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 application of the Danckwerts condition on the enthalpy allows to express the normal total heat flux (conduction, convection, and radiation) at the inlet boundary as proportional to the mass flow rate and the upstream enthalpy Hupstream:

For large flow rates , advective heat transfer dominates over conductive and radiative heat transfer. In this case, only the convective part remains in the left-hand side of Equation 4-21, leading to , or:

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.

As the heat capacity Cp is positive, in the absence of pressure contribution to the enthalpy, zero enthalpy variation induces the following constraint on temperature

For low flow rates or in the presence of large heat sources or sinks next to the inlet, the conductive and radiative heat fluxes cannot be neglected. The first integral in Equation 4-22 has for effect to adjust the inlet temperature to balance the energy brought by the flow at the inlet and the energy transferred by conduction and radiation from the interior.

Pressure losses in the virtual channel upstream to the inlet boundary are handled through the pressure contribution to the enthalpy (the second integral in Equation 4-22).