-
Notifications
You must be signed in to change notification settings - Fork 148
CookBook%2FHeatTransfer
This example was originally provided by fred2 <at></at> qnet.com in http://thread.gmane.org/gmane.comp.python.fipy/911
The model problem of a (compressible) gas confined between two infinite plates is a useful test case for a Navier-Stokes solver. For stationary walls maintained at fixed (but different) temperatures, and assuming continuum no-slip boundary conditions, the the Navier-Stokes equations can be solved analytically.
The energy equation simplifies to the (1D) heat equation (i.e., a `DiffusionTerm`) to be solved for the temperature profile.
which is solved with no-slip boundary conditions (strictly applicable only for Knudsen number
The normal momentum equation simplifies to
The exact steady-state temperature profile is
Starting from a linear profile, it takes only a few sweeps to reach convergence.
Reference `Wadsworth:1993` compares finite difference Navier-Stokes and particle simulation method predictions in the rarefied flow (i.e., slip) regime for which some experimental data are available.