This script solves the laminar flow with heat transfer problem in a square duct. It has SUPG / PSPG / LSIC stabilization implemented. The flow is hydrodynamically developped (fully developped velocity profile imposed at inlet) and thermally developping. It yields a Nusselt number of 4.88 compared to 6.44 in Shah & London, Laminar Flow Forced Convection in Ducts, 1978. This difference may come from the meshing of the square duct: a better meshing at the wall where the temperature gradient is calculated is probably needed.
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Fenics Incompressible Navier-Stokes
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