Global Variables
This section describes variables defined by integrals. A concise notation denotes the different domains of integration: Ω is the geometry domain, ∂Ωext represents the exterior boundaries, and ∂Ωint represents the interior boundaries.
Total Accumulated Heat Rate
The total accumulated heat rate variable, dEiInt, is the variation of internal energy per unit time in the domain:
Total Net Heat Rate
The total net heat rate, ntfluxInt, is the integral of Total Heat Flux over all external boundaries:
This indicates the sum of incoming and outgoing total heat flux through the system.
Total Heat Source
The total heat source, QInt, accounts for all domain sources, interior boundary, edge and point sources, and radiative sources at interior boundaries:
Total Fluid Losses
The total fluid losses, WnsInt, correspond to the work lost by a fluid by degradation of energy. These works are transmitted to the system through pressure work and viscous dissipation:
Total Accumulated Energy Rate
The total accumulated energy rate, dEi0Int, is the variation of total internal energy per unit time in the domain:
where the total internal energy, E0, is defined as
Total Net Energy Rate
The total net energy rate, ntefluxInt, is the integral of Total Energy Flux over all external boundaries:
This indicates the sum of incoming and outgoing total energy flux through the system.
Heat Balance
The following equality between COMSOL Multiphysics variables holds:
dEiInt + ntfluxInt = QInt - WnsInt
This is the most general form that can be used for time-dependent models. At steady-state the formula is simplified. The accumulated heat rate equals zero, so the total net heat rate (the sum of incoming and outgoing heat rates) should correspond to the heat and work sources:
ntfluxInt = QInt - WnsInt
The sign convention used in COMSOL Multiphysics for QInt is positive when energy is produced (as for a heater) and negative when energy is consumed (as for a cooler). For WnsInt, the losses that heat up the system are positive and the gains that cool down the system are negative.
For stationary models with convection by an incompressible flow, the heat balance becomes:
ntfluxInt = QInt
which corresponds to the conservation of convective and conductive flux as in:
Energy Balance
The following equality between COMSOL Multiphysics predefined variables holds:
dEi0Int + ntefluxInt = QInt
In stationary models, dEi0Int is zero so the energy balance simplifies into:
ntefluxInt = QInt
At steady state, and without any additional heat source (QInt equal to zero), the integral of the net energy flux on all boundaries of the flow domain, ntefluxInt, vanishes. However, the corresponding integral of the net heat flux does not, in general, vanish. It corresponds instead to the losses from mass and momentum equations, such as WnsInt for pressure work and viscous dissipation in fluids. Hence, energy is the conserved quantity, not heat.