SUMMARYBoundary conditions come from Nature. Therefore these conditions exist at natural boundaries. Often, owing to limitations in computing power and means, large domains are truncated and confined between artificial synthetic boundaries. Then the required boundary conditions there cannot be provided naturally and there is a need to fabricate them by intuition, experience, asymptotic behaviour and numerical experimentation. In this work several kinds of outflow boundary conditions, including essential, natural and free boundar conditions, are evaluated for two flow and heat transfer model problems. A new outflow boundary condition, called hereafter the f?ee boundary condition, is introduced and tested. This free boundary condition is equivalent to extending the validity of the weak form of the governing equations to the synthetic outflow instead of replacing them there with unknown essential or natural boundary conditions. In the limit of zero Reynolds number the free boundary condition minimizes the energy functional among all possible choices of outflow boundary conditions. A review of results from applications of the same boundary conditions to several other flow situations is also presented and discussed.KEY WORDS Open boundary conditions Backward-facing step Unbounded flow Free boundary condition
Non-isothermal, melt film-blowing is analysed by means of a nonlinear integral constitutive equation that incorporates shear history effects, spectrum of relaxation times, shear thinning and extension thinning or thickening. The temperature history, as predicted by the simultaneously solved energy equation, is introduced into the constitutive equation by means of the appropriate shift factor incorporated in the linear modulus of the constitutive equation. The resulting system of integrodifferential equations is solved by finite element discretization and Newton iteration. Bubble shape, velocity, temperature, stress and thickness profiles are predicted simultaneously. Predicted film thickness, temperature and stress profiles of blowing of polystyrene are compared with experimental data taken from the literature.
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