.

For selected boundary zones, you can compute the following quantities:

  • The mass flow rate through a boundary is computed by summing the dot product of the density times the velocity vector and the area projections over the faces of the zone.

  • The total heat transfer rate through a boundary is computed by summing the total heat transfer rate, , over the faces, where is the convective heat transfer rate and is the radiation heat transfer rate. The computation of the heat transfer through the face depends on the specified boundary condition. For example, the conduction heat transfer on a constant-temperature wall face would be the product of the thermal conductivity with the dot product of the area projection and the temperature gradient. For flow boundaries, the total heat transfer rate is the flow rate of the conserved quantity. Depending on the models that are being used, the total heat transfer rate may include the convective flow of sensible or total enthalpy, diffusive flux of energy, etc. Note that the reference temperature in all enthalpy calculations is always 298.15 K.


    Important:  Note that in the case of moving walls with compressible flow, the pressure work is also added while reporting heat flux; this is also true with incompressible flow if the energy equation includes the pressure work (enabled through the define/models/energy? text command) or the viscous dissipation terms (enabled automatically for the density-based solver, or through the Viscous Heating option in the Viscous Model dialog box for the pressure-based solver).


  • The radiation heat transfer rate through a boundary is computed by summing the radiation heat transfer rate over the faces.

  • The pressure work rate () is calculated for a fluid zone that undergoes normal zone motion relative to an adjacent solid zone, according to the following equation. This rate is included in the total heat transfer rate for boundary on the moving fluid zone (but not for the boundary of the adjacent solid zone).

    (25–1)

    where is the mesh velocity, is the surface element, is the normal vector of the surface element directed inside the fluid, is the pressure, and is the boundary surface area.

  • The viscous work rate () through a boundary is computed by taking the integral of the product of viscous stress with velocity over the boundary with the boundary normal directed inside, according to the following equation. This rate is included in the total heat transfer rate with the pressure-based solver.

    (25–2)

    where is the fluid velocity, is the surface element, is the normal vector of the surface element directed inside the fluid, is the viscous stress tensor, and is the boundary surface area.

For example, you might use flux reporting to compute the mass flow through a duct with pressure boundaries specified at the inlet and exit after running a simulation with these settings.