Modelling of Heat Boundaries
To model heat transfer in a thermal fluid flow, in addition to the flow boundary conditions described in Flow module, the thermal variables should also be specified on all boundaries of the computational domain. Closely related to the flow boundary conditions, the thermal boundary conditions can be broadly categorized into four types: inlet, outlet, wall and symmetry. The description of the thermal boundary conditions is presented in this section.
Inlet Boundary Conditions
At an inlet, both the thermal variables and the rates of energy transfers need to be determined. For both subsonic and supersonic inflows, the thermal variables can be determined when either static or total temperature is given. Introducing 
and 
to represent the static and total inlet temperature, respectively, we have:
Fixed Static Temperature:
Total Inlet Enthalpy:
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Total Inlet Energy:
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where 
, 
and 
are the pressure, density and velocity at the inlet, determined by inlet flow boundary conditions.
The net transport of energy at inlet consists of both the convection and diffusion components. The convection component is the product of inflow mass flow rate and the total enthalpy obtained by equation 5.381. The diffusion component, however, depends on the temperature gradient at the inlet. By default, it is assumed to be negligible compared to advection, and equated to zero.
Fixed Total Temperature
Static Inlet Temperature
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With the computed static inlet temperature, the total inlet enthalpy, energy and net transport of energy are calculated in the same way as described above.
Outlet Boundary Conditions
Subsonic Outlet: Zero temperature gradient is assumed to apply for the subsonic outlet boundaries
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where 
and 
are the neighboring cell and outlet boundary temperature, respectively.
As in the inlets, the total enthalpy and energy are calculated based on the static temperature and outlet flow conditions.
Supersonic Outlet: No boundary values are required.
Symmetry Boundary Conditions
For symmetry boundaries, the thermal condition imposed is zero-gradient of temperature:
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Wall Boundary Conditions
Thermal wall boundary conditions can be determined by the following methods:
Adiabatic Wall: The Adiabatic Wall boundary condition allows zero heat transfer across the wall boundary:
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Fixed Temperature: The static temperature is specified at the wall boundary:
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Wall Heat Flux: The heat flux is specified at the wall boundary:
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With the given thermal boundary conditions, the thermal boundary layer is modelled using the near-wall approach described in Turbulence module.
Convection/Radiation
Convection/Radiation is a thermal boundary condition in which the heat flux is a function of the convective heat transfer or radiative heat transfer. For convective heat transfer, the heat flux is based on an external convection ambient temperature and exchange coefficient. For radiative heat transfer, the heat flux is based on emissivity and an external radiation ambient temperature.
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where
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Heat flux (W/m2) |
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Exchange coefficient (W/m2-K) |
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Convection ambient temperature (K) |
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Radiation ambient temperature (K) |
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Boundary temperature (K) |
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Emissivity |
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Stefan-Boltzmann constant = 5.67 x 10-8 W/(m2-K4) |
Convection
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Radiation
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