1-D Area-Averaged Navier-Stokes Equations
The Thermal Hydraulics Module (THM) solves for conservation of mass, momentum, and energy with 1-D area averages of the Navier-Stokes equations,
∂t∂(Aρf)+∂x∂(Aρfu)=0 ,(1)
∂t∂(Aρfu)+∂x∂(Aρfu2+AP)=P~∂x∂A−2Dhfρfu∣u∣A(2)
∂t∂(AρfEf)+∂x∂[Au(ρfEf+P)]=Hwaw(Twall−Tbulk)A(3)
where x is the coordinate along the flow length, A is the channel cross-sectional area, ρf is the fluid density, u is the x-component of velocity, P~ is the average pressure on the curve boundary, Ef is the fluid total energy, f is the friction factor, Hw is the wall heat transfer coefficient, aw is the heat transfer area density, Twall is the wall temperature, and Tbulk is the area average bulk fluid temperature.