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  • Chemical Engineering  (1,448)
  • Engineering  (32)
  • Theoretical, Physical and Computational Chemistry
  • Wiley-Blackwell  (1,480)
  • 1965-1969  (1,480)
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  • Wiley-Blackwell  (1,480)
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  • 1
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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
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  • 2
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    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.
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  • 3
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    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
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  • 4
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    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.
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  • 5
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    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.
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  • 6
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    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.
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  • 7
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    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.
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  • 8
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    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.
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  • 9
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    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.
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  • 10
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    International Journal for Numerical Methods in Engineering 1 (1969) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
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  • 11
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    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.
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  • 12
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    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.
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  • 13
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    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.
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  • 14
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    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.
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  • 15
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    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.
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  • 16
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    International Journal for Numerical Methods in Engineering 1 (1969), S. 201-203 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
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  • 17
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    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.
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  • 18
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    International Journal for Numerical Methods in Engineering 1 (1969), S. 224-224 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
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  • 19
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    International Journal for Numerical Methods in Engineering 1 (1969) 
    ISSN: 0029-5981
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    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.
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  • 21
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    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.
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  • 22
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    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.
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    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
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  • 24
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    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.
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    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.
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    International Journal for Numerical Methods in Engineering 1 (1969) 
    ISSN: 0029-5981
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    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.
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    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.
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    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’.
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    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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    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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    International Journal for Numerical Methods in Engineering 1 (1969), S. 395-395 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
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    AIChE Journal 13 (1967), S. 1196-1202 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Two-phase, gas-liquid concurrent flow in packed beds was investigated with the use of an air-water system and 2-, 4-, and 6-in. diameter columns packed with tabular alumina particles of 0.025 and 0.027 ft. diameters. Total pressure drop, column operating pressure, and liquid saturation were measured as functions of gas flow rate, fluid temperatures, and flow direction at several constant liquid flow rates for each column.Correlation of the frictional pressure loss was achieved in terms of a defined two-phase friction factor and a second correlating parameter which is a function of the liquid and gas Reynolds numbers. A viscosity correction factor was required to extend the friction factor correlation to include liquid viscosities widely divergent from that of water.The liquid saturation data for both upward and downward flow were correlated in terms of the ratio of mass flow rates of the respective phases.
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    AIChE Journal 14 (1968), S. 37-45 
    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 illustrates the synthesis of nonlinear feedforward controllers for chemical reactors. In most of the theoretical development and application of feedforward control only linear systems have been considered. There are, however, no inherent linear limitations in feedforward control. Since chemical reactors are usually nonlinear, the effectiveness of control should be improved by including nonlinearities in the design of feedforward controllers. This is particularly true for batch reactors because of the large changes in variables during a batch cycle. Continuous stirred-tank reactors are studied with single and consecutive reactions of first and higher order. Effectiveness of linear and nonlinear feedforward controllers is compared for disturbances of various magnitude and direction. Feedforward control of batch and tubular reactors is also discussed.
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    AIChE Journal 14 (1968), S. 57-61 
    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 effect of standing waves of controlled amplitude and frequency on the steady state rate of mass transfer through thin horizontal liquid layers is studied experimentally. The variables studied are the film thickness, the amplitude and frequency of the waves, and the spacing between the probes generating the waves. A bulk motion of complicated pattern known as drift is caused by the finite amplitude of the waves. The rate of mass transfer in the absence of imposed vibration is two to three times greater than that expected by molecular diffusion alone. Vibration increases the rate up to an order of magnitude or more, depending on the hydrodynamic conditions. The data at low frequencies are correlated by an expression of the form (i-io)/idiff = KAf3/4h1/2L-1/2.
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    AIChE Journal 14 (1968), S. 85-91 
    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 general method has been developed for controlling deterministic systems described by linear or linearized dynamics. The discrete problem has been treated in detail. Step-by-step optimal controls for a quadratic performance index have been derived. The method accommodates upper and lower limits on the components of the control vector.A small binary distillation unit was considered as a typical application of the method. The control vector was made up of feed rate, reflux ratio, and reboiler heat load. Control to a desired state and about a load upset was effected.Calculations are performed quite rapidly and only grow significantly with an increase in the dimension of the control vector. Extension to much larger distillation units with the same controls thus seems practical.
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    AIChE Journal 13 (1967), S. 311-315 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
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    Notes: A previous paper introduced the pair-type-probability (PTP) function for use in molecular corresponding states theory. The present paper develops the predictive equations of Scatchard and Hildebrand and the correlation equations of Wohl from particular pair and triplet weighting functions for clusters of two and three molecules in a liquid mixture. The cluster-weighting idea therefore unifies the major prediction and correlation schemes now in engineering use.
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    AIChE Journal 13 (1967), S. 303-311 
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    Notes: There are four points of flexibility in present molecular formulations of the corresponding states idea. At these points the procedure followed or the numerical values can be tailored to achieve better agreement between predicted and experimental properties without violation of physical principles. These flexibilities are the exponent values used in the pair-potential function, the averaging procedure used to obtain an effective mixture pair-potential function, the combination rule for unlike-pair parameters, and the selection of a reference substance. The first two flexibilities are used in this paper to show that the conformal-parameter equations can correlate excess free energy and activity coefficient data of highly nonideal liquid mixtures. A pair-type-probability function is introduced in the averaging procedure used to obtain a mixture pair-potential function. Any macroscopic or molecular property may be used in this weighting function to improve mixture-property prediction.
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    AIChE Journal 13 (1967), S. 316-318 
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    Keywords: Chemistry ; Chemical Engineering
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    Notes: The observation that large bubbles entrained in accelerating viscoelastic fluids may suddenly stop and remain stationary for long periods of time, although imbedded in a region of high fluid velocities, is noted and described. An analysis of this phenomenon, termed the Uebler effect, shows that it may be expected to occur with all particulate matter provided that the continuum field fluid is accelerating sufficiently rapidly to generate high stresses as a result of fluid stretching, and provided these stresses change sufficiently rapidly in the direction of the velocity vector in the flow field.
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    AIChE Journal 13 (1967), S. 319-326 
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    Notes: For a number of polymerization models, we have developed equations that enable one to follow in time the moments of the polymer size distribution and the conversion. The exact and approximate solutions for the leading moments of the size distribution are presented for polymerization with initiation, propagation, and termination by combination. Approximate solutions for polymerizations with the additions of termination by disproportionation, chain transfer to monomer, and chain transfer to solvent show how these reactions decrease the average polymer size. From a simple model that exhibits autoacceleration a concomitant increase in the average polymer size also occurs.
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    AIChE Journal 14 (1968), S. 235-241 
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    Keywords: Chemistry ; Chemical Engineering
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    Notes: The extraction of lanthanum and barium from single falling drops of the uranium-chromium eutectic into magnesium was studied at 1,000°C. Because of the short contact times involved, the data best fit the stagnant diffusion model for lanthanum. For barium, the fraction extracted was governed by external resistance of the magnesium phase. Drop velocities were adequately represented by the Hu-Kintner correlation.
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    AIChE Journal 14 (1968), S. 260-265 
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    Notes: The external velocity field associated with the fall of a single drop through a quiescent liquid phase is discussed. The field responsible for the transfer of vorticity from the point of generation to the disperse phase is assumed to be almost identical with the field that transfers mass from the drop interface. The stream surfaces associated with this field are made visible by means of dye trails. Since the field is not amenable to mathematical formulation, and since many reports appear in the literature concerning correlations between measurable flow parameters and the physical properties of the system, the field configurations relative to mass transfer mechanisms are considered qualitatively. The delineation of the flow patterns behind the drop gives some indication of the manner in which the external flow contributes to the transfer coefficients.
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    AIChE Journal 14 (1968), S. 275-279 
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    Keywords: Chemistry ; Chemical Engineering
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    Notes: This paper presents an investigation of the equations of motion to find the conditions under which these equations admit exact viscometric solutions for certain unsteady torsional flows of incompressible simple fluids. In general, for the cone and plane and the parallel disk geometries, curvilineal solutions do not exist for arbitrary members of the class of simple fluids; however, if the inertia terms can be neglected in the equations of motion, curvilineal solutions can be found for the complete class of simple fluids.
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    AIChE Journal 14 (1968), S. 301-310 
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    Keywords: Chemistry ; Chemical Engineering
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    Notes: This paper presents a theoretical study of the stability of chemical reaction on the external surface of a single spherical particle in stagnant surroundings. The analysis, which invokes methods of linear stability theory, yields necessary and sufficient conditions for stability of a steady state solution to small disturbances for the cases of very small and very large solid thermal conductivity. It is shown that heat losses from the solid surface may lead to transient behavior which is characteristically different from that for adiabatic surfaces, and that the unsteady state is strongly affected by the thermal capacity of the solid material. A numerical example is employed to illustrate the possible significance of unstable situations.
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    AIChE Journal 14 (1968), S. 311-317 
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    Notes: A comparison of the kinetic and diffusional models for solid-gas reactions occurring in a spherical particle is presented. The similarities and differences of the unreacted-core shrinking model and the homogeneous model are examined in light of the rate-controlling factors. In view of the similarity of the two models, it is shown that erroneous conclusions in regard to the mechanism and the activation energies may be drawn from an analysis of the experimental data. A more versatile model is presented in order to augment the two models so that wider varieties of solid-gas reaction systems may be treated. The concept of effectiveness factors in solid-gas reactions is introduced, and the influence of diffusion is ascertained.
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    AIChE Journal 14 (1968), S. 350-351 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
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    AIChE Journal 14 (1968), S. 356-356 
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    AIChE Journal 14 (1968), S. 368-368 
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    AIChE Journal 14 (1968), S. 371-371 
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    AIChE Journal 14 (1968), S. 523-525 
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    Keywords: Chemistry ; Chemical Engineering
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    AIChE Journal 14 (1968), S. 370-526 
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    AIChE Journal 14 (1968), S. 295-300 
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    Keywords: Chemistry ; Chemical Engineering
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    Notes: In a previous paper, an analogy was presented which related the rise velocity of bubbles in liquids of infinite extent to the velocity of surface waves over infinitly deep liquids. In the present paper, a corresponding analogy is found which relates bubble velocities in bounded liquids to wave velocities over liquids of finite depth.
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    AIChE Journal 14 (1968), S. 392-397 
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    Keywords: Chemistry ; Chemical Engineering
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    Notes: In gas-metal permeation, diffusion is normally considered to be the rate-controlling step. In addition, the diffusivity is usually taken to be independent of concentration. Under these conditions, the time lag (a characteristic of the system which depends on the time required to achieve steady state flow) is found to be (and theoretically should be) independent of the gas pressure applied to the inlet surface of the metal membrane. Furthermore, the time lag can then be directly related to the diffusivity of the system.In this paper, data on the hydrogen type 321 stainless steel system are presented which show a pronounced effect of pressure on measured values of the time lag. Taken alone, these data can be explained either by a concentration-dependent diffusivity or by resistance to flow at the metal surface. From steady state data it is shown that surface resistance is the better explanation. A model of the permeation process is presented which is consistent with the time lag data, and an estimate is made of the diffusivity of hydrogen in type 321 stainless steel.The variables studied were hydrogen pressure at the entrance surface of the membrane (0.1 to 30.0 atm.), temperature (300° to 800°C.), and membrane wall thickness (0.0252 to 0.2475 cm.).
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    AIChE Journal 14 (1968), S. 415-420 
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    Notes: A packed bed model has been adopted to develop a general correlation applicable to the flow of Newtonian fluids through all types of woven metal screens. Both of the main theoretical approaches to studying pressure drop in packed systems have been used by visualizing the screen as a collection of submerged objects with surface area to unit volume ratio a for laminar flow, and as a bundle of tubes of diameter D for turbulent flow. In the usual manner viscous and inertial energy losses are added to give an expression for the total pressure loss. Rearrangement of the general equation to the form of a friction factor yields a unique definition of the Reynolds number for screens NRe = ρu/μa2D. Procedures are described for collection of pressure drop-velocity data for the flow of nitrogen and helium through plain square, full twill, fourdrinier, plain dutch, and twilled dutch weaves. The data are used to derive a viscous resistance coefficient α = 8.61 and an inertial resistance coefficient β = 0.52. The validity of the correlation equation is tested by using additional data from the literature. The correlation successfully predicts pressure drop for a Reynolds number range of 0.1 to 1,000, void fractions from 0.35 to 0.76, screen pore diameters from 5 to 550 μ, mesh sizes from 30 to 2,400 wires/in., and surface area to unit volume ratios from 1,200 to 29,000 ft.-1.
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    AIChE Journal 14 (1968), S. 352-352 
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    Keywords: Chemistry ; Chemical Engineering
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    AIChE Journal 14 (1968), S. 357-357 
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    AIChE Journal 14 (1968), S. 363-363 
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    AIChE Journal 13 (1967), S. 395-396 
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    Keywords: Chemistry ; Chemical Engineering
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    AIChE Journal 14 (1968), S. 372-379 
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    Notes: Pool nucleate boiling heat transfer curves for pure nitrogen, oxygen, argon, methane, and carbon tetrafluoride have been measured on a horizontal, flat, circular, platinum plated disk for saturation pressures ranging from 1 atm. or less to the immediate vicinity of the critical pressure for each liquid. The results have been compared with various suggested nucleate boiling correlations, and the correlations of McNelly, of Kutateladze, and of Borishanskiy-Minchenko are found to be roughly equally successful and all distinctly superior to those of Rohsenow, of Gilmour, and of Forster and his collaborators for these liquids. For oxygen, argon, methane, and carbon tetrafluoride, boiling hysteresis of a type not previously reported was observed at intermediate and high saturation pressures on this surface.
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    AIChE Journal 14 (1968), S. 388-391 
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    Notes: The movement of solids associated with the rise of a single gas bubble in an incipiently fluidized bed has been determined. The bulk volume, measured at the porosity of incipient fluidization, of tracer solid which is transported across the original interface between undyed glass spheres in the upper region and dyed glass spheres (tracer solid) in the lower region, is approximately 30% of the bubble volume. The measurements relate to bubble volumes from 14 to 200 ml. in a glass column, 4 in. diam. Solids used were glass spheres of diameter 380 μ. The profile created when a bubble rises through a layer of fluidized tracer solids into the fluidized solids above the tracer layer has been approximately determined. The distance by which the solids were displaced upward, due to the passage of the bubble, was found to be greater than would have been the case if the behavior were that of a sphere in an inviscid liquid.
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    AIChE Journal 14 (1968), S. 411-414 
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    Notes: The profile of a growing droplet was determined with a pressure balance which was similar to that derived by Laplace for the static droplet. An additional term was added to the balance to account for the pressure on the interface due to the motion of the fluid within the droplet. The entire pressure balance was then combined with differential equations describing the geometry of the droplet. Computed profiles compared favorably with those obtained experimentally.An additional result was the definition of a parameter, f, indicating the importance of internal fluid motion on the shape of the profile. A method of estimating this parameter without solving the equations was developed.
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    AIChE Journal 14 (1968), S. 426-434 
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    Notes: A Bench-scale size fluidization system was constructed for the purpose of conducting experiments to determine density and pressure fluctuations in gas fluidized beds. Density fluctuations and bubble sizes were measured with a photocell device and β-ray absorption. Pressure fluctuations were determined with a conductivity cell. The frequency distributions of the density and pressure fluctuations and bubble sizes were determined as functions of several variables. They could be described by dimensionless coefficients and X2-distributions with different degrees of freedom. Such variables as distance from the gas distribution plate, bed height, particle size, gas flow rate, and internal screens were considered.
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    AIChE Journal 14 (1968), S. 421-425 
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    Notes: Dialysis of binary aqueous solutions of several sugars through a cellophane membrane was studied in a stirred batch dialyzer. Sherwood numbers describing mass transfer resistance in the fluid adjacent to the membrane were determined as a function of the corresponding Reynolds and Schmidt numbers. The results establish a reproducible environment for membrane testing in which a known controllable and small interfacial resistance is placed in series with that of the membrane. The results are also shown to support, for this geometry, the postulation of a third power relationship between eddy diffusivity and dimensionless distance from the phase boundary as well as the Sherwood-Ryan nondimensionalization of this distance.
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    AIChE Journal 14 (1968), S. 458-467 
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    Notes: A method is developed for predicting rates of gas absorption into laminar rippling films in terms of the surface velocities. The description is an extension of the surface-stretch model of mass transfer (1) and is therefore useful for cases of high Peclet number. The description can be used with any of the presently known hydrodynamic models of rippling films and with any future models which may be developed, provided they satisfy two relatively nonrestrictive conditions: (1) the ripples are of a two dimensional nature, being of constant thickness in the direction normal to their direction of propagation, and having no velocity components in this transverse direction; and (2) the ripples propagate at constant celerity and with constant shape. It can be used for both traveling and standing waves and can be extended to describe the effects of high net-mass transfer rates and combined diffusion and chemical reaction.
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    AIChE Journal 14 (1968), S. 473-479 
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    Notes: Experimental data and a mathematical model for the dehydrogenation of cyclohexane on a platinum-on-alumina catalyst in the presence of excess hydrogen are presented. Differential rate data were obtained by using a fixed bed flow reactor over a temperature range of 400° to 500°C., and a pressure range of 21.3 to 41.8 atm. at modified Reynold's numbers of 20 to 65. Cyclohexane concentration was varied from 16 to 25 mole %. In the development of the basic model, complete transport control of the overall reaction rate with equilibrium at the fluid external surface interface is assumed. The average deviation between experimentally determined and basic model calculated rates was 5.65%.Modification of the model by replacing the equilibrium assumption by a crude surface rate expression resulted in a reduction in average deviation to 4.3% and the maximum deviation was reduced from 22 to 12%.
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    AIChE Journal 14 (1968), S. 490-496 
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    Notes: A finite difference method combined with the quasilinearization technique is used to solve the nonlinear two-point boundary value problems. This method does not have the stability problem connected with the marching integration techniques. A scheme which can be used to reduce the rapid access memory requirements of digital computers is also proposed. The steady state equations resulting from mass and energy balances in a tubular reactor with axial diffusion are solved by this method. With very poor initial approximations, only three to seven iterations are needed to obtain the correct answer.
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    AIChE Journal 13 (1967), S. 438-442 
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    Notes: In a high-pressure process, feed streams are continually pressurized and product streams are continually depressurized. A flow work exchanger offers an efficient and economical scheme for simultaneously pressurizing a fluid stream and depressurizing a substantially equivalent volume of another fluid stream. Its applicability is however limited to fluids under condensed state. A flow work exchanger uses a displacement vessel to form a closed loop with a processing system. The displacement vessel is alternately filled by a low-pressure feed and a high-pressure product, both pressurized and depressurized, respectively, by substantially nonflow processes. The pressurized feed is pushed into the processing system by the high-pressure product stream and the depressurized product stream is pushed out of the displacement vessel by the low-pressure feed stream. The application of a flow work exchanger is illustrated by means of several high-pressure processes and the direct and indirect advantages obtainable are described.
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    AIChE Journal 13 (1967), S. 443-449 
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    Notes: Local and average holdup and drop size distribution as function of flow rates were measured for kerosene drops and water in a countercurrent, 15-cm. I.D., 160-cm. long, spray column. The range of flow rates was 5 to 40 liters/min. of kerosene and 0 to 50 liters/min. of water. At the same pairs of flow rates of the dispersed and the continuous phases in spray columns, three modes of drop packings can be obtained. These are termed, in order of increasing average holdup and increasing regularity of flow patterns, dispersed, restrained, and dense packings. For dispersed packing, at low flow rates of the two phases, the holdup and the drop size are constant along the column. At high flow rates the drop size increases from bottom to top of the column and the holdup increases from top to bottom of the column. The range of flow rates for the operation of a spray column is extended by the use of a conical entry section (Elgin design) at the bottom of the column, by the formation of an equilibrium region in the conical section.The average holdup increases with increased flow rates of both phases for dispersed and restrained packings, and with decreased flow rates of both phases for dense packing.The best definitions of flooding in a spray column are either the point of maximum average specific area of the drops, which corresponds to the onset of coalescence in the column, or the start of rejection of drops from the column proper.
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    AIChE Journal 13 (1967), S. 449-452 
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    Keywords: Chemistry ; Chemical Engineering
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    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: An analytic solution of the Nernst-Planck equations is derived which applies to a selective resin when film diffusion controls. The selectivity has a marked effect on the rate of exchange for a wide range of diffusivities. The unit-selectivity solution of Schlögl and Helfferich is included as a special case of the more general solution.
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    AIChE Journal 13 (1967), S. 453-456 
    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 are presented which indicate that the application of a fixed intensity of ultrasonic waves to a water-tetrachloride solution containing dissolved air provides yields of chlorine varying from zero to maximum simply as a function of the liquid height in the capillary above the transducer. The difference in heights of the liquid between zero and maximum yields is found to be equal to one-quarter the wavelength of the ultrasonic wave in the liquid. A mathematical model to explain this phenomenon is presented.
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    AIChE Journal 13 (1967), S. 457-465 
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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: Removal of methane from a helium stream by adsorption on Columbia SXC activated carbon was studied experimentally and theoretically. A mathematical model for the process was developed and the governing differential equations were solved numerically. The model incorporates heat and mass transfer resistances within and around the adsorption particle. Wall effects and moderate heat loss to the surroundings are also included. The required heat and mass transfer correlations were obtained from the literature. Simple expressions were developed to determine the relative resistances for heat and mass transfer within and around the adsorption particles.
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    AIChE Journal 13 (1967), S. 465-475 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
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    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Frequency response methods were used to compare dynamic models for gas mixing and first-order reaction in a fluidized-bed reactor and for the experimental determination of interphase transfer characteristics. Theoretical predictions of frequency response characteristics were derived for two models based on the two-phase theory of fluidization. Experimental frequency response for a 1-ft. high bed were correlated better by a model based on perfect mixing in the dense phase than by a model based on plug flow in the dense phase. Excellent correlation was also obtained by a simple empirical model.
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    AIChE Journal 14 (1968), S. 650-650 
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    Keywords: Chemistry ; Chemical Engineering
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    AIChE Journal 14 (1968), S. 658-659 
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    Keywords: Chemistry ; Chemical Engineering
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    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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    AIChE Journal 14 (1968), S. 661-662 
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    AIChE Journal 14 (1968), S. 666-667 
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    AIChE Journal 14 (1968), S. 671-673 
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    Keywords: Chemistry ; Chemical Engineering
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    AIChE Journal 14 (1968), S. 673-673 
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    AIChE Journal 14 (1968) 
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    Notes: Various modifications of the Prandtl mixing-length model for turbulent momentum transport in pipes and between parallel plane walls are discussed. The most complete modification, due to Gill and Scher, is improved by replacing one of their two empirical constants by a theoretically calculable parameter. The new theory is compared with experimental data from the literature and found to reproduce frictional resistance data accurately for all values of the Reynolds number. It is somewhat in error for velocity profiles at high Reynolds numbers, but accurately reproduces velocity profile data in the transition region. The new theory represents the first accurate semi-theoretical calculation of frictional resistance coefficients for all regimes of flow (laminar, transitional, and turbulent) for both pipes and parallel plane ducts, and of velocity profiles in the transitional flow regime in either geometry.
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    AIChE Journal 14 (1968), S. 703-708 
    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 of oxygen absorption by blood flowing through a small oxygen-permeable fiber in steady state laminar flow is presented. The rigidity and geometry of the fibers eliminate unpredictable shunting and distention, permitting a more detailed analysis of blood-membrane factors than has previously been undertaken. The mathematical analysis treats the blood as a homogeneous, non-Newtonian fluid with a reversible nonlinear oxygen sink (erythrocytes). The differential equations are solved numerically and the results of the parametric analysis are presented. The parameters that have a major influence on residence time necessary to obtain a specified oxygen content are the Grashof number, the concentration of hemoglobin in the blood, and wall Nusselt number, γ: γ = DLαL/DMαM In [1 + tm/R] where D = diffusion coefficient, α = Bunsen solubility coefficient, subscript L = liquid in tube, subscript M = tube material, R = inner radius of tube, tm = tube wall thickness.Comparison of the experimental results to the model indicate that mixing due to the heterogeneous nature of blood is minimal and that the major limitation in oxygen absorption is the blood film. Means of reducing this resistance are discussed.
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  • 83
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    AIChE Journal 14 (1968), S. 866-869 
    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 to evaluate pulses as a forcing function on a 24-plate distillation column. Pulses of two shapes, rectangular and displaced cosines, and of different widths were used as inputs to the reflux return line from the condenser to the column. The effect of the disturbance was a change in the liquid return rate which correspond to the shape and size of the pulse. The output responses of the system were temperatures measured at different times and at different plates in the column.Bode diagrams were plotted from the experimentally determined data. From these plots, it was determined that the system could be approximated by linear first-order equatons. The time constants for the linear system were determined both by direct sinusoidal forcing and by pulse forcing. Pulse data were considered acceptable when the values of the time constant and the phase angle determined by the pulse compared favorably with those determined by steady state sinusoidal forcing.
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    AIChE Journal 14 (1968), S. 903-908 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Free convective effects on forced convective mass transfer in the Stokes flow region were studied experimentally by using a single drop in a liquid-liquid system.Liquids used to form the drops were methyl acetate or 2-ethoxyethyl acetate with distilled water as the continuous medium. Spherical drops were formed on the capillary tip of a 0.58 cm. O.D. capillary glass tube centered in a 2.5 cm. O.D. pyrex tubular flow cell.Results are presented graphically as NSh vs. NPe, NSh vs. NRe, and NSh/NRa1/4 vs. NPe to show the variation of mass transfer with flow rate and free convection. The range of variables was 10 ≤ NPe ≤35,000; 0.1 ≤ NRe ≤ 30; 578 ≤ NSc ≤ 1,149; and 12.3 ≤ NGr ≤ 75.7.Satisfactory comparisons were also made with other investigators' findings.Results substantiate that at low flow rates (Reynolds number 〈 10, Peclet number 〈 1,000) free convective effects either reinforce or interfere with mass transfer. This interference takes place until flow becomes high enough to overcome interfering effects of free convection.
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    AIChE Journal 14 (1968), S. 934-939 
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    Keywords: Chemistry ; Chemical Engineering
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    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: If the transient equations of a plug flow tubular reactor are transformed into a set of corresponding ordinary differential equations, stability information for the former may be obtained graphically from knowledge about the transients of the latter. The analysis presented in this paper combines this simplification with the definitions and theorems of Weiss and Infante to propose a method of direct computation whereby transient bounds may be found for this important class of distributed-parameter chemical reactor systems.
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    AIChE Journal 14 (1968), S. 813-813 
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    AIChE Journal 13 (1967), S. 540-545 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
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    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Methods are presented for the determination of the transient values of the vaporization efficiencies from the knowledge of various combinations of the transient values of operating variables. For the case where the temperature and the composition of the liquid phase for each plate are known, a direct solution for the vaporization efficiencies is presented. Also, a method is presented for the determination of the mixing parameters of a generalized plate model on the basis of known transient values of certain operating variables.
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    AIChE Journal 13 (1967), S. 545-550 
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    Keywords: Chemistry ; Chemical Engineering
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    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Irreversible, first-order, simultaneous heterogeneous and homogeneous reactions in an isothermal tubular reactor under laminar flow conditions are studied. Accurate values of the eigenvalues, eigenfunctions, and radial concentration profiles are found for the dilute system. Criteria are given as to when the homogeneous reaction may be neglected with respect to the heterogeneous reaction and vice versa. It is found that for a certain range of the rate parameters well-known limiting solutions apply. Outside this range, the new solutions must be used.
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    AIChE Journal 15 (1969), S. 155-156 
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    AIChE Journal 15 (1969), S. 18-24 
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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: 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.
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    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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    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.
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    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.
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    AIChE Journal 14 (1968), S. 946-955 
    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 presents the cause of instabilities which arise during the numerical solution of ordinary differential equations. By using the numerical integration routines presently available, one actually approximates the differential equation by a difference equation. If the difference equation is of a higher order than the original differential equation, the approximate solution contains extraneous solutions which are not at all related to the true solution. It is the behavior of these extraneous solutions that one is usually concerned with in a stability analysis.Also presented is a procedure for obtaining a bound on the largest allowable integration step size for a class of chemical engineering problems. A detailed explanation of the procedure is illustrated for unsteady state distillation calculations.
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    AIChE Journal 14 (1968), S. 966-969 
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    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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    AIChE Journal 14 (1968), S. 977-979 
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    Keywords: Chemistry ; Chemical Engineering
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    AIChE Journal 14 (1968), S. 986-988 
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    AIChE Journal 15 (1969), S. 3-3 
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    AIChE Journal 15 (1969), S. 146-149 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
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    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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