Showing papers on "Schmidt number published in 1972"
TL;DR: In this article, the Nusselt number was used for the analysis of turbulent heat and mass transfer in pipes, channels, and boundary layers, where the dimensionless coefficients of the universal logarithmic equations for the velocity and temperature profiles were derived.
279 citations
TL;DR: In this paper, mass transfer rates between solid nickel surfaces and the ferro-ferri-cyanide electrolyte flowing in a 1 in.square duct have been measured for smooth and six similar rough surfaces, the latter having V-shaped grooves of 2-14 mil depth normal to the flow direction.
174 citations
TL;DR: In this paper, the dispersion in curved tubes and channels is analyzed using the velocity distribution of Topakoglu and Goldstein for tubes and that of Goldstein (1965) for curved channels, and it is found that the present dispersion coefficient contains the Erdogan & Chatwin result as a limiting case.
Abstract: Dispersion in curved tubes and channels is treated analytically, using the velocity distribution of Topakoglu (1967) for tubes and that of Goldstein (1965) for curved channels. The result for curved tubes is compared with that obtained previously by Erdogan & Chatwin (1967) and it is found that the presentdispersion coefficient contains the Erdogan & Chatwin result as a limiting case.The most striking difference between the results is that Erdogan & Chatwin predict that the dispersion coefficient is always decreased by curvature if the Schmidt number exceeds 0.124, which is the ease for essentially all systems of practical interest. In contrast, the present result, equation (76), predicts that the dispersion coefficient may be increased substantially by curvature in low Reynolds number flows, particularly in liquid systems which would be of interest in biological systems.Two competing mechanisms of dispersion are present in curved systems. Curvature increases the variation in residence time across the flow in comparison with straight systems and this in turn increases the dispersion coefficient. The secondary flow which occurs in curved tubes creates a transverse mixing which decreases the dispersion coefficient. The results demonstrate that the relative importance of these two effects changes with the Reynolds number, since the dispersion coefficient first increases and then decreases as the Reynolds number increases. Since secondary flows are not present in curved channels the dispersion coefficient is increased over that in straight channels for all cases.
89 citations
TL;DR: In this article, an experimental study was made of the variation of the radial and tangential eddy diffusivities of heat and mass in a fully developed turbulent flow in a plain tube.
49 citations
TL;DR: In this paper, the mass transfer in a parallel plate electrochemical cell under both laminar and turbulent flow was investigated and a Leveque-type equation modified to include the cell aspect ratio as an additional parameter.
Abstract: Experimental investigations have been made of ionic mass transfer in a parallel plate electrochemical cell under both laminar and turbulent flow. The results obtained in the laminar flow region were found to be well represented by a Leveque-type equation modified to include the cell aspect ratio as an additional parameter. The influence of decreased mass transfer at the edges of the electrodes due to changes in the velocity profile was found to be small. For the turbulent region, there is a correlation of the mass transfer coefficient with Reynolds number to an exponent of 0.875 and Schmidt number to exponent of 0.21. This is in accord with existing correlations for heat and mass transfer in similar geometries over the range studied.
48 citations
TL;DR: In this article, an experimental investigation of stable laminar ethylene and propylene diffusion flames burning on a nozzle in weightlessness was performed at the NASA-Lewis 2.2 Second Drop Tower.
Abstract: An experimental investigation of stable laminar ethylene and propylene diffusion flames burning on a nozzle in weightlessness was performed at the NASA-Lewis 2.2 Second Drop Tower. For a range of low flow conditions, visual evidence indicated that the flames reaction zone was burning over a wide range of combustion rates; however, for the purposes of correlating flame length the stoichiometric burning rate appeared adequate. It was found that if Re is the ambient pure fuel Reynolds number based on nozzle radius, Sc is the ambient pure fuel Schmidt number, and c, is the mole fraction of fuel burning stoichiometrically in air, the ratio of flame length to nozzle radius was predicted and experimentally verified to be proportional to Sc1/2 Re ln1/2 (1/(1−c8)).
35 citations
TL;DR: In this paper, the Schmidt number of order unity was used to predict the thickness of the withdrawal layer of a reservoir with respect to the distance from the sink, where inertia forces were assumed to be equal to buoyancy and viscous forces.
Abstract: A reservoir is assumed to be filled with water which has a linear variation of density with depth. The geometry of the boundaries is simplified to a parallel walled duct with the line sink at the centre of the fluid. The primary focus is on partitioning the flow into distinct flow regimes and predicting the withdrawal-layer thickness as a function of the distance from the sink; the predictions are verified experimentally.For fluids with a Schmidt number of order unity, the withdrawal layer is shown to be composed of distinct regions in each of which a definite force balance prevails. The outer flow, where inertia forces are neglected, changes from a parallel uniform flow upstream to a symmetric self-similar withdrawal layer near the sink. For distances from the sink smaller than a critical distance, dependent on the flow parameters, inertia forces become of equal importance to buoyancy and viscous forces. The equations valid in this inner region are derived. Using the inner limit of the outer flow as the upstream boundary condition, these inner equations are solved approximately for the withdrawal-layer thickness by an integral method. The inner and outer variations of δ, the withdrawal-layer thickness, are combined to yield a composite solution and it is seen that the inclusion of inertia forces yields layers thicker than those obtained from a strict buoyancy-viscous force balance. In terms of the inner variables the only parameter remaining is the Schmidt number.Laboratory experiments were carried out to verify the theoretical conclusions. The observed withdrawal-layer thicknesses were shown to be closely predicted by the integral solution. Furthermore, the data could be represented in terms of the inner variables by a single curve dependent only on the Schmidt number.
32 citations
TL;DR: In this paper, the effect of screen-produced turbulence in the free stream on the overall and the local mass-transfer rates was determined at large Schmidt number of 1230, and the location of the separation point was determined.
18 citations
TL;DR: In this paper, the current collection characteristics of flush mounted electrostatic probes on a flat plate in ionized hypersonic flows were investigated, and the effects of probe size, position, bias, and local flow properties were explored in detail.
Abstract: Numerical studies were conducted to determine current collection characteristics of flush mounted electrostatic probes on a flat plate in ionized hypersonic flows. The effects of probe size, position, bias, and local flow properties were explored in detail. To this end, the charged particle conservation equations were solved with the two- and three-dimensional Poisson equation, and the results compared with thick sheath probe data obtained in hypersonic "hock tunnel experiments. Agreement with the experimental data is good. Nomenclature diffusion coefficient Damkohler number, krL?/D0 electron charge probe current current density Mach number number density pressure probe radius Reynolds number Schmidt number temperature time flow velocity probe voltage distance from plate leading edge source term distance normal to surface of flat plate ratio of ion to electron diffusion coefficient boundary-layer thickness D Da e / J M N,n p R Re Sc T t 17, u V x vv Y, y
18 citations
TL;DR: In this paper, the authors present a systematical derivation of the equations of Row in porous media with heat and mass transfer, and of the different types of approximations used in applications.
Abstract: Publisher Summary This chapter presents a systematical derivation of the equations of Row in porous media with heat and mass transfer, and of the different types of approximations used in applications. Physical interpretation and estimates of order of magnitude, rather than intricate mathematical derivations, are emphasized. The considerations are limited to the cases of an immobile and inert solid matrix and a slightly compressible liquid undergoing a slight density variation that is, having a low solute concentration and a moderate temperature drop. The flow is assumed to be in the Darcian regime. The Schmidt number (viscosity over diffusion coefficients) is of order 10 3 . Mass transfer in isothermic conditions is studied with applications to problems of mixing of fresh and salt waters in aquifers, miscible displacements in oil reservoirs, spreading of solutes in fluidized beds and crystal washers, salt leaching in soils, and so on. Heat transfer, in the case of a homogeneous fluid, is studied less systematically, but rather extensively, with relation to different applications, like: dynamics of hot underground springs; terrestrial heat flow through aquifer; hot fluid and ignition front displacements in reservoir engineering; heat exchange (with evaporation and condensation) between surface soil and atmosphere; flow of moisture through porous industrial materials; heat exchanges with fluidized beds, and so on.
12 citations
TL;DR: In this paper, the problem of mass transfer in a duct is considered for the limit of large σ (Prandtl or Schmidt number) and the results depend on the behavior of the eddy diffusivity near the solid surface.
Abstract: The problem of developed turbulent heat or mass transfer in a duct is considered for the limit of large σ (Prandtl or Schmidt number). The limiting results depend on the behavior of the eddy diffusivity near the solid surface. Since there is a question about whether this variation begins with ϵ ∝ y+3 + … or ϵ ∝ y+4 + … for y+ near zero, both possibilities are considered. In each case the first three terms of the asymptotic expansion for σ ∞ are obtained. The first term of the asymptotic expansion agrees with limiting results derived earlier, while the correction terms indicate the errors associated with earlier simplifying assumptions.
By proper scalling, it is demonstrated that in the limit of σ ∞ the results are independent of geometry and boundary conditions for situations involving parallel plates, circular tubes and concentric annuli with either constant surface heat flux or temperature. The correction terms to the σ ∞ asymptote can be significant, although the effect of Reynolds number on the correction terms is very small.
A comparison between a typical numerical integration and the asymptotic formula shows excellent agreement. The asymptotic formulae are used to correlate large Schmidt number mass transfer data.
TL;DR: In this paper, the theory of the rotating spherical electrode has been extended to include the correction terms for convective diffusion at small Schmidt numbers, and the resulting rate equation expressed in the form of an asymptotic series permits a good approximation of the transfer rate for.
Abstract: Using a method of singular perturbation, the theory of the rotating spherical electrode has been extended to include the correction terms for convective diffusion at small Schmidt numbers. The resulting rate equation expressed in the form of an asymptotic series permits a good approximation of the transfer rate for . Within this region the accuracy of the theory increases with increasing Schmidt numbers; the maximum error, occurring at , is less than 5%.
TL;DR: In this article, the ion current to the forward stagnation region of a highly negative probe is analyzed by using the boundary-layer approximation, where the ratio of the sheath thickness to the boundary layer thickness is assumed in the range from a few tenths to 1.
Abstract: The ion current to the forward stagnation region of a highly negative probe is analyzed by using the boundary-layer approximation. The ratio of the sheath thickness to the boundary-layer thickness is assumed in the range from a few tenths to 1. The effects of various parameters on the ion current are made clear. The dimensionless current-voltage characteristic which depends on the velocity profile, the ambipolar Schmidt number and the Prandtl number has been introduced. This relation is avbailable to calculate the ion number density from the measured current and applied probe potential. Numerical examples are shown for typical cases. It is shown that the ion current increases with the absolute value of the probe potential and a constant saturation current cannot be obtained.
TL;DR: In this article, the authors proposed a number based on probe length path length between horns (microwave interferometer) or probe length Mach number particle mass particle density Reynolds number and Schmidt number for probe length dimensionless mobility ion Schmidt number fluid to probe temperature ratio freestream velocity angle of attack phase difference in radians.
Abstract: width of waveguide (interferometer) electron charge current to probe dimensionless probe current I/neu^n^ sin# ion mobility Knudsen number based on probe length path length between horns (microwave interferometer) or probe length Mach number particle mass particle density Reynolds number based on probe length dimensionless mobility ion Schmidt number fluid to probe temperature ratio freestream velocity angle of attack phase difference in radians (microwave interferometer) dielectric constant conical probe half-angle Debye length over probe length free space wavelength (microwave interferometer)
TL;DR: In this article, a dimensionless mass transfer coefficient for a laminar boundary layer flow with tangentially moving interface is derived. But it is implied that the flow is similar and the dimensionless stream function is known and the functional relation is analogous with that by Beek and Bakker.
Abstract: Mass transfer coefficient is numerically obtained for a laminar boundary layer flow with tangentially moving interface. It is implied that the flow is similar and the dimensionless stream function is known. Dimensionless mass transfer coefficient can be approximately expressed as a function of a single parameter containing the velocity and the velocity gradient at the interface. The functional relation is analogous with that by Beek and Bakker and applicable to all similar boundary layer flows. It is also numerically shown that the general correlation gives a good estimate even in the case of small Schmidt number for uniform flow over a flat interface.