This section assumes a heat transfer model that only solves for the temperature T. In particular, for a fluid, the velocity field
u and pressure field
p are user defined or computed from another physics interface. In this case, the heat balance in a domain follows the identity below (chapter 11.2 in
Ref. 5), derived from
Equation 4-11. It expresses the idea that internal energy variations in time and net heat flux are balanced by external heat and work sources.
The different variables in this formula are defined in Total Heat Flux and Energy Flux. For this equality to be true, the provided dependent variables (velocity field
u and pressure field
p for the Navier-Stokes equations) must satisfy a mass and a momentum conservation equation. The dissipation power,
Wstr, Int, contains both pressure work and viscous dissipation in fluids. The heat sources
QInt include domain sources, interior boundary, edge and point sources, and radiative source at interior boundaries.
Equation 4-175 is more visually represented by the diagram of
Figure 4-35 below.
When the temperature T is solved together with additional mass and momentum equations, the total energy flux also becomes a conserved quantity and the following equation holds (chapter 11.1 in
Ref. 5):
