At the inlet boundary of a fluid domain, the Inflow boundary condition defines a heat flux that accounts for the energy that would normally be brought by the fluid flow if the channel upstream to the inlet was modeled.
The enthalpy variation between the upstream conditions and inlet conditions, ΔH, depends in general both on the difference in temperature and in pressure, and is defined as
where Tupstream is the upstream temperature,
T is the inlet temperature,
pupstream is the upstream absolute pressure,
pA is the inlet absolute pressure,
Cp is the fluid heat capacity at constant pressure,
ρ is the fluid density, and
αp is its coefficient of thermal expansion. See
Equation 4-5 for details about the definition of the enthalpy.
For large flow rates, advective heat transfer dominates over conductive heat transfer at the inlet. In this case, the left-hand side of Equation 4-21 is small compared to its right-hand side. As the heat capacity
Cp is positive, in the absence of pressure contribution to the enthalpy, this induces the following constraint on temperature