Abstract
AbstractThe lubrication theory is extended for transient free‐surface flow of a viscous fluid inside three‐dimensional cavities of general symmetric shape but of small thickness. The problem is closely related to the filling stage during the injection molding process. The moving domain is mapped onto a rectangular domain at each time step of the computation. A modified pressure is introduced, which in this case is governed by the Laplace's equation, and it is expanded in a Fourier series along the flow direction. The expansion coefficients are obtained using the finite‐difference method. This approach is valid for simple and complex cavities as illustrated for the cases of a flat plate and a curved plate. Only a few modes are needed to secure convergence in general. It is found that the flow behaviour is strongly influenced by the shape of the initial fluid domain, the shape of the cavity, cavity thickness, and the inlet flow. Copyright © 2002 John Wiley & Sons, Ltd.
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