where the components of K are the Lagrange multipliers that are used to implement the boundary condition. Similarly, the tangential temperature gradient results from the difference of the gradient and its normal projection:

tT = T – n T n

U S E V I S C O U S S L I P

When viscous slip is used, select Maxwell’s Model to calculate Ls using:

2 – v

L = ---------------

s v

R E F E R E N C E

1. G. Kariadakis, A. Beskok, and N. Aluru, Microflows and Nanoflows, Springer Science and Business Media, 2005.

Theory for the Vacuum Pump Outlet Condition

Vacuum pumps (devices) can be represented using lumped curves implemented as boundary conditions. These simplifications imply also some assumptions. In particular, it is assumed that a given boundary can only be either an inlet or an outlet. Such a boundary should not be a mix of inlets/outlets nor should it change during a simulation.

Manufacturers usually provide curves that describe the static pressure as a function of flow rate for a vacuum pump.

D E F I N I N G A D E V I C E A T A N O U T L E T

In this case, the device’s inlet is the interior face situated between the blue (cube) and green (circle) domain while its outlet is an external boundary, here the circular boundary of the green domain. The lumped curve gives the flow rate as a function of the pressure difference between the interior face and the external boundary. This boundary condition implementation specifies vanishing viscous stress along with a Dirichlet condition on the pressure.

The vacuum pump boundary condition sets the following conditions:

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