  In the context of transpiration cooling, a 1D porous medium model consisting
of a temperature system and a mass-momentum system is derived from the 2D/3D
Darcy-Forchheimer equations. The temperatures of the coolant and the solid are
assumed to be in local nonequilibrium. This system is analytically verified to
have a unique solution. Transpiration cooling simulations are performed by a
two-domain approach, coupling the assembled 1D porous medium solutions with 2D
solutions of a hot gas flow solver. A comparison of results obtained by
applying the 1D porous medium model with the temperature system either
including or neglecting fluid heat conduction justifies the use of the latter
simplified system.
