Mass Transfer Sherwood Number Research Articles

Nanofluid flow of Higher order Radiative Chemical reaction with effects of Melting and Viscous dissipation

In this paper, authors investigatenon-Darcy homogeneous chemical reactions of order ‘n’ofnanofluid is discussed.The porous medium in which vertically plate kept with constant temperature and concentration. Melting and dissipation of viscosity observed in the nanofluid flow. The influence of double dispersion and radiation is analyzed. The flow maintained with invariant of time, constant density, laminar, forced and natural convection taken into account for the problem, the physical significance extracted from mathematical statements in terms of partial derivatives along with boundary conditions. The nonlinear governing partial mathematical derivatives converted into standard ordinary differential mathematical equations with the aid of similarity variable. These equations are numerically solved by MATLAB ‘bvp4c’ iterative programming methodology to seek out results of velocity-field, temperature-field, concentration-field extensively. The effect of dimensionless parameters such as Brownianmotion, thermal dispersion, melting, radiation, thermophoresis, and dimensionless numbers such as Eckert, Lewis, Prandtl, are analyzed.The heat transfer-Nusselt number and mass transfer-Sherwood number that characterize the heat transfer rate and mass transfer rate respectively outlined.

Investigation on the mechanism of convective mass transfer from a horizontal rotating cylinder without air jet flow

The local and mean convective mass transfer coefficients from the surface of a large-diameter horizontal circular rotating cylinder without air jet flow were investigated by measuring the concentration gradient. The results indicate that rotation performs different effects on the convective mass transfer at different regions. Based on the experimental data, the correlation equations of the mean convective mass transfer Sherwood number Sh and the critical Reynolds number Rer,cri have been formulated as follows: \( Sh = 0.32[(8.5Re_{\text{r}}^{2} + Gr) \cdot Sc]^{1/3} \) and \( Re_{\text{r,cri}} = 0.44(Gr \cdot Sc)^{1/2} \).

Numerical simulation of laminar flow development with heat and mass transfer in PEM fuel cell flow channels having oxygen and hydrogen suction at one channel wall

Numerical simulation has been carried out of the fluid flow, heat and mass transfer for the developing laminar flow in polymer electrolyte membrane (PEM) fuel cell cathode and anode flow channels, respectively. Each flow channel is considered to be composed of two parallel walls, one porous (simulating electrode surface) and one non-porous, or impermeable, wall (simulating bipolar plate surface). Various flow situations have been analyzed, and the local and the averaged friction coefficient, Nusselt number for heat transfer and Sherwood number for mass transfer are determined for various flow conditions corresponding to different stoichiometries, operating current densities and operating pressures of the cell. The effect of suction or injection (blowing) wall boundary condition has also been investigated, corresponding to the oxygen consumption in the cathode and hydrogen consumption in the anode. Correlations for the averaged friction coefficient, Nusselt and Sherwood numbers are developed, which can be useful for PEM fuel cell modeling and design calculations. Copyright © 2010 John Wiley & Sons, Ltd.

UV Disinfection of E. coli Between Concentric Cylinders: Effects of the Boundary Layer and a Wavy Wall

UV inactivation of E. coli in a plug flow reactor between concentric cylinders was investigated. The concentration boundary layer thickness was computed for laminar, turbulent and Taylor-Couette flow in terms of the respective mass transfer Sherwood number. It is demonstrated that the concentration boundary layer is thin and that the mass transfer coefficient is large and comparable in size for both turbulent and laminar Taylor-Couette flow in contrast to laminar flow. Computation of the fluence distribution for each flow pattern indicate that turbulent and especially Taylor-Couette flow subject E. coli to an equal flux of photons corresponding to ideal plug flow. However, experiments with turbulent flow that require large axial velocities indicate that very long reactor lengths are necessary to inactivate E. coli. Finally, rotor wavy wall modifications are explored to increase the inactivation of microorganisms in Taylor-Couette flow.

A study of transient processes in a closed vessel due to injection of hot liquid sprays

An experimental study to investigate the transient processes which occur when hot liquid spray droplets are suddenly injected into a gas contained in a closed chamber was reported previously [Proc. Inst. Mech. Eng. 215E (2001) 79]. That work also presented a macroscopic (bulk) analysis model, which agreed reasonably well with the experimental data. This work presents an analysis based on the simultaneous solution of the energy and mass balance equations for a single droplet and the gas-vapour control volume associated with the droplet. Good agreement has been found between the experimental data and the results of the single droplet analysis. The values of the heat transfer Nusselt number and the mass transfer Sherwood number, found using this approach, are approximately equal to 1. This agrees well with the results obtained from the macroscopic analysis reported previously and studies on heat transfer from dense evaporative droplet sprays.

Measurement of local and overall mass-transfer coefficients to a sphere in a quiescent liquid using a limiting current technique

The mass-transfer rate to a sphere in a quiescent ferri–ferrocyanide solution was determined from measurement of the limiting current through the spherical cathode. Mass-transfer rates to local areas on the sphere, without mass transfer to the rest of the sphere, were also measured. Convective movement of the electrolyte was observed visually although the experimental apparatus was jacketed for maintaining a constant temperature. Under this condition, the experimental Sherwood number for mass transfer to the whole sphere was 110 rather than 2 as for pure diffusion. The local Sherwood number for a 2 mm spot on the sphere was 275, which was about 1.7 times that of a 8 mm spot on the sphere. The local mass-transfer rate, in the absence of mass transfer to the rest of the sphere surface used in the present study, did not change significantly with the angular position to the upward vertical as it does when mass transfer occurs over the whole sphere simultaneously. The transient transfer approached steady state at the dimensionless time ( tu/ d) of about 20. The mass-transfer rate did not vary significantly with the distance between the two electrodes varied from 2.5 to 11 radii of the spherical cathode.

A three-dimensional numerical study on the correlation of spatial structure, hydrodynamic conditions, and mass transfer and conversion in biofilms

A three-dimensional model for convection, diffusion, and reaction in a porous, heterogeneous system has been implemented. It is used to analyse the influence of hydrodynamics and structural heterogeneities on mass transfer and conversion processes of solutes in biofilm systems. The mathematical model comprises the full incompressible Navier–Stokes equations and mass transfer with nonlinear reactions in the biofilm. It is found that increased biofilm surface roughness means decreased mass conversion in the solid biofilm. Secondly, a correlation between bulk flow Reynolds number and the Sherwood number for mass transfer across the irregular liquid/solid interface is formulated. In a further study the contribution of convective transport to overall mass transfer from bulk liquid into the biofilm was analysed. The main result was that the experimental observation of high convective flux of solutes in biofilm channels not necessarily is coupled with an equally high net convective contribution to mass transfer from bulk liquid into biofilm.

Distribution of Liquid‐Solid Heat Transfer Coefficient among Suspended Particles in Vertical Holding Tubes of an Aseptic Processing System

ABSTRACTMass transfer coefficients between sucrose coated particles and water as the suspending fluid, were measured to obtain values of the heat transfer coefficient by analogy with mass transfer. In a vertical holding tube configuration, the mass transfer coefficient spanned considerable range for those particles with comparable residence time. At Reynolds number 26100, the average mass transfer Sherwood number expressed in terms of residence time was Sh= ‐110.4t+215.1, and it scattered normally with standard deviation 19.2. The results indicated that heat transfer coefficients vary among particles with different residence times and may be significantly different even for particles with the same residence time.

Measurements of airway dimensions and calculation of mass transfer characteristics of the human oral passage.

This paper presents measurements of the geometric shape, perimeter, and cross-sectional area of the human oral passage (from oral entrance to midtrachea) and relates them through dimensionless parameters to the depositional mass transfer of ultrafine particles. Studies were performed in two identical replicate oral passage models, one of which was cut orthogonal to the airflow direction into 3 mm elements for measurement, the other used intact for experimental measurements of ultrafine aerosol deposition. Dimensional data were combined with deposition measurements in two sections of the oral passage (the horizontal oral cavity and the vertical laryngeal-tracheal airway) to calculate the dimensionless mass transfer Sherwood number (Sh). Mass transfer theory suggests that Sh should be expressible as a function of the Reynolds number (Re) and the Schmidt number (Sc). For inhalation and exhalation through the oral cavity (O-C), an empirical relationship was obtained for flow rates from 7.5-30.0 1 min-1: Sh = 15.3 Re0.812 Sc-0.986 An empirical relationship was likewise obtained for the laryngeal-tracheal (L-T) region over the same range of flow rates: Sh = 25.9 Re0.861 Sc-1.37 These relationships were compared to heat transfer in the human upper airways through the well-known analogy between heat and mass transfer. The Reynolds number dependence for both the O-C and L-T relationships was in good agreement with that for heat transfer. The mass transfer coefficients were compared to extrathoracic uptake of gases and vapors and showed similar flow rate dependence. For gases and vapors that conform to the zero concentration boundary condition, the empirical relationships are applicable when diffusion coefficients are taken into consideration.

Solutal convection and mass transfer in inclined enclosures

Both experimental and numerical work are performed to study the solutal convection flow and transport process in the enclosures that can be inclined at different angles. The enclosure is filled with an aqueous solution containing CuSO4 + H 2SO4, where the flow structure is visualized by both a particle tracer and shadowgraph. With a nonintrusive optical method the concentration fluctuations at desired locations are measured. The mass transfer Sherwood numbers across the enclosure at various inclinations are also measured and the results are correlated in terms of relevant nondimensional parameters. In the experiments, the Rayleigh number ranges from 1.126 x 10 8 to 1.157 x 10 11, the Schmidt numbers from 2500 to 3989, the angles of inclination from 30 to 150 deg, and the aspect ratios of the enclosure from 0.25 to 1. The SIMPLE algorithm developed by Patankar is employed to calculate the solutal convection, and the results are compared with the data. It was found that both the inclination and the aspect ratio of the enclosure have a significant effect on the flow structure and mass transfer. For a large angle of inclination, the accumulation of solutal boundary-layer flow leads to stratification of the core and reduction of the mass transfer. For a small inclination, generation and protrusion of solutal plumes leads to oscillation of concentration and enhancement of mass transfer.

Effect of Flow Angle-of-Attack on the Local Heat/Mass Transfer From a Wall-Mounted Cube

An experimental study of the local mass transfer over the entire surface of a wall-mounted cube is performed with a particular emphasis on the effects of flow angles-of-attack (0 deg ≤ α ≤ 45 deg). Invoking an analogy between heat transfer and mass transfer, the presently obtained mass transfer results can be transformed into their heat transfer counterparts. Reynolds number based on the cube height and mean free-stream velocity varies between 3.1 × 104 and 1.1 × 105. To substantiate the mass transfer results, streakline patterns are visualized on the cube surfaces as well as the endwall using the oil-graphite technique. Significantly different flow regimes and local mass transfer characteristics are identified as the angle-of-attack varies. The overall convective transport is dominated by three-dimensional flow separation that includes multiple horseshoe vortex systems and an arch-shaped vortex wrapping around the rear portion of the cube. In addition to the local study, power correlations between the surface-resolved mass transfer Sherwood number and the Reynolds number are presented for all α values studied. Mass transfer averaged over the entire cube is compared with that of its two-dimensional counterpart with crossflow around a tall prism.

Momentum, heat and mass transfer in turbulent pipe flow: The extended random surface renewal model

A model is presented for a quantitative prediction of the transfer coefficients of momentum, heat and mass, and the radial profiles of the axial velocity, the temperature, and the concentration in the near-wall fluid of a turbulent pipe flow. In this model, the tube wall is assumed to be covered by a mosaic of fluid elements of random age and laminar flow with unsteady profiles of velocity, temperature, or concentration. This model, which is an extension of the RSR model developed by Fortuin and Klijn, is the extended random surface renewal model, and is referred to as the ERSR model. The distribution and the mean value of the ages of the fluid elements at the tube wall govern the local time-averaged transfer coefficients and radial profiles in the wall region. The mean age of the fluid elements is derived from the friction factor and the Reynolds number using the ERSR model. Both the distribution and the mean ages of the fluid elements at the tube wall agree quantitatively with the experimental results obtained from velocity signals measured with a laser-Doppler anemometer in turbulent pipe flow at thirteen Reynolds numbers between 5 × 10 3 and 43 × 10 3. The equations derived from the ERSR model for the local time-averaged heat and mass transfer coefficients in turbulent pipe flow, and the radial profiles of the axial velocity, the temperature and the concentration in the wall region, agree with correlations or experimental data presented in literature. The analogy between momentum, heat and mass transfer in turbulent pipe flow is elucidated by introducing a dimensionless number for momentum transfer. This so-called Fanning number for momentum transfer ( Fa = k m d/v), is comparable with the Nusselt number for heat transfer and the Sherwood number for mass transfer. Furthermore, the ERSR model provides a basis for both explaining the Chilton-Colburn analogy and the relationship between transfer rates and measured mean ages of fluid elements at the wall in turbulent pipe flow.

Transfer of brownian particles to continuous moving surfaces

A theoretical analysis of particle deposition from a dilute suspension (or aerosol) subject to laminar flow onto moving continuous plates (sheets) and cylinders (wires) is presented. Complete transport equations have been formulated, taking into account specific surface interactions such as London-van der Waals and electrical double-layer forces. By solving these equations numerically the dimensionless mass transfer Sherwood number has been determined for a variety of conditions characteristic for suspensions and aerosols. It has been found that the effects of attractive double-layer forces are very important, especially for thin double-layers, increasing mass transfer rates by more than an order of magnitude for larger particles (at distances close to the entrance point). For Péclet numbers Pe < 10 −6 (small particles) the specific interactions play a less important role and the Sherwood number can be accurately approximated by an analytical expression derived for neglible particle dimensions (ions). The major finding of this study is that compared to deposition on a stationary surface, deposition on moving continuous surfaces is larger by at least one order of magnitude, both in the presence or absence of specific surface forces.

Particle transfer to a plate in uniform flow

A theoretical analysis of particle deposition from a dilute suspension onto a plate immersed in a uniform laminar flow with zero angle of incidence is presented. The complete transport equation was solved numerically, taking into account specific surface interactions such as London-van der Waals dispersion and electrical double-layer forces, as well as external forces such as gravity and electric fields. From these solutions, the dimensionless mass transfer Sherwood number was determined for a variety of conditions characteristic for suspensions and aerosols. It is shown that the theoretical analysis applies also to particle deposition within the entrance region of a parallel-plate channel, provided that the hydrodynamic boundary layer is much smaller than the distance between the plates. It is found that the effects of specific surface interactions are important for distances close to the suspension inlet point (leading edge) and for large particles. The effects are generally less pronounced for aerosols in which gravity and electrostatic forces (if present) play a dominant role.

Deposition of particles under external forces in laminar flow through parallel-plate and cylindrical channels

A theoretical analysis of particle deposition kinetics onto walls of parallel-plate and cylindrical channels is presented. Rigorous transport equations are formulated by taking into account specific surface forces as well as external forces, e.g., gravity. By solving the transport equations numerically, the dimensionless mass transfer Sherwood number is determined as a function of various dimensionless parameters introduced such as Pe, Gr, Ad, and Dl, accounting for convection and diffusion, and for gravity, dispersion, and electrical double-layer interactions, respectively. The influence of attractive surface forces and gravity on the deposition kinetics is graphically presented and discussed. For large particles, i.e., about 1-μm diameter (Pe > 1), and for short distances from the point where deposition starts, a considerable increase in particle flux (up to an order of magnitude) is predicted over previous analytical values when strong attractive double-layer forces are present. For particles smaller than 0.1-μm diameter ( Pe < 10 -4) our numerical results show that particle deposition rates may be successfully predicted by an analytical formula derived for particles of negligible size even in the presence of double-layer attractions (provided external forces are absent). Experimental results reported in the literature obtained under conditions of negligible gravity force are reinterpreted in terms of the present theory. A somewhat closer agreement with experimental data as compared to the analytical formula mentioned above is found in cases of strong double-layer attractions.