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Showing papers on "Schmidt number published in 1971"


Journal ArticleDOI
TL;DR: In this article, a set of Boussinesq approximations were shown to have solutions of similarity form for combined buoyancy effects, for vertical flows adjacent to surfaces and in plumes, and the resulting equations were integrated for air and water for various practical values of the Schmidt number.

553 citations


Journal ArticleDOI
TL;DR: In this article, the effect of Reynolds number, Grashof number and Schmidt number on mass transfer rates in packed beds is investigated and it is suggested that an improved method for interpreting mass transfer results is to determine asymptotic relations for different ranges of variables.

117 citations


Journal ArticleDOI
TL;DR: In this article, an expression for the eddy diffusivity in the turbulent boundary layer near a smooth wall for fluids of high Prandtl number is obtained from emperical considerations.

81 citations


Journal ArticleDOI
TL;DR: In this paper, a finite difference solution for a scalar boundary layer under the influence of a harmonic oscillation in the velocity field is proposed, where the principal assumptions used in the calculations are that the fluctuating scalar field is described by a linearized form of the conservation equation and that the velocity varies linearly with distance from the wall.

70 citations



Journal ArticleDOI
TL;DR: In this article, boundary-layer solutions are given for free convection in laminar three-dimensional systems driven by a temperature-dependent or composition-dependent density, and the results of Acrivos [1] for power-law fluids are generalized.

57 citations



Journal ArticleDOI
TL;DR: In this article, the authors reported the results of an experimental investigation, which employs the technique of diffusion controlled electrolysis, for the determination of mass-transfer rates in the separated and redeveloping regions downstream of a sudden enlargement of a circular pipe.

48 citations


Journal ArticleDOI
TL;DR: In this article, the effect of ventilation on the rate of evaporation of cloud drops falling at terminal velocity in air subsaturated with respect to water was investigated, and local Sherwood numbers have been calculated for spheres with Reynolds numbers in the range 0.05-300 and for a fluid with a Schmidt number of 0.71.
Abstract: Accurate, numerical solutions of the Navier-Strokes equations of motion and the equation of mass transfer have been obtained for the steady-state transfer of a chemically inert substance from the surface of a single rigid sphere moving at its terminal velocity in an unbounded fluid. Local Sherwood numbers have been calculated for spheres with Reynolds numbers in the range 0.05–300 and for a fluid with a Schmidt number of 0.71. The objective of this study was to model the effect of ventilation on the rate of evaporation of cloud drops falling at terminal velocity in air subsaturated with respect to water.

44 citations


Journal ArticleDOI
TL;DR: In this paper, the expression for eddy diffusivity in a previous analysis was revised and good agreement was obtained between the predicted and experimental results for mass transfer at Schmidt numbers between 800 and 15,000.

42 citations


Journal ArticleDOI
TL;DR: In this paper, the effect of viscosity and diffusivity variations on concentration polarization during the ultrafiltration of protein solutions in two-dimensional stagnation flows is investigated by numerical integration of the equations of continuity and motion.
Abstract: The effect of viscosity and diffusivity variations on concentration polarization during the ultrafiltration of protein solutions in two-dimensional stagnation flows is investigated by numerical integration of the equations of continuity and motion. It is found that these effects are surprisingly small and insensitive to the forms of concentration dependence postulated. The high Schmidt numbers and low permeation rates characteristic of these systems result in considerable simplification of the analysis and permit use of a modified Chilton-Colburn relation for predicting the onset of sludge formation at the membrane-solution interface. The predicted dependence on Schmidt number agrees with published experimental data for other boundary-layer flows and suggests the possibility of improved prediction of equipment performance.

Journal ArticleDOI
R. L. Webb1
01 Dec 1971
TL;DR: A critical evaluation of analytical solutions and Reynolds analogy based correlations for heat transfer with constant properties to turbulent flow of liquids and gases in smooth tubes is presented in this paper, where a new Reynolds analogy correlation is developed which agrees with the solutions of DeissleR, and Sparrow et al., within ± 2 percent.
Abstract: A critical evaluation of recently proposed analytical solutions and Reynolds analogy based correlations for heat transfer with constant properties to turbulent flow of liquids and gases in smooth tubes is presented. A new Reynolds analogy correlation is developed which agrees with the solutions of DeissleR, and Sparrow et al., within ±2 percent. The ability of this equation to correlate constant properties heat transfer data is compared with the equations proposed by FRiend and MetzneR, and Petukhov and Popov. Both the new equation and the Petukhov and Popov equation provide a very good correlation of existing data for.7

Journal ArticleDOI
TL;DR: In this article, the Levich theory of the rotating disk has been extended to the case of rotating spherical electrodes by means of a series expansion method, and it is shown that the rate of mass transfer near the pole of rotation is the same as on a rotating disk.
Abstract: The Levich theory of the rotating disk has been extended to the case of rotating spherical electrodes by means of a series expansion method. It is shown that the rate of mass transfer near the pole of rotation is the same as on a rotating disk. It decreases, however, in meridional direction toward the equator. Results for a sphere or hemispherical electrode can be summarized as where and are the Sherwood and the Reynolds numbers based on the sphere radius, and is the Schmidt number.

Journal ArticleDOI
TL;DR: In this paper, a model for the eddy diffusivity and mean velocity distributions in fully developed turbulent isothermal smooth pipe flow (4 x lo3 < Re < 5 x 10').
Abstract: A model was developed for the eddy diffusivity and mean velocity distributions in fully developed turbulent isothermal smooth pipe flow (4 x lo3 < Re < 5 x 10'). Reichardt's tworegion eddy diffusivity models were modified so as to fulfill the requirements that the eddy diffusivity be represented by a smooth, continuous curve, and vanish with the third power of the distance from the wall; the continuity equation be satisfied; and the ratio of the bulk velocity to centerline velocity agree with experimental data. The descripition is in excellent agreement with Laufer's experimental mean velocity data and, in general, provides a method of accurately predicting the mean velocity distribution. n turbulent flow, the instantaneous flow properties I are normally expressed as the sum of a time-averaged component and a fluctuating component. In an effort to provide engineering solutions to problems involving turbulent processes, which are difficult to describe on a mechanistic basis, the eddy diffusivity concept has been widely used to provide models for the fluctuating motion'". Unfortunately, the eddy diffusivity of momentum, a major parameter in most models, has not been well described in a manner consistent with the boundary conditions and available experimental data'a'. An objective of this work is, therefore, to generate an expression for the eddy diffusivity which will be compatible with both the boundary conditions and experimental data. A second concurrent objective is the development of a consistent expression for the mean velocity distribution. The approach used involves the iterative solution of mutually dependent expressions for the velocity distribution and eddy diffusivity in response to experimental and analytical constraints, in order to develop the most consistent over-all picture. Although an incompressible constant property fluid in fully-developed pipe flow is assumed in the model, such assumptions are often made in initial, idealized analyses of practical systems.

Journal ArticleDOI
TL;DR: In this paper, the mass transfer between a liquid drop during its formation and the surrounding liquid phase was directly evaluated by a photographic technique, and the measured coefficients are substantially higher than would be expected for free drops.
Abstract: The mass transfer occurring between a liquid drop during its formation and the surrounding liquid phase was directly evaluated by a photographic technique. Slightly soluble organic drops containing no additional solute were formed in a continuous aqueous phase so that only the continuous phase resistance existed. Effects of nozzle diameter and both phase flow rates were evaluated and the possible influence of surfactant was investigated. Mass transfer coefficients were observed to decrease sharply with time early in the formation period. This, together with the parameteric study of dispersed phase feed rate, indicates the strong effect of internal drop convection for this high Schmidt number system. The measured coefficients are substantially higher than would be expected for free drops.

Journal ArticleDOI
G. A. Hughmark1
TL;DR: In this article, three mass transfer models for the vapor phase were developed for a free interface between the liquid and vapor and yields the Schmidt number as the correlating variable, and design equations were developed from this analysis.
Abstract: Three mass transfer models are developed for the vapor phase. The first model assumes a rigid interface between the liquid and vapor and yields the Schmidt number as the correlating variable. The other two models represent a free interface with the penetration theory as the mechanism for one model and eddy diffusion as the mechanism for the other model. Both free interface models correlate experimental data within the error of the data. A liquid-phase mass transfer model is developed for a free interface and the penetration theory as the mass transfer mechanism. Design equations are developed from this analysis.

Journal ArticleDOI
TL;DR: In this article, the eddy diffusivities of mass in the central region of the tube were measured for turbulent air flow using axial concentration distributions, and a modified evaluation procedure has been used.

Journal ArticleDOI
TL;DR: In this paper, the relationship between the velocity, temperature and concentration profiles along a porous flat plate with carbon dioxide injected at the surface was investigated, and it was found that the local concentration and velocity can be correlated by using an assumption of a constant turbulent Schmidt number through the layer for given conditions.

Journal ArticleDOI
TL;DR: In this article, the local convective mass transfer of smooth and rough particles was investigated with an electrochemiluminescence technique at a Schmidt number Sc ≈ 103 for Reynolds numbers 3 × 103 104, which may help to explain the growth of big hailstones.
Abstract: The local convective mass transfer (i.e., the mass transfer as a function of polar angle) of smooth and rough particles has been investigated with an electrochemiluminescence technique at a Schmidt number Sc ≈ 103 for Reynolds numbers 3 × 103 104, which may help to explain the growth of big hailstones.

Journal ArticleDOI
TL;DR: An experimental and theoretical study has been made of the turbulent mass transfer for large Schmidt numbers in the entrance region of a circular tube in which a turbulent boundary layer with small negative pressure gradients develops as mentioned in this paper.
Abstract: An experimental and theoretical study has been made of the turbulent mass transfer for large Schmidt numbers in the entrance region of a circular tube in which a turbulent boundary layer with small negative pressure gradients develops. Measurements of the local and the over-all mass transfer rates were carried out by use of an electrochemical method for Reynolds numbers of 1×104, 2×104 and 3×104 and Schmidt number of 1561. A method for the prediction of mass transfer rates in the turbulent boundary layers is also provided. The equation of conservation of matter is reduced into a form of the heat conduction equation by using von Mises transformation. The equation is then solved by assuming that the distribution of the eddy diffusivity in the developing boundary layer at the entrance region of a circular tube is the same as that for fully developed tube flow and using an eigenvalue technique. The solution agrees fairly well with the experimental results. This suggests that the above mentioned assumption for the eddy diffusivity distribution in the boundary layer is valid.

Journal ArticleDOI
TL;DR: In this paper, the influence of nonequilibrium dissociation on the flow field in laminar mixing of homogeneous air flows is investigated by a perturbation method and the Mach, Prandtl, and Schmidt numbers are selected as problem parameters.
Abstract: The influence of nonequilibrium dissociation on the flow field in laminar mixing of homogeneous air flows is investigated by a perturbation method. The Mach, Prandtl, and Schmidt numbers are selected as problem parameters. The solution is obtained taking account of four approximations.