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  • 1
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Industrial and engineering chemistry 22 (1983), S. 183-186 
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 30 (1987), S. 289-296 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: This study is concerned with the effects of surface tension on the steady potential flow of a liquid issuing from a two-dimensional slot with inclined walls. The mathematical problem, which is characterized by a nonlinear boundary condition along the free streamline, is solved using a novel numerical technique based on the fast direct Poisson solver. Numerical solutions were obtained for various Weber numbers and slot angles, and the results are compared with the free streamline shapes and contraction coefficients of the corresponding classical potential solutions without surface tension, and with some available theoretical results. When the numerical grid size is reduced or when the Weber number is sufficiently small, undesirable standing waves appear on the free surface that violate a causality condition. The cause of these waves was examined. A criterion was found for the occurrence of the waves.
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of polymer research 3 (1996), S. 39-48 
    ISSN: 1572-8935
    Keywords: Converging cone ; Non-Newtonian jet ; Finite-element method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The effects of the rheological properties on the fluid motion of non-Newtonian jets emanating from a converging cone have been investigated theoretically. Three typical non Newtonian fluid models have been considered; i.e. the power-law fluid, the modified Bingham ngham fluid and the Oldroyd-B fluid. The effects of five parameters on the flow field are analyzed in detail; these parameters are: the contraction ratio of the radius of the cone far upstream to that at the cone exit L; the converging angle of the cone 6; the power-law index n; the Bingham number Bn and the Weissenberg number We. The Galerkin finite-element method incorporated with the upwind scheme was applied to solve the flow problems numerically. Full Newton iteration was used to solve the flow fields and the free-surface positions of power-law and modified Bingham fluids. However, the free-surface position of the Oldroyd-B fluid has to be updated by kinematic iteration to avoid numerical oscillations.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of polymer research 5 (1998), S. 1-7 
    ISSN: 1572-8935
    Keywords: 3-D Finite element method ; Carreau model ; Truncated power law model ; Coat-hanger die
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract A simple numerical approach that is based on the lubrication approximation is developed for the optimal design of a linearly tapered coat-hanger die. This approach does not require the analytic pressure drop / flow rate equations for flow in the manifold and in the slot section, therefore any generalized Newtonian fluid model can be easily incorporated. Example calculations have demonstrated that the predictions based on this approach are reasonably accurate as compared with those from the complete 3-D finite element simulations.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 28 (1988), S. 1517-1526 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: We describe the computer-aided engineering analysis of a linearly tapered coat-hanger die in this paper. The general governing equation for flow distribution inside the die was derived first. On the basis of this equation, we have developed the design formula for a die to deliver uniform flow. In addition, we have also examined the variations of lateral flow uniformities and residence time distributions of polymeric liquids under several different design and operating conditions: (1) using manifolds with non-circular cross-sections, (2) adjusting production widths, (3) delivering fluids with different viscosities, and (4) enlarging manifolds for practical production considerations.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 28 (1988), S. 1559-1564 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The pressure drop/flow rate equation for non-Newtonian fluid flow in channels of irregular cross-section is determined theoretically by two numerical methods. Two representative non-Newtonian fluid models, the Ellis and the Herschel-Bulkley models, have been studied for several commonly encountered non-circular channels. The empirical methods proposed by Kozicki, et al, and Miller have been analyzed. The validity of their methods is discussed.
    Additional Material: 4 Ill.
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  • 7
    Electronic Resource
    Electronic Resource
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 34 (1994), S. 541-550 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: A simple unified lubrication approach has been proposed to design a coat-hanger die that can deliver wide and uniform liquid sheets. This approach requires that the wall stress in the manifold be constant. With this constraint, any inelastic non-Newtonian fluid model can be used to describe the liquid motion inside the die. Fluid models that can represent the pseudoplastic or viscoplastic behavior of polymeric liquids have been selected for illustration. A general equation that can be solved to determine the effect of production variations on flow uniformity inside the die has also been derived.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 34 (1994), S. 827-834 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The Galerkin finite element method has been applied to study the three-dimensional flow field of power-law fluids inside an extrusion die. Two inlet designs, i.e., center-fed and end-fed, have been considered. The effects of inertial force as represented by the Reynolds number Re, inlet geometry, and the power-law index n on lateral flow uniformity and vortex formation in the entrance region have been examined. A flow visualization technique has been carried out to experimentally verify the theoretical prediction of the three-dimensional flow field inside a die. It has been found that increasing Re or decreasing n will deteriorate flow uniformity. Depending on the direction of the inlet jet stream, the inertial force may create a flow peak in the central region of a center-fed die, or the maximum flow rate will appear close to the end of the die for an end-fed die. For highly shear-thinning fluids, lower flow rates are always observed close to the end of the dies. It is concluded that creating a plug flow in the inlet tube of the extrusion die is advantageous for both center-fed and end-fed designs.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 505-514 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical technique has been developed to solve a system that consists of m linear parabolic differential equations with coupled nonlinear boundary conditions. Such a system may represent chemical reactions, chemical lasers and diffusion problems. An implicit finite difference scheme is adopted to discretize the problem, and the resulting system of equations is solved by a novel technique that is a modification of the cyclic odd-even reduction and factorization (CORF) algorithm. At each time level, the system of equations is first reduced to m nonlinear algebraic equations that involve only the m unknown grid points on the nonlinear boundary. Newton's method is used to determine these m unknowns, and the corresponding Jacobian matrix can be computed and updated easily. After convergence is achieved, the remaining unknowns are solved directly. The efficiency of this technique is illustrated by the numerical computations of two examples previously solved by the cubic spline Galerkin method.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 30 (1990), S. 1220-1227 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The effects of cavity shapes, particularly the expansion and contraction angles, and the Theological properties of polymeric liquids on vortex formation in the cuter cavity of a dual-cavity coat-hanger die have been examined. For power-law fluids, a vortex may appear in the expansion side of the outer cavity, and the size of the vortex is influenced by the expansion angle, the power-law index, and the Reynolds number. Two viscoelastic fluids were used in the flow visualization experiment; for an aqueous polyacrylamide solution, a vortex may appear in the contraction side of the outer cavity and this vortex is influenced by the contraction angle and the fluid elasticity, but no vortex was observed for a Boger fluid.
    Additional Material: 17 Ill.
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