This approach requires the introduction of mathematical simplifications and semi-empirical models. The two-dimensional flow equations are obtained by analytically integrating the three-dimensional continuity and momentum equations across the fluid layer above the electronic devices. The result are the so-called depth-averaged (DA) flow equations. Since the devices protrude from the circuit board the fluid layer has a variable depth. The change in depth affects the velocity field through its influence in the depth-averaged continuity equation, and in the pressure gradient terms in the depth-averaged momentum equations. The shear stresses on the top and bottom of the fluid layer are also included in the depth-averaged momentum equations via correlations of shear stress for fully-developed duct flow.
The idea of depth-averaging is not new. It has been used for years to study flows in rivers, bays and other large bodies of water. It has also been used to simulate the flow and heat transfer in compact heat exchangers, and in film-cooled turbine blades. As far as I know, the PCBCAT is the only application of depth-averaging to the modeling of printed circuit boards.
A more detailed description of the depth-averaged flow model is available in a paper I presented at the 1995 International Mechanical Engineering Congress and Exposition. The papers web page contains links to the abstract and a postscript version of the complete text.
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