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  • 1965-1969  (4,609)
  • Organic Chemistry  (3,129)
  • Chemical Engineering  (1,448)
  • Engineering
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  • 1
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 3-28 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element methods can be formulated from the variational principles in solid mechanics by relaxing the continuity requirements along the interelement boundaries. The combination of different variational principles and different boundary continuity conditions yields numerous types of approximate methods. This paper reviews and reinterprets the existing finite element methods and indicates other alternative schemes. Plate bending problems are used to compare the relative merits of the various methods.
    Additional Material: 10 Ill.
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 1-2 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 47-66 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Three methods for finding natural frequencies and modes of complex structures composed of beam elements are described and compared. The analysis is extended to include hysteretic damping for the determination of response and transmissibility without a modal analysis. Experimental comparison is given for the response of a simple engineering structure.
    Additional Material: 10 Ill.
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 101-122 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The derivation of the stiffness matrix for a refined, fully compatible triangular plate bending finite element is presented. The Kirchhoff plate bending theory is assumed. Six parameters or degrees of freedom are introduced at each of the three corner nodes resulting in an 18 degree of freedom element. This refined element is found to give better results for displacements and particularly for internal moments than any plate bending element, regardless of shape, previously reported in the literature.
    Additional Material: 9 Ill.
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  • 6
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 67-73 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite difference treatment of two-dimensional problems in elastostatics is usually based on the differential equations for the displacement vector or the Airy stress function, depending on whether boundary conditions are on displacement or stress. In either case, determination of stresses requires numerical differentiation and therefore use of a rather fine grid. Moreover, neither method is suited to the treatment of mixed boundary conditions. The alternative method developed in this paper uses the first derivatives of the displacement components at the grid points as basic variables and hence does not require numerical differentiation in the evaluation of stresses. Appropriate finite difference equations are established, and their use is discussed in connection with a specific example with known explicit solution.
    Additional Material: 4 Ill.
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  • 7
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 29-45 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The theory, function generator routine and testing procedures are given for a six-node 18 degree of freedom triangular element. At corner nodes the variables are the displacement and the two slopes. At midside nodes the variables are the displacement, the slope normal to the side, and the rate of change of this along the side - i.e., the rate of torsion. Of two options, one divides the triangle into three and takes different quartic displacements in the three regions, and the other uses displacement functions with singularities at the vertices. According to a test which compares the energies of the two formulations by eigenvalues, the second is the better if the integration is accurate. The same test, together with others based on finite differences and on nodal values, etc. checks the correctness of the routine decisively.
    Additional Material: 2 Ill.
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  • 8
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 123-133 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The large deflection problem of a rectangular plate is analysed by using the finite element method and employing the iteration technique. In the present study, the stiffness matrix of a rectangular plate element for bending proposed by Greene is employed, and results of numerical examples duly justifies applicability of the present method.
    Additional Material: 9 Ill.
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  • 9
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 75-100 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents first a general formulation of the elasto-plastic matrix for evaluating stress increments from those of stresses for any yield surface with an associated flow rule. A new ‘initial stress’ computational process is proposed which is shown (1) to yield more rapid convergence than alternative approaches (2) to permit large load increments without violating the yield criteria and thus simply to establish lower bound solutions. Several solutions showing stress distribution, strain development and growth of plastic enclaves are given both for the von Mises and for Coulomb (Drucker) type yield surfaces. Load reversal and thermoplastic behaviour are dealt with.
    Additional Material: 18 Ill.
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  • 10
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 11
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 151-162 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The direct Finite Element Analysis which was successfully employed in the solution of dynamic flexural traveling wave problems is extended herein to provide the transient behaviour of finite beams and plates in which shear deformation and rotatory inertia are considered. The particle and angular velocities are exponentially damped so that the static solutions for these problems are obtained with the same analysis which provided the dynamic and transient cases. Three special cases are chosen as examples. In the first, a sinusoidally varying shear force is applied at the tip of a cantilever beam. The resonant characteristics of this beam for both the undamped and damped cases are studied. In the second, a step shear loading is applied to a cantilever beam and its damped dynamic history is studied. Finally, a circular plate whose outer edge is simply supported is impacted at its inner edge by a step moment and its damped transient behaviour is determined. The idea of the methods is potentially applicable to dynamic problems in general.
    Additional Material: 8 Ill.
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  • 12
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 135-149 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The assumed stress distribution approach is used to derive the stiffness matrix of a plate-bending element of general polygonal shape having any number of nodes. The effect of assuming various numbers of unknown coefficients in the stress distributions is examined and the convergence properties of the resulting elements compared with others derived form assumed displacements.
    Additional Material: 13 Ill.
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  • 13
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 169-175 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method for obtaining the Green's functions for Laplace's, Poisson's, and the transient heat diffusion equations is presented. The Green's functions thus obtained are then employed to rapidly obtain numerical solutions of the above equations by matrix multiplication, with subsequent considerable savings in machine time.
    Additional Material: 3 Tab.
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  • 14
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 177-180 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The solution of the large numbers of non-linear algebraic equations occurring in analyses of non-linear structural systems using finite differences or finite elements is time consuming even for the fastest computers. This paper presents a method of solution based on a Taylor's expansion technique which is an aid in the solution of such systems of equations.Examples presented show that in the finite element analysis of moderately non-linear structural systems the technique provides sufficiently accurate solutions. For more non-linear systems the technique provides excellent starting values for the Newton-Raphson method.
    Additional Material: 1 Ill.
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  • 15
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 163-167 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Deformation functions which, in addition to satisfying the continuity conditions at nodes. Also satisfy. Approximately, the governing differential equation within the element allow system eigenvalues to be found more accurately, with a given number of elements, than is possible with previously published deformation functions. This is illustrated for the case of beams.
    Additional Material: 2 Ill.
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  • 16
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 201-203 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 17
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 205-221 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a general theory of finite elements. The concept of finite elements is cast in a general topological framework valid for spaces of finite dimension. It is shown that the idea of finite element models can be developed in higher-dimensional spaces, independent of specific co-ordinate systems, for any type of continuous abstract function defined on the space. Generalizations of the familiar Lagrange and Hermite interpolation functions are presented as well as a general statement of the notion of generalized variables and conjugate fields. It is also shown that admissible finite elements can be developed for non-Euclidean spaces of finite dimension. Topological properties of finite element models are examined in Part I of the paper. Part II is devoted to certain applications.
    Additional Material: 4 Ill.
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  • 18
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 224-224 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 19
    Electronic Resource
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 20
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 225-245 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method is presented based on matrix algebra for the dynamic analysis of a mixed rotating and non-rotating vibration system. Such systems occur in practice when turbo-alternator sets are mounted on flexible steel foundations.The mathematical model considered consists of a rotating non-uniform, bi-symmetric shaft connected via three or more flexible-film bearings to a flexible structure throughout which mass is distributed. The shaft, which is assumed to rotate at constant speed, is heavy, flexible and carries several rigid axi-symmetric discs. Viscous damping is assumed to act in all parts of the system and gravitational effects are ignored.
    Additional Material: 8 Ill.
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  • 21
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 181-200 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Surface displacements at the end of a semi-infinite, circular cylinder due to an axisymmetric ring of forces on the end are examined. The solution which has been found may then be used to find surface displacements for general axisymmetric loadings by convolution. The solution, in tabular form, is given as corrections to the counter-part half-space solution.The method of solution involves a three step superposition process. First, the displacement due to a ring of forces on a half-space is found by using the Boussinesq solution. Then, the excess tractions on the half-space, over that of the cylinder, are removed. This is done in two parts. The problem of an infinite cylinder with linearly varying pressure and shear over a short length of the lateral surface is solved by using Fourier integrals. This is used for the removal of the pressure and shear on the lateral surface of the cylinder by convolution. Next, the stresses at the mid-section of the infinite cylinder are removed. This is done by finding a set of boundary conditions for the end which yields zero tractions on the lateral surface. Then a series of these boundary conditions is used to approximate the tractions which must be removed.With the solution thus obtained, two sample problems are shown: 1. an elastic cylinder in contact with a half-space; 2. a rigid punch in contact with an elastic cylinder.
    Additional Material: 10 Ill.
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  • 22
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 247-259 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In Part I of the this paper, topological properties of finite element models of functions defined on spaces of finite dimension were examined. In this part, a number of applications of the general theory are presented. These include the generation of finite element models in the time domain and certain problems in wave propagation, kinetic theory of gases, non-linear partial differential equations, non-linear continuum mechanics, and fluid dynamics.
    Additional Material: 2 Ill.
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  • 23
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 275-277 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Tab.
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  • 24
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 261-274 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A presentation is made of a rectangular plate bending element, the use of which corresponds to the finite difference method. The element stiffness matrix is arrived at by approximation of the strain energy of the element by suitably selected finite difference expressions which contain not only values in respect of the deflection, but also values of its first derivatives. On the basis of the connection found between the two methods, some changes are suggested in the finite difference method, which involve a more realistic way of considering the detailed distribution of the loading. The effect of these modifications is illustrated in two applications.
    Additional Material: 5 Ill.
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  • 25
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 279-299 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: When calculating complex interconnected systems (electrical, power, water supply, gas systems, etc.) by digital computer, a number of common problems arise, connected both with the mathematically correct formulation of the problem under investigation, and with the algorithms of the solution, the programming of which makes it possible to reduce the computing time, the store capacity and the volume of input data required. The present article is devoted to the solution of these problems. The procedure is illustrated by formulating and manipulating the equations relating to complex interconnected mine ventilation networks.
    Additional Material: 2 Ill.
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  • 26
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 27
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 301-310 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Solution of plane elastic problems by piecewise linear approximation is outlined. This method is based upon Galerkin error distribution technique, which leads to simultaneous algebraic equations identical to those associated with the Finite Element Method. In addition, this method permits definition of the discretization error, which can be computed once the displacement components are known. Properties of the interpolation functions are discussed, and a sequence of internally compatible plane elastic elements is defined.
    Additional Material: 1 Ill.
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  • 28
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 311-331 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A review is given of some mathematical programming methods suitable for optimization of structures needing matrix methods for analysis. An application is presented for elastic flat grillages made of straight orthogonal beams normally loaded. Empirical relationships are used to relate beam section properties so that each beam element has only one design variable. Optimization results are obtained by methods of stress-ratio, linear programming-cutting plane and usable-feasible gradient directions. A comparison of the efficiency of these methods is given for the grillage designs which are shown to have non-convex stress constraints and numerous relative optima. Instances are given of non-fully stressed global optima and fully stressed designs which are not local optima for cases with only stress constraints. Discussions include locating the global optima for grillage designs and extensions of the methods presented to other structural design problems.
    Additional Material: 5 Ill.
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  • 29
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 333-349 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a method for reducing the size of a vibration analysis by generating an inertia matrix referred to a limited set of ‘master’ vibrational freedoms. In designing a computer program to perform this mass condensation process, the emphasis has been on providing a two way interface between structural analysis and vibration analysis programs. The transformation from the full set of degrees of freedom to the master set makes extensive vibration calculations economically feasible giving solutions in terms of the amplitudes of the master freedoms. However, by reversing the transformation after completion of a vibration analysis, it is possible to restore the full set of freedoms, allowing automatic plotting of mode shapes in full detail, and re-entry to the structural analysis program for the purpose of computing dynamic stresses.A worked example is given. This is a realistic machine tool structure rather than the simple plates or beams which are usually used for illustration purposes. Natural frequencies and mode shapes, calculated with various degrees of condensation, are compared with those obtained by using all possible freedoms. A comparison is also made with an intuitive selection of ‘lumped masses’.
    Additional Material: 9 Ill.
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  • 30
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 351-378 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The application of non-linear programming methods for the optimum design of statically indeterminate structures is discussed, with special emphasis on the design of elastic grillages loaded laterally and in plane. Some features of SUMT (sequential unconstrained minimization technique) are demonstrated by means of numerous examples of varying complexity. The Variable Metric method of search is discussed and compared to Powell's Direct Method. It is shown that non-convex sets of design variables are often encountered in structural problems of the grillage type. SUMT may still be used, but the choice of starting value and initial response factor decisively influences the chance of finding the global optimum.It is demonstrated that a fully stressed design may not necessarily correspond to the minimum weight design. Optimum design of grillages which are simultaneously subjected to lateral and in-plane loads may be performed efficiently by means of non-linear programming.
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  • 31
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 379-394 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A completely numerical method for steady state linear viscoelastic stress analysis is presented by means of the finite element approach. Numerical representations of the measured viscoelastic constitutive relations are used. This method is developed to obtain steady state solutions to mixed boundary value problems in which the character of the boundary conditions at a point changes with time. Such problems cannot be handled by direct application of the correspondence theorem. A numerical example of viscoelastic sheet rolling is presented along with an experimental verification of the solution by photo-viscoelastic observations.
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  • 32
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 395-395 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 33
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    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 15 (1969), S. 155-156 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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  • 34
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    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 15 (1969), S. 18-24 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Effects of pore diffusion in the catalytic oxidation of ethylene on copper oxide-alumina have been studied by varying the catalyst size and maintaining constant the ratio of the tube to the pellet diameter. Hydrocarbon analysis was determined with a flame ionization detector; infrared analyzers were used to determine carbon monoxide and carbon dioxide concentrations. Other reaction products were analyzed with a gas chromatograph. Curvature of the Arrhenius plots and increase in reaction order with temperature indicated a transition region between kinetic control at lower temperatures and pore diffusion control at higher temperatures. A calculation procedure which was developed to predict the conversion considering pore diffusion effects provided satisfactorily agreement between calculated and experimental results.
    Additional Material: 10 Ill.
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  • 35
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    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 15 (1969), S. 35-39 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The rate of attrition of a catalyst sample, of a single particle size, can be expressed by a simple function of initial diameter and time. The initial rate is a function of initial diameter, whereas the decrease in attrition rate of a catalyst of a given size as it ages depends only on time.The attrition equation for a single size of particles is introduced into the particle size distribution function and, through mathematical analyses, yields a relationship for the attrition of a full size-range catalyst. The form of this relationship, which includes terms for attritability and severity of attrition conditions, is verified by laboratory and commercial attrition data on two full-range catalysts. The size distribution of an attrited sample is not expressible in simple analytical form, but is readily obtained by numerical analysis.
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  • 36
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    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 15 (1969), S. 94-100 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Process design computations are represented by directed graphs whose edges correspond to streams of information flow between computational units. Algorithm I-R extends existing algorithms for finding the minimal sized blocks of units between which no recycle exists. Algorithm II-R orders the sequence of unit computations within a block to minimize the number of recycle parameters. Algorithm III-R uses the concept of indexing to order computations which evade algorithm II-R. This work is directed toward the evolution of efficient programs for computer-aided process design.
    Additional Material: 17 Ill.
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  • 37
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The permeation of carbon dioxide through polyethylene membranes has been studied at pressures up to 54.4 atm. and at temperatures above and below the critical temperature of the gas (31.0°C.). The permeability coefficient is independent of pressure at the highest experimental temperature (61.0°C.), but becomes increasingly pressure-dependent as the temperature is lowered. The principle of corresponding states can be used to correlate the solubility of both gases and vapors in polyethylene over a wide range of temperatures. This principle can also be invoked to obtain an upper limit for the penetrant pressure above which the permeability coefficient becomes pressure-dependent. The effect of pressure on the permeability, solubility, and diffusivity of gases and vapors in polyethylene is discussed in some detail.
    Additional Material: 5 Ill.
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  • 38
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    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 15 (1969), S. 3-3 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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  • 39
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    AIChE Journal 15 (1969), S. 146-149 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 3 Ill.
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  • 40
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    AIChE Journal 15 (1969), S. 214-219 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Differently shaped bubbles were observed growing during nucleate boiling of water at atomspheric pressure. The surface temperature beneath the bubbles was measured simultaneously with a fast response surface thermocouple. The evaporation from the base necessary to account for the observed cooling was calculated. A comparison of the ratio of vapor volume formed at the base to the total volume of the bubble shows a dependency on bubble shape. The ratio is smallest for spherical bubbles, largest for hemispherical and intermediate for oblate bubbles.
    Additional Material: 9 Ill.
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  • 41
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Solubilities and diffusivities of various gases (helium, nitrogen, carbon dioxide, argon, neon, krypton, and monochlorodifluoromethane) in molten or thermally softened polymers (polyethylene, polypropylene, polyisobutylene, polystyrene, and polymethylmethacrylate) have been correlated with structural characteristics, temperature, and pressure. Temperature dependence of both Henry's Law constants and diffusivities were of the Arrhenius equation form. No appreciable effect of pressure was found for either Henry's Law constants or diffusivities up to 300 atm. Earlier correlations for Henry's Law constants in solid polymer systems were found to be inapplicable for molten and thermally softened polymers. New correlations were developed individually for the latter systems. The correlating factor used was the gas Lennard-Jones force constant. Existing correlations for diffusivities were also found not to apply to molten and thermally softened systems. New correlations were again developed on an individual polymer basis. These related diffusivity to gas Lennard-Jones collision diameter or molecular diameter. Generalized correlations were also developed that held for a number of polymers. These were for both Henry's Law constants and diffusivities.
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  • 42
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    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 15 (1969), S. 303-305 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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  • 43
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    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 15 (1969) 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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  • 44
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    AIChE Journal 15 (1969), S. 276-281 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: This paper describes a numerical procedure for optimizing a large set of interconnected systems with respect to a given index of performance. The method automatically constructs the vector differential equation of the complete system from (a) the vector differential equations describing the behavior of the components of the system and (b) the manner of their interconnection. A hill-climbing method is then used to select optimum values of the system's parameters to maximize a given index of performance. An example of the procedure applied to a high order system is included.
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  • 45
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    AIChE Journal 15 (1969), S. 442-449 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: An absolute rate theory based on a plausible model of the activated state, was developed for the interfacial kinetics of crystal growth from the melt. Except for liquid metals the theory predicts the growth rates of pure materials within about an order of magnitude. A microinterferometric technique was employed to observe liquid compositions near the faces of crystals growing from binary melts. For the simple eutectic system composed of salol and thymol, the theory represents the composition and temperature dependence of the growth rate.
    Additional Material: 7 Ill.
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  • 46
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    AIChE Journal 15 (1969), S. 308-311 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 4 Ill.
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  • 47
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    AIChE Journal 15 (1969), S. 327-333 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The laminar boundary layers on a moving continuous flat surface in non-Newtonian fluids characterized by the power law model are investigated using exact and approximate methods. Both pseudoplastic and dilatant fluids are considered. Numerical solutions of the boundary-layer equations are obtained for values of the parameter n in the power law model ranging from 0.1 to 2.0. An integral solution of the momentum equation, which can be used to obtain values of the dimensionless shearing stress that are in good agreement with the exact values, is developed. An integral solution to the energy equation is also presented.
    Additional Material: 8 Ill.
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  • 48
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    AIChE Journal 15 (1969), S. 357-362 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Forced convection heat transfer from vertical cylinders normal to an air-water spray flow stream was measured over an air velocity range from 60 to 140 ft./sec. and a water spray density range from 0.03 to 0.50 lb.m/(min.) (sq. in.). Local heat transfer coefficients were determined at 15 deg. intervals around the circumference of both a 1.5 and a 1.0 in. diam. cylinder. It was found that the addition of 0.426 lb.m/(min.) (sq. in.) of water spray to a 133 ft./sec. air stream raised the stagnation point heat transfer coefficient from 45 to 1,650 B.t.u./(hr.) (sq. ft.) (°F.). Similar intensification was found for other angles around the cylinder circumference; however, the magnitude decreased with increasing distance from the stagnation point. Local heat transfer coefficients were normalized with respect to their corresponding stognation point values and plotted parametrically as a function of angle and air velocity. These profiles showed that the normalized heat transfer coefficients decreased with increasing air velocity at angles other than the stagnation point. Average cylinder heat transfer coefficients were calculated from the air-water data and two correlations were obtained relating these coefficients to the air and the water spray Reynolds number.
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  • 49
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    AIChE Journal 15 (1969), S. 387-392 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A study was made of the radiolytic oxidation of cyclohexane in aqueous solution by using cobalt 60 gamma radiation. In the presence of dissolved oxygen gas the reaction proceeds irreversibly with the formation of a number of oxidation products. Those identified were cyclohexanol, cyclohexanone, and hydrogen peroxide. Trace quantities of carbon dioxide were also detected in the liquid phase. Using a constant dose rate of 15 × 104 rad./hr. in all runs, radiation yields were G(C6H11OH) = 0.49, and G(C6H10O) = 1.08. When molecular oxygen was excluded from the system, neither cyclohexanol nor cyclohexanone was formed on irradiation. A simplified kinetic model based on competition by the various solutes in the system for a single primary radical species produced by radiolysis of the solvent molecules is developed. Results generated using the mathematical model are compared with the experimental data. Excellent agreement between the observed and computed trends is noted at radiation doses up to 50 × 104 rad.
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  • 50
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    AIChE Journal 15 (1969), S. 414-418 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The optimal unsteady control of a jacketed tubular reactor with and without heat generation due to chemical reaction in response to a step disturbance in the feed stream concentration is computed. More rigorous control action was found to be necessary for the case with heat generation than without heat generation. Convergence of the method was also investigated with fixed and free final time.
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  • 51
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    AIChE Journal 15 (1969), S. 434-441 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: An analysis is performed of the strongly coupled heat and mass transfer processes which result from sublimation of mass from the walls of a duct into a flowing gas, the latent heat being provided solely by convective transfer from the gas. The flow is assumed to be laminar and hydrodynamically developed. Results are given for the streamward variations of the bulk and wall temperatures and mass fractions, of the heat and mass transfer rates, and of the local heat transfer coefficient. Representative temperature and mass fraction profiles are also presented. Entrance lengths characterizing the near approach to fully developed conditions are tabulated. Comparisons are made of the present results (based on a parabolic velocity profile) with those based on a slug flow velocity profile. A subsidiary analysis using the Lévěque model is also performed and the results compared with those of the principal solution.
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  • 52
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    AIChE Journal 15 (1969), S. 712-715 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The liquid that moves along the duct walls in the annular regime observed in gas-liquid flows often consists of a series of flow surges (roll waves) moving over a thin liquid film (base film). At a given gas velocity there is a critical flow rate of the liquid below which roll waves are not present. Measurements of the height and wall stress are presented to support the notion that the conditions in the base film are close to those which exist at the critical liquid flow rate.
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  • 53
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    AIChE Journal 15 (1969), S. 727-733 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Data are reported for heat transfer from water to melting ice spheres and for mass transfer in the case of dissolving spheres of pivalic acid suspended in water agitated in a stirred vessel. The transport coefficients are found to depend on agitator power input but not on agitator design, in agreement with the Kolmogoroff theory. These experimental results are used with others in the literature to develop a correlation involving Nusselt and Prandtl or Schmidt numbers together with a dimensionless group involving agitation power. The correlation is essentially independent of solid-liquid density ratio in the range 0.8 to 1.25, and in this range the gravity group also appears to be unimportant.
    Additional Material: 5 Ill.
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  • 54
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    AIChE Journal 15 (1969), S. 592-596 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Heat transfer and pressure drop data were taken on commercial plate heat exchange equipment. Nusselt and Euler correlations were determined for each of the six commercial heat exchangers investigated. These correlations were combined to establish a single heat transfer-pressure drop relationship for any plate type of heat exchanger channel.The results of this investigation were tested by using the correlations developed in Part I of this series to predict pressure drop data for the commercial unit based on their channel geometries. These predicted pressure drops were then used with the results of this part of the series to predict and compare heat transfer data.The correlations developed in this work allow one to determine the heat transfer characteristics in a ribbed rectangular channel from the pressure drop characteristics of the channel in question.
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  • 55
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    AIChE Journal 15 (1969), S. 615-617 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 1 Tab.
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  • 56
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    AIChE Journal 15 (1969), S. 829-836 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A generalized approach to reverse osmosis process design is presented for solution-membrane-operating systems characterized by the dimensionless parameters γ, θ, and λ defined in terms of the pure water permeability constant A, solute transport parameter (DAM/Kδ), mass transfer coefficient k on the high pressure side of the membrane, and the properties of the solution. Analytical expressions are derived, in terms of dimensionless quantities, for the change of volume of solution, concentration of the bulk solution and that of the concentrated boundary solution on the high pressure side of the membrane, the change in the permeating velocity of solvent water through the membrane, solute separation, and the other related quantities, at any instance, as a function of concentration of the product solution on the atmospheric pressure side of the membrane, or time from the start of the operation for reverse osmosis systems specified by γ, θ, and λ. The equations are applicable to membranes for which (DAM/Kδ) is independent of solute concentration and feed flow rate, and for aqueous feed solutions whose molar density can be assumed constant and whose osmatic pressure is proportional to mole fraction. The equations are developed first for the case of batch-by-batch operation, and their applicability to the flow case is then indicated.
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  • 57
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    AIChE Journal 15 (1969), S. 861-865 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The final stages of condensation polymerization are characterized by a rapid rise in molecular weight, as the condensation product is formed and diffuses out of the polymer. The process occurring is one of desorption accompanied by a chemical reaction. The penetration theory equations for a generalized condensation polymerization reaction have been solved and some solutions are presented. The penetration theory solution, obtained by finite-difference computations, is compared with an analytical solution for the special case of no diffusional resistance.
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  • 58
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    AIChE Journal 15 (1969), S. 933-935 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: No Abstracts.
    Additional Material: 5 Ill.
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  • 59
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    AIChE Journal 15 (1969), S. 815-822 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Equations were developed for evaluating the laminar flow behavior of high-solids suspensions from the physical properties of the liquid and solid components. A technique was developed for calculating suspension flow rates as a function of pressure drop. The technique is applicable to the design of pipe lines. Flow measurements were made in pipe-line viscometers of a unique design that minimized entrance and exit effects. Experimental flow data were obtained for suspensions consisting of nickel, alumina, copper, or glass solids in sodium, xylene, or glycerine vehicles with solids concentrations of 28 to 55 vol. %. The basis for the correlation of the data was an analytical investigation of the flow behavior that considered the particle-particle interaction that takes place in a settled suspension. The correlation equations fit all systems investigated. They take into account the effects of liquid viscosity, liquid and solid densities, particle size, size distribution, particle surface area, volume fraction of solids in the suspension, and volume fraction of solids at maximum settled conditions.
    Additional Material: 4 Ill.
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  • 60
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    AIChE Journal 15 (1969), S. 853-860 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A realistic CSTR model was developed and verified experimentally. The reaction studied was the exothermic, base sodium hydroxide catalyzed decomposition of hydrogen peroxide. The model was used to evaluate the usefulness of the following stability analyses: steady state analysis, local linearization and Liapunov's direct method through Krasovskii's theorem. The effect of control valve hysteresis on the system was also investigated.
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  • 61
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    AIChE Journal 15 (1969), S. 866-872 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The local volume average of the equation of motion is taken for an incompressible fluid flowing through a porous structure under conditions such that inertial effects may be neglected. The result has two terms beyond a pressure gradient: g, the force per unit volume which a flowing fluid exerts on a porous structure, and the divergence of the local volume-averaged extra stress tensor (viscous portion of the stress tensor).Constitutive equations for g are examined with the aid of the principle of material indifference. When g is assumed to be a function of the velocity of the fluid relative to the solid as well as various scalars, the usual results for a nonoriented (isotropic) porous structure are obtained. When g is assumed to be a function of the local porosity gradient as well, we derive a new expression for g applicable to oriented (anisotropic) porous structures.For a Newtonian fluid with a constant viscosity, the divergence of the local volume-averaged extra stress tensor is proportional to the Laplacian of the averaged velocity vector. Boundary conditions for the averaged velocity vector are discussed. Three problems are solved for the flow of an incompressible Newtonian fluid in a nonoriented permeable medium. These solutions, as well as an order-of-magnitude analysis, suggest that we may often neglect both the Laplacian of average velocity and the boundary conditions for the tangential components of averaged velocity at an impermeable wall.Two specific constitutive equations for g are proposed for the flow of incompressible Noll simple fluids in nonoriented porous structures. Flow through a porous medium bounded by an impermeable cylindrical surface is solved for these two constitutive equations, and the results are compared with previously available experimental data.
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  • 62
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    AIChE Journal 15 (1969), S. 3-155 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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  • 63
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    AIChE Journal 15 (1969), S. 4-10 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A dye tracer technique was utilized to measure the residence time distribution of the drops in a spray column, operating with a dispersed or a dense packing of drops, for a wide range of flow rates, in a 15 cm.in diameter, 150 to 160 cm. long column proper.For dispersed packing of drops and for flow rates below the onset of coalescence, the flow of the drops was approximately plug flow, with a variance of the residence time distribution of 0.095. For flow rates above the onset of coalescence within the column, the variance increased sharply to 0.55 and decreased at higher flow rates.For dense packing of drops the variance of the residence time distribution was in the range of 0.1 to 0.5. This variance is attributed to the effect of bypassing water and kerosene near the wall of the column. A mathematical model based on this effect showed reasonable fit with the experimental results. This model predicts an approach to plug flow of the drops for large diameter columns.
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  • 64
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    AIChE Journal 15 (1969), S. 57-63 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A sensitivity matrix is defined as a measure of trajectory deviations to small parameter variations of both open and closed loop controlled nonlinear parabolic and first-order hyperbolic systems. In general the parameters may enter through the system equations or the boundary conditions and may be time or spatially dependent. The introduction of a positive measure of the sensitivity, the norm of the sensitivity matrix, into the performance index is shown to be effective in limiting the trajectory deviations due to the parameter variations. The open and closed loop control of a double pipe heat exchanger is analyzed with the open loop problem solved by an approximate procedure. The sensitivity reformulation is successful in reducing trajectory sensitivity, however at the cost of decreased overall performance.
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  • 65
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    AIChE Journal 15 (1969), S. 81-85 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Axial dispersion was studied experimentally for turbulent flow through a 1 1/4-in. piping system containing 90 deg. elbows. The Reynolds number range was 15,400 to 96,555. The imperfect pulse tracer technique was used with the axial dispersion numbers being obtained from the difference in variances of concentration-time curves observed at two points in the system.Elbows interconnected by short lengths of pipe with each succeeding one reversed so as to cause a change in the direction of flow, increased axial dispersion by 35 to 61% over that expected for straight pipe, while the same elbows turned so as to form a helix decreased the dispersion substantially; however, the amount of axial dispersion was still 8 to 22% greater than that observed for straight pipe.The equivalent lengths of the elbows depend upon both their arrangement and the Reynolds number. Closely placed, helically arranged elbows required equivalent lengths of from 2.9 to 5.1 diam., while a reversed arrangement required 6.9 to 11.6 diam. Elbows separated by a developing length and randomly arranged yielded an equivalent length range of 3.6 to 10.6 diam. The geometical l/d ratio of the elbows used was 2.05.
    Additional Material: 7 Ill.
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  • 66
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    AIChE Journal 15 (1969), S. 100-105 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A region into which particles arrive in a random manner, remain a random amount of time, and then leave is considered. This model is used in penetration theories of heat and mass transfer. From observations of the number of particles present at any time, it is desired to estimate arrival and exit statistics, residence time statistics, and average rates of transfer across the region. Assuming arrival is a Poisson process, equations governing the above statistics are derived. Some problems in spectral analysis arising from the use of nondifferentiable stochastic processes are solved. Estimators for important parameters are discussed, and it is shown that generally they are biased. A derivation linking the rate of transfer across the region with the rates of transfer of particles is obtained and compared with other such results.
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  • 67
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    AIChE Journal 15 (1969), S. 126-127 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 3 Ill.
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  • 68
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    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Differential equations were derived to describe the system characterized by a rapid, irreversible reaction of a fluid species in a flowing fluid with a fixed bed of solids in which the reaction rate was controlled by mass transfer of the reacting fluid from the bulk fluid to the reaction site in the solid. Two kinds of mass transfer resistances were assumed, external or film diffusion resistance, and internal pore diffusion resistance. The set of differential equations were solved by a finite-difference method for both the generalized case and for the specific case of reaction of hydrogen in a stream of helium with fixed beds of copper oxide pellets.The hydrogen-copper oxide reaction is one step in a proposed method for removal of hydrogen as a contaminant in the helium coolant of nuclear reactors. This reaction was experimentally investigated in tests with both differential and deep beds of copper oxide in the temperature range of 400 to 600°C., at pressures of 10.2 to 30.0 atm., with gas mass flow rates of 0.0050 to 0.050 g./sq.cm.-sec, and with inlet hydrogen concentrations of 0.0008 to 1.21 vol. %. These tests showed that the system could be described by the two rate-limiting steps: film and pore diffusion of hydrogen. Differential-bed tests were used to establish hydrogen transport properties within the porous copper oxide pellets, and tests with deep beds were used to establish external mass transport properties.Generalized breakthrough curves were determined by a computer solution of the mathematical model. These curves can be the basis for design of fixed-bed copper oxide oxidizers for gas-cooled, nuclear reactor purification systems and for design of any fixed-bed system which follows the assumed reaction mechanism.
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  • 69
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    AIChE Journal 15 (1969), S. 133-135 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 3 Ill.
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  • 70
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    AIChE Journal 15 (1969), S. 136-137 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 2 Ill.
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  • 71
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    AIChE Journal 15 (1969), S. 144-146 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 3 Ill.
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  • 72
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    AIChE Journal 15 (1969) 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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  • 73
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 74
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    AIChE Journal 15 (1969), S. 171-177 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Liapunov's direct method is used to establish a finite region of asymptotic stability for nonlinear systems with an arbitrary number of state variables. The procedure is a geometric one in multidimensional space which uses the Fletcher-Powell minimization technique to find the maximum time derivative of the Liapunov function on the closed Liapunov hypersurface. Three detailed examples are presented, the first being the classical 2-variable CSTR with heat transfer and the third being a 32-variable 16-stage model of an adiabatic tubular reactor with axial diffusion.
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  • 75
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    AIChE Journal 15 (1969), S. 194-199 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A shell progressive kinetic model is used to determine the temperature rise in a spherical pellet for a gas-solid diffusion controlled reaction. The effects of heat and mass transfer resistances in the gas film as well as inside the pellet are investigated. The predicted temperature rise may be severe enough to cause sintering to catalyst pellets in which reactions such as combustion of coke occur.
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  • 76
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    AIChE Journal 15 (1969), S. 220-226 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 4 Ill.
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  • 77
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    AIChE Journal 15 (1969), S. 208-214 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Experiments have been carried out to measure the permeation of tritium-labeled toluene through polyethylene films fully swollen with chlorobenzene, mesitylene, cumene, toluene, ethylbenzene, cyclohexane, tetrahydronaphthalene, and decahydronaphthalene. The results show characteristic Arrhenius temperature dependence over the range 25 to 40°C. The permeation of toluene through the films appears to be enhanced by increased solubility of the swelling agent (estimated from the work of others) in the film and there also appears to be a rough correlation between permeability of toluene and the boiling points and vapor pressures of the swelling agents. The range of permeabilities measured at 25°C. is 2.09 × 10-7 to 0.51 × 10-7 sq.cm./sec., the extremes of measured permeation activation energy, Ep, are 11.41 to 16.68 kcal./mole, and the pre-exponential factor, Po, falls within the interval 36.59 to 1.29 × 105 sq.cm./sec. A very definite linear relationship or compensation effect is evident between Po and Ep. Except as mentioned above, none of these quantities appears to correlate uniformly with the following properties of swelling solvent: molecular weight, dipole moment, specific gravity, vapor pressure, boiling point, heat of vaporization, critical temperature, viscosity, surface tension, molar volume, molecular area or other molecular dimensions.
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  • 78
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    AIChE Journal 15 (1969), S. 245-249 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Oxidation-reduction rates have been determined in stirred liquid-liquid systems wherein tetravalent cerium ions in a continuous aqueous phase were reduced by tetrachlorohydroquinone contained in dispersed organic droplets. Kinetic data obtained (using low volume fractions (〈0.06) of dispersed organic phase) indicate that the rate of reduction of ceric cerium is proportional to the extent of the interfacial area of the stirred liquid-liquid system. Two possible rate-limiting mechanisms are discussed to explain the observed kinetic behavior.This liquid-liquid electron exchange system might find potential use as a chemical tool for measuring changes in interfacial area as influenced by various mixing parameters.
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  • 79
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    AIChE Journal 15 (1969), S. 256-263 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Pressure-temperature data were obtained along isenthalps for nitrogen, methane, and three ternary nitrogen-methane-ethane mixtures. These data were differentiated to obtain Joule-Thomson coefficients over the temperature range from ambient to 200°K. and at pressures from 165 atm. to about 5 atm. Data for nitrogen was obtained down to 140°K.The resulting Joule-Thomson coefficients were compared with predictions based on the Beattie-Bridgeman and Benedict-Webb-Rubin equations of state and on the virial equation of state truncated after the third virial coefficient. These comparisons show that the Benedict-Webb-Rubin equation could predict the data with a deviation averaging 1.7%. The Beattie-Bridgeman predictions were highly dependent upon the mixture rules used, with the best set of mixture rules giving an absolute average deviation of 4.8%. Predictions using the virial equation with virial constants obtained from the Lennard-Jones potential energy function using a geometric mean minimum potential energy deviated from the experimental data by 5%.In all of these comparisons, the virial coefficients of ethane appear to be in greatest uncertainty, and the predictions of mixture data high in ethane least satisfactory. Thus it appears that improved data on the pure components, particularly ethane, are vital to any satisfactory evaluation of mixture properties.
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  • 80
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    AIChE Journal 15 (1969), S. 281-288 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The effects of ultrasonic vibrations on heat transfer to water and methanol by natural convection and by boiling were measured at three ultrasonic energy levels with frequency ranging from 20.6 to 306 kcycles/sec., using electrically heated platinum wires of diameters 0.007 and 0.010 in. Up to an eight-fold increase in heat transfer coefficient was obtained in natural convection, but the effects diminished with increased temperature difference and became negligible in the well-developed nucleate boiling region. High-speed photographs showed that the increase was due to the motion of cavitation bubbles on the wire surface. The heat transfer results were correlated by local cavitation activity values measured by a technique developed for this work.
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  • 81
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    AIChE Journal 15 (1969), S. 301-303 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 3 Ill.
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  • 82
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    AIChE Journal 15 (1969), S. 475-476 
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    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 83
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    AIChE Journal 15 (1969), S. 323-327 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A laser doppler flowmeter is used to obtain velocity profiles in circular glass tubes downstream from a plug composed of brass screens. The apparatus for measuring point velocities of particles suspended in a fluid is described. Measurements were made very close to the plug at Reynolds numbers of 16.5, 47, and 274, and the flow development followed down the tube. The results show that the entrance flow development is dependent on the inlet profile shape and the Reynolds number for Reynolds numbers below 300.The flow development at Reynolds numbers less than 300 was considerably slower than that predicted by the boundary-layer solution of the equations of motion starting with a flat profile.
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  • 84
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    AIChE Journal 15 (1969), S. 339-350 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: When a porous solid is penetrated by a reactive fluid which changes the pore geometry, the macroscopic properties of that porous material may be greatly changed. A model is proposed in which the matrix is visualized as being a number of short cylindrical pores dispersed randomly throughout the solid. The change in the distribution of these cylindrical pores is then represented by a integrodifferential equation which is solved for two special cases.The evolution of the pore size distribution is determined by the particular way in which the solid-liquid boundary takes place. The case considered here is that of a surface reaction which dissolves the solid thus continuously enlarging the pores. The rate of reaction is calculated theoretically using a laminar flow diffusion model and this growth rate expression is then taken as the basis for numerical calculations relating to the action of dilute hydrochloric acid on limestone.A comparison is made with experimental results and it is found that the model behaves in much the same way as the real system although the observed rate of pore growth was two to three times that predicted by the diffusion model. Several possible explanations for this discrepancy are being tested.An exact solution of the integrodifferential equation for highly retarded reaction rates has been found with the change in permeability being given in terms of the change in porosity. This result will permit a prediction of the stimulation that can be achieved in acidizing oil wells with retarded acids.
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  • 85
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    AIChE Journal 15 (1969), S. 379-383 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The stability of high speed laminar Newtonian jets is studied as a function of ambient air pressure. For Weber numbers less than 5.3 (based on air density) air pressure has no effect on stability. Ambient viscosity, through the effect of shear stresses acting on the jet surface, gives rise to the maximum in the breakup curve. For large Weber numbers ambient pressure effects can alter, and eventually control, the appearance of the maximum.
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  • 86
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    AIChE Journal 15 (1969), S. 393-400 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The gradient technique and Lagrange multiplier are used to obtain the optimum of complex chemical plants. The advantage of this approach is its ability to handle nearly all types of complex stages in a natural way. This approach is used to solve a heterogeneous complex chemical process with recycle. It is shown that although there are many different iteration loops, the convergence rate is fast even with rough starting values and only 0.3 minute is needed to obtain the optimum operating conditions.
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  • 87
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    AIChE Journal 15 (1969), S. 410-414 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The necessary conditions for optimization of a system governed by a nonlinear vector first-order partial differential equation with two (space and time) independent variables, such as governs the unsteady behavior of tubular flow reactors, are derived. Rather general objective functionals and boundary conditions, such as the recycle of unconverted reactant with an appropriate time delay for separation and a free choice of final time, are allowed. A gradient technique in control space is formulated, and it is shown that distinct computational advantages can accrue from the use of the method of characteristics.
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  • 88
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    AIChE Journal 15 (1969), S. 426-434 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: An analysis based on the Townsend-Bakewell model of the eddies in the wall regions of turbulent shear flows shows that viscoelastic fluid properties must lead to significant reductions in the rate of production of turbulent energy. This analysis in turn leads to the proper form of the similarity laws for drag reducing fluids, heretofore deduced empirically.Measurements of the axial and radial turbulence intensities for flow through smooth round tubes are reported, as are measurements of the time-averaged velocity profiles and the drag coefficients. These indicate that for solutions exhibiting drag reduction at all Reynolds numbers the flow may be transitional to Reynolds numbers of the order of 105. This transitional flow consists of alternating patches of laminar and turbulent fluid, within each of which the flow characteristics are approximately similar to those of Newtonian fluids. At high Reynolds number conditions with the turbulent field fully developed the velocity profile in the core is flatter under drag-reducing conditions than for turbulent Newtonian fluids, a change dependent on the increased isotropy of the turbulent field of the drag-reducing fluid. These effects appear to be a result of increases in the time scales of the radial fluctuations caused by the fluid properties.Design calculations based upon the present results suggest that in large diameter pipelines, or in boundary layers on large objects, drag reduction may not be attainable under conditions of practical interest until fluids having relaxation times an order of magnitude larger than those presently available, but with comparable viscosity levels, are developed or, alternately, until fluids exhibiting Weissenberg numbers which do not change with deformation rate, can be found.
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  • 89
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    AIChE Journal 15 (1969), S. 460-460 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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  • 90
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    AIChE Journal 15 (1969), S. 482-636 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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  • 91
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    AIChE Journal 15 (1969), S. 483-489 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: This study concerns rates of evaporation and mass transfer of water vapor from a heated salt solution through a water repellent porous membrane to a cooled water condensate. This transfer is a result of temperature differences and corresponding vapor pressure differences across the membrane. Three groups of experiments were carried out which indicate that the major factor influencing the rates of transfer is diffusion through a stagnant gas in the membrane pores. However, an equation considering film heat transfer coefficients, membrane thermal conductivity, and an empiricial correction based on temperature driving force appears to be necessary for representing all the data. The empirical correction appears to be related to internal condensation and possibly diffusion along surfaces.
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  • 92
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    AIChE Journal 15 (1969), S. 515-520 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Experimental results for the adsorption of the binary gas mixtures oxygen-nitrogen, oxygen-carbon monoxide and nitrogen-carbon monoxide on two synthetic zeolites are reported. In all of these experiments the temperature was -200°F. and the total pressure was 1 atm. Also reported are the isotherms for the three pure gases on the two zeolites at -200°F. The results indicate that these zeolites have a surface selectivity which is independent of any sieving effect based on the size of the adsorbed molecules. It does not appear that the strong separations obtained can be explained in terms of the van der Waals forces which are generally believed to be dominant in physical adsorption. The available methods of predicting binary adsorption data from the pure gas isotherms have been examined.
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  • 93
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    AIChE Journal 15 (1969), S. 533-547 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The effects of a trace quantity of a surface-active agent on creeping flow past a bubble or droplet are investigated. The equations describing mass and momentum transfer are simultaneously solved by a perturbation technique, consistent with the jump mass and momentum balances at the phase interface. The stream function for the velocity distribution is evaluated as an infinite series of spherical harmonics. Galerkin's method, which reduces the partial differential equation of continuity to a set of ordinary differential equations, is used to evaluate the concentration distribution of surfactant.A sample calculation is carried out for relative motion between an air bubble and an infinite body of water which contains a trace of isoamyl alcohol. The relative velocity of the water at an infinite distance from the bubble is found to be highly sensitive to small changes in surfactant concentration from zero, although the bubble varies imperceptibly from a spherical shape.
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  • 94
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    AIChE Journal 15 (1969), S. 560-564 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Partial removal of dissolved or absorbed solvent from polymers can be accomplished during the process of screw extrusion. This paper shows how two simple transport models based either on an effective diffusivity or on an empirical mass transfer coefficient can be combined with the fluid mechanical equations which describe polymer flow during screw extrusion. In this way, the drying of solvent from a polymer during extrusion can be correlated in terms of the design and operating parameters of the extruder screw and a mass-transfer coefficient or an effective diffusivity. This approach is illustrated employing data obtained by using two extruders of different size and two different solvent-polymer systems. Furthermore, it is pointed out how the results can be used to predict the extent of drying during screw extrusion as well as how modifications in extruder-screw design can permit more extensive drying of polymers during the extrusion process.
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  • 95
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    AIChE Journal 15 (1969), S. 585-592 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Plexiglas models of rectangular channels were fabricated with various rib shapes to determine the effects of rib and channel geometry on the pressure drop. Pressure drops in twenty-four individual variations of channel geometry were investigated using plexiglas models.From this investigation, an empirical correlation for the pressure drop across the ribbed section of the channel was determined as a function of the linear fluid velocity and the geometric characteristics of the channels. This empirical correlation involves functions of seven geometric parameters of rib pattern and channel geometry.Ribbed section pressure drops for commercial plate heat exchanger channels were predicted using the geometric characteristics of the commercial plates with the empirical correlations developed from the plexiglas channel studies. The total pressure drop for commercial channels was predicted by adding an average entrance and exit pressure drop to the predicted ribbed section pressure drop.The correlations developed in this work allow one to determine the pressure drop in a ribbed rectangular channel from the geometric characteristics of the ribs and the channel in question.
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    AIChE Journal 15 (1969), S. 612-614 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 3 Ill.
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    AIChE Journal 15 (1969), S. 624-624 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
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    AIChE Journal 15 (1969), S. 631-634 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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    AIChE Journal 15 (1969), S. 643-653 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Shear stress and first normal stress difference data are presented for several polymer solutions undergoing steady shear rates from 1.0 to 100,000 sec.-1. The steady shear response is divided into three regions as a function of increasing shear rate. These are the diffusion controlled linear region, a moderate shear rate region where shear controls the entanglement-disentanglement process, and a high shear rate region where aggregation of polymer molecules occurs. The transitions between the three regions are clearly illustrated by using a group designated as the rotation rate function.A molecular model is derived for the shear controlled region that allows prediction of the first normal stress difference from the viscosity function and one additional constant that depends only on the molecular species. The White-Metzner equation is found to adequately describe the aggregation region at high shear rates.
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    AIChE Journal 15 (1969), S. 670-679 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Steady state multiplicity in an adiabatic loop reactor was studied in experiments employing the reaction between sodium thiosulfate and hydrogen peroxide in aqueous solution. The steady state characteristics of the loop reactor were predicted by a method which utilized batch reactor data of temperature vs. time directly. The method was based on the assumption of plug flow with negligible axial dispersion and on a single-step chemical kinetic model. Experimental results verify the existence of multiple steady states on ranges of feed flow rates and recycle ratios and demonstrate the capability of the simple model for predicting the qualitative and quantitative features of the reactor steady state.Some observations were made of the effect of large disturbances on the stability of the reactor while operating in a multiple state region. Results for such cases illustrate reactor instability in the sense that a transition to a new steady state takes place provided the disturbance is sufficiently large.
    Additional Material: 14 Ill.
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