Freezing of liquids in turbulent flow inside tubes

The problem of steady-state freezing of liquids in turbulent flow inside a tube with its walls kept at a uniform temperature lower than the freezing temperature of the liquid is solved for a wide range of Reynolds and Prandtl numbers, 10⁴ ≤ Re ≤ 10⁴ and 0 ≤ Pr ≤ 10³. The effects of Prandtl and Reynolds number on the location of the solid-liquid interface and on the heat transfer rate as a function of position along the tube are established.     

Mass transfer downstream of nozzles in turbulent pipe flow with varying Schmidt number

Local mass transfer rates at the wall of a pipe downstream of constricting nozzles have been measured using the electrochemical limiting diffusion current technique for different electrolyte Schmidt numbers. The familiar peaked axial distribution of mass transfer downstream of the nozzle was verified and the peak mass transfer values were found to agree well with the data of Tagget al. [1]. An overall correlation of the data in terms of both Reynolds number and nozzle expansion ratio produced the equation $$({{Sh_{2P} } \mathord{\left/ {\vphantom {{Sh_{2P} } {Sh_{2FD} }}} \right. \kern-\nulldelimiterspace} {Sh_{2FD} }})({{D_1 } \mathord{\left/ {\vphantom {{D_1 } {D_2 }}} \right. \kern-\nulldelimiterspace} {D_2 }})^{ - 0.7} = 14.39Re_2^{ - 0.182} $$ Limiting current-time traces produced evidence of the highly turbulent flow in the recirculation zone near the position of peak mass transfer.     

Mass transfer from bubbles in cocurrent flow

An experimental study has been made of liquid phase mass transfer from bubbles travelling cocurrently with liquid in a horizontal pipe. A simple model of the process based on streams of spherical bubbles has been developed and solved in the form of fractional absorption as a function of dimensionless groups. The derivation of and results obtained from this model are presented and explained. Experimental absorption rates measured in turbulent liquid flow over very wide ranges of bubble frequencies support the predictions of this model. A very effective bubble-frequency counter has also been developed capable of counts as high as 1600/min.     

Mass transfer between a drop or gas bubble and an isotropic turbulent flow

Theoretical formulas have been set up for calculating the coefficients of mass transfer between a drop or gas bubble and an isotropic turbulent flow for various Peclet and Reynolds numbers. The mass transfer coefficients depend mainly on the characteristics of the isotropic turbulent flow (energy dissipation, turbulence length scale, turbulence time scale), on the properties of the medium, and on the particle size. A number of practical formulas for calculating the mass transfer coefficients for turbulent flow are presented. The calculated data are compared with experimental data.     

Mass transfer in a turbulent radial wall jet

Experimental and theoretical coefficients are reported for mass transfer in a turbulent radial wall jet initiated by an impinging free jet. The hydrodynamic solution was obtained by the momentum integral technique, and mass transfer was predicted by analogy. Point mass transfer data were obtained for air-naphthalene and cinnamic acid-water systems. At low Schmidt numbers, experimental coefficients were slightly above the theoretical prediction, and followed the theoretical trend with radial distance and nozzle Reynolds number from 10,000 to 60,000. Coefficients at high Schmidt numbers showed large positive deviations from theory, which decreased with radial distance and increased with Schmidt number. These discrepancies were attributed to surface roughness effects.     

Enhancement of heat transfer and entropy generation analysis of nanofluids turbulent convection flow in square section tubes

In this article, developing turbulent forced convection flow of a water-Al₂O₃ nanofluid in a square tube, subjected to constant and uniform wall heat flux, is numerically investigated. The mixture model is employed to simulate the nanofluid flow and the investigation is accomplished for particles size equal to 38 nm.     

Mass transfer from cylindrical pellets submerged in parallel flowing fluid streams

A model is proposed wherein overall mass transfer from single cylinders of benzoic acid placed in parallel flowing water streams depends on different hydrodynamic regimes prevailing along the surfaces of the cylinder. The results for laminar and turbulent conditions are correlated in terms of Sherwood and Reynolds numbers. The mass transfer in the wake region of the cylinder is observed to be significantly different from the boundary layer mass transfer through the lateral surface or the stagnation and boundary layer mass transfer through the leading frontal area.     

Mass transfer between two turbulent liquid phases

The effect of forced turbulence on interfacial mass transfer between two liquid phases is investigated. A theoretical model is derived on the assumption that the mass transfer is controlled by unsteady diffusion into the vortices of the viscous subrange of the range of universal equilibrium. Mutual interaction of the turbulent fields in both phases is also accounted for. Experimental mass transfer rates for binary and ternary systems are presented; these were measured in a mixing cell of a new design. The model presented is shown to describe the process well, provided that the chosen liquid system is interfacially stable. The deviations due to interfacial instabilities are demonstrated for the case of the water—acetone—carbon tetrachloride system.     

Mass transfer in cylindrical couette flow

Theoretical equations for mass transfer to a section of the inner cylinder for laminar cylindrical couette flow are presented. The effects of curvature, the non-linear velocity profile, and the elliptic nature of the convective diffusion equation are included to extend the result of a previous treatment by Gabe and Robinson. The equations indicate that the correction to the result of Gabe and Robinson is dominated by elliptic effects for short electrodes and by curvature and velocity profile effects as the electrode comprises a larger proportion of the inner cylindrical circumference.     

Mass transfer from a spherical cap bubble in laminar flow

A theoretical account of mass transfer from a spherical cap bubble in laminar flow is given, based on the flow field derived by J.-Y. Parlange. The existence of concentration boundary layers on the bubble surface and on the surface of the spherical vortex wake is demonstrated, together with the presence of concentration wakes. The mass transfer process is described in qualitative terms. An approximate theory based on neglecting the thickness of the bubble is obtained, and the results compared with those given in various experimental accounts.     

Heat transfer to molten polymer flow in tubes

This article presents the results of a numerical study (finite differences) of the heat transfer problem in flowing polymer melts. The tube wall is assumed to be at a constant temperature. The rheological behavior of the melt is described by a power law temperature-dependent model. A convective and a viscous dissipation term are included in the energy equation. Temperature profiles, bulk temperatures, and Nusselt numbers are presented for a variety of flow entry temperatures.     

Laminar and turbulent mass transfer simulations in a parallel plate reactor

Laminar and turbulent mass transfer in a parallel plate reactor at high Schmidt number obtained from numerical simulation is compared with literature data. In a first step, the fluid flow is determined numerically in the reactor by solving the Navier–Stokes equations. For turbulent flow, a low Reynolds number k— model is used to calculate the turbulent viscosity. Using the obtained flow field and turbulent viscosity, the current density distribution is calculated for different flow velocities by solving the equations describing the transport of multiple ions due to diffusion, convection and migration. For the laminar case, a very good agreement with literature data is obtained. For turbulent flow, different numerical models for turbulent mass transfer are proposed in the literature. A detailed study of the behaviour close to the wall of these different turbulence models is presented, together with a comparison of the calculated results with literature correlations. This allows identification of the benefits and disadvantages of each of the turbulence models for the numerical calculation of mass transfer at high Schmidt numbers in a parallel plate reactor.     

Mass transfer accompanied by parallel reversible chemical reactions

Theoretical effects of parallel reversible chemical reactions on the rate of mass transfer are investigated in this paper. On the basis of the film theory, an analytical equation has been derived for gas absorption accompanied by first-order parallel rversible reactions. Analytical approximate equations have been developed and finite difference techniques applied to study the enhancement of mass transfer by second-order complex reactions. Results of this study indicate that when the diffusion is accompanied by second-order parallel reactions, the mass transfer rate increases with the concentration of the liquid reactant in the bulk, and approaches that of diffusion and first-order parallel reactions if the product of the diffusivity and bulk concentration of the liquid reactant is much larger than that of the gas reactant.     

The flow of thin films inside rotating cylindrical tubes

A mathematical model was derived for the calculation of the film thickness, total holdup and overall residence time of a thin liquid film flowing inside a rotating cylindrical tube, as a function of the liquid throughput and physical properties and of the tube diameter, length, rotational speed and angle of inclination. The experimental data with short tubes showed good agreement with the model for average film thickness above a certain critical value (which may indicate a change in the flow regime).     

Mass transfer in a magnetoelectrolytic flow cell

The effect of natural convection and forced flow on dc electrolysis in a superimposed uniform magnetic field was studied in a range of low Reynolds numbers. The critical magnetic field strength for limiting currents is lowered by increasing electrolyte flow rate and concentration. The dimensionless equation

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adequately correlates relative mass transfer rates with the pertinent process parameters.