Modified Boundary Integral Equations for Closely Spaced Surfaces

3 Modified Boundary Integral Equations for Closely Spaced Surfaces 

For a thin-walled molding, the distance between the opposing cavity surfaces (i.e., part thickness) is typically orders of magnitude smaller than the length and width of the part. In this case, the traditional boundary integral formulation leads to 

Associated with the midsurface, each variable has two different variables at top and bottom defined by a normal vector n to the mid-surface, one can use superscript + and on the variables (e.g., T and T ) to indicate values on the different sides. An extra formula is thus derived for the additional degree of freedom. For point ro on the midsurface, the following two boundary integral equations are solved  

The cooling channel surfaces have been divided into N cylindrical segments. For a point rq on the axis of the jth cylindrical segment of the cooling channel, one has 

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