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Peclet Number (peclet + number)

Distribution by Scientific Domains

Engineering	41%
Chemistry	35%

Selected Abstracts

Estimation of Joule heating effect on temperature and pressure distribution in electrokinetic-driven microchannel flows

ELECTROPHORESIS, Issue 3 2006
Reiyu Chein Professor
Abstract In this study we present simple analytical models that predict the temperature and pressure variations in electrokinetic-driven microchannel flow under the Joule heating effect. For temperature prediction, a simple model shows that the temperature is related to the Joule heating parameter, autothermal Joule heating parameter, external cooling parameter, Peclet number, and the channel length to channel hydraulic diameter ratio. The simple model overpredicted the thermally developed temperature compared with the full numerical simulation, but in good agreement with the experimental measurements. The factors that affect the external cooling parameters, such as the heat transfer coefficient, channel configuration, and channel material are also examined based on this simple model. Based on the mass conservation, a simple model is developed that predicts the pressure variations, including the temperature effect. An adverse pressure gradient is required to satisfy the mass conservation requirement. The temperature effect on the pressure gradient is via the temperature-dependent fluid viscosity and electroosmotic velocity. [source]

Analysis of a Vertical Dipole Tracer Test in Highly Fractured Rock

GROUND WATER, Issue 5 2002
William E. Sanford
The results of a vertical dipole tracer experiment performed in highly fractured rocks of the Clare Valley, South Australia, are presented. The injection and withdrawal piezometers were both screened over 3 m and were separated by 6 m (midpoint to midpoint). Due to the long screen length, several fracture sets were intersected, some of which do not connect the two piezometers. Dissolved helium and bromide were injected into the dipole flow field for 75 minutes, followed by an additional 510 minutes of flushing. The breakthrough of helium was retarded relative to bromide, as was expected due to the greater aqueous diffusion coefficient of helium. Also, only 25% of the total mass injected of both tracers was recovered. Modeling of the tracer transport was accomplished using an analytical one-dimensional flow and transport model for flow through a fracture with diffusion into the matrix. The assumptions made include: streamlines connecting the injection and withdrawal point can be modeled as a dipole of equal strength, flow along each streamline is one dimensional, and there is a constant Peclet number for each streamline. In contrast to many other field tracer studies performed in fractured rock, the actual travel length between piezometers was not known. Modeling was accomplished by fitting the characteristics of the tracer breakthrough curves (BTCs), such as arrival times of the peak concentration and the center of mass. The important steps were to determine the fracture aperture (240 ,m) based on the parameters that influence the rate of matrix diffusion (this controls the arrival time of the peak concentration); estimating the travel distance (11 m) by fitting the time of arrival of the centers of mass of the tracers; and estimating fracture dispersivity (0.5 m) by fitting the times that the inflection points occurred on the front and back limbs of the BTCs. This method works even though there was dilution in the withdrawal well, the amount of which can be estimated by determining the value that the modeled concentrations need to be reduced to fit the data (,50%). The use of two tracers with different diffusion coefficients was not necessary, but it provides important checks in the modeling process because the apparent retardation between the two tracers is evidence of matrix diffusion and the BTCs of both tracers need to be accurately modeled by the best fit parameters. [source]

Interpretation of the enhancement of field-scale effective matrix diffusion coefficient in a single fracture using a semi-analytical power series solution

HYDROLOGICAL PROCESSES, Issue 6 2009
Tai-Sheng Liou
Abstract A power series solution for convergent radial transport in a single fracture (PCRTSF) is developed. Transport processes considered in PCRTSF include advection and hydrodynamic dispersion in the fracture, molecular diffusion in the matrix, diffusive mass exchange across the fracture-matrix interface, and mixing effects in the injection and the extraction boreholes. An analytical solution in terms of a power series in Laplace domain is developed first, which is then numerically inverted by de-Hoog et al.'s algorithm. Four dimensionless parameters determine the behaviour of a breakthrough curve (BTC) calculated by PCRTSF, which are, in the order of decreasing sensitivity, the matrix diffusion factor, two mixing factors, and the Peclet number. The first parameter is lumped from matrix porosity, effective matrix diffusion coefficient, fracture aperture, and retardation factors. Its value increases as the matrix diffusion effect becomes significant. A non-zero matrix diffusion factor results in a , 3/2 slope of the tail of a log,log BTC, a common property for tracer diffusion into an infinite matrix. Both mixing factors have equal effects on BTC characteristics. However, the Peclet number has virtually no effect on BTC tail. PCRTSF is applied to re-analyse two published test results that were obtained from convergent radial tracer tests in a discrete, horizontal fracture in Silurian dolomite. PCRTSF is able to fit the field BTCs better than the original channel model does if a large matrix diffusion coefficient is used. Noticeably, the ratio of field-scale to lab-scale matrix diffusion coefficients can be as large as 378. This enhancement of the field-scale matrix diffusion coefficient may be ascribed to the presence of a degraded zone at the fracture-matrix interface because of karstic effects, or to flow channeling as a result of aperture heterogeneity. Copyright © 2009 John Wiley & Sons, Ltd. [source]

RHEOLOGICAL PROPERTIES OF NONCOHESIVE APPLE DISPERSION WITH HELICAL AND VANE IMPELLERS: EFFECT OF CONCENTRATION AND PARTICLE SIZE

JOURNAL OF FOOD PROCESS ENGINEERING, Issue 5 2000
DENIS CANTÚ-LOZANO
ABSTRACT The proportionality constant, ks, between shear rate, ,, and agitation velocity, N, for a helical ribbon-screw (HRS) agitator was 17.8. Using the HRS agitator, values of consistency index K and the flow behavior index n of 14 apple pulp suspensions at seven different solids concentrations and two average particle diameters 0.71 mm and 1.21 mm were determined; in addition, values of the Casson viscosity ,c and yield stress ,OC were also calculated. The magnitudes of K increased and of n decreased with increase in pulp concentration. Experimental values of the vane yield stress, ,O,, measured with a six-blade vane increased with increase in pulp content. The values of ,OC obtained using the Casson model were close to the experimental values ,O,. The effect of particle size on the relative viscosity, ,r, was correlated with Peclet number. [source]

Sorption dynamics in fixed-beds of inert core spherical adsorbents including axial dispersion and Langmuir isotherm

AICHE JOURNAL, Issue 7 2009
M. Khosravi Koocheksarayi
Abstract The effects of axial dispersion and Langmuir isotherm on transient behavior of sorption and intraparticle diffusion in fixed-beds packed with monodisperse shell-type/inert core spherical sorbents are studied. The system of partial differential equations of the mathematical model is solved numerically using finite difference methods. Results are presented in the form of breakthrough curves for adsorption and desorption processes. Results reveal that the shape of the breakthrough curves is influenced by both hydrodynamic and kinetic factors. Hydrodynamic factor is governed by axial dispersion and is controlled by changes of Peclet number. Simulation results reveal that when linear adsorption isotherm is used, the effect of axial dispersion on breakthrough curves of the system is important for Peclet numbers smaller than 50, whereas, for Langmuir isotherm axial dispersion is considerable for Peclet numbers less than 80. In addition, effects of type of adsorption isotherms and size of adsorbents on breakthrough curves are investigated, and results are compared with existing reports in the pertinent literature. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source]

A posteriori error estimation for convection dominated problems on anisotropic meshes

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 7 2003
Gerd Kunert
Abstract A singularly perturbed convection,diffusion problem in two and three space dimensions is discretized using the streamline upwind Petrov Galerkin (SUPG) variant of the finite element method. The dominant convection frequently gives rise to solutions with layers; hence anisotropic finite elements can be applied advantageously. The main focus is on a posteriori energy norm error estimation that is robust in the perturbation parameter and with respect to the mesh anisotropy. A residual error estimator and a local problem error estimator are proposed and investigated. The analysis reveals that the upper error bound depends on the alignment of the anisotropies of the mesh and of the solution. Hence reliable error estimation is possible for suitable anisotropic meshes. The lower error bound depends on the problem data via a local mesh Peclet number. Thus efficient error estimation is achieved for small mesh Peclet numbers. Altogether, error estimation approaches for isotropic meshes are successfully extended to anisotropic elements. Several numerical experiments support the analysis. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Heat transfer behavior of melting polymers in laminar flow field

POLYMER ENGINEERING & SCIENCE, Issue 3 2004
Sadao Sato
Heat transfer coefficients were investigated by insertion of a probe into melting polymers under laminar flow at 200,240°C and a flow velocity of 0.5,2.7 mm/sec. The average heat transfer coefficients of melting polypropylene (PP) and polystyrene (PS) were found to be 160,220 W/m·°C and 180,270 W/m·°C, respectively. These coefficients show remarkable dependence on flow velocity, and the average heat transfer coefficient of PS is about 13%,23% higher than that of PP. When the flow velocity of flowing melting PP and PS exceeds about 0.078mm/sec, heat transfer by convection becomes dominant, whereas under lower flow velocities, since the equivalent conduction layer thickness ,, in which the quiescent state without flow approaches infinity, heat transfer by conduction becomes dominant. The Prandtl number (Pr) and Nusselt number (Nu) of melting PP are 125,133 × 106 and 38.6,51.4, respectively, and those of melting PS are 63,64 × 106 and 42.3,61.3. In the case of constant flow velocity, the Peclet number (Pe) and Stanton number (St) are dependent on the specific heat of melting polymer. Polym. Eng. Sci. 44:423,432, 2004. © 2004 Society of Plastics Engineers. [source]

The Effects of Surface Waviness and Length on Electrokinetic Transport in Wavy Capillary

THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 1 2006
Noor Quddus
Abstract An electrokinetic model for a wavy capillary has been developed. Poisson-Nernst-Planck and Navier-Stokes equations constitute the model that governs fluid and ionic fluxes and electric potential distribution inside the capillary. In the present paper, a finite wavy cylindrical capillary with a large reservoir at both capillary ends is analyzed using finite element method. The model is used primarily to examine the influence of capillary surface waviness on the electrokinetic transport behaviours. Different frequencies and amplitudes of the wavy surface are considered to investigate the influence of surface waviness on electrokinetic transport. Fluctuations in potential and ionic concentration distribution increase with the increase in either amplitude or frequency of the capillary surface waviness. However, for higher frequencies the fluctuation diminishes for all surface waviness amplitudes. It is observed that for any irregularity in the capillary surface results in higher salt rejection. Salt rejection is found to be dependent on capillary axial length as well as flow velocity. A critical Peclet number, beyond which salt rejection attains a constant steady value, dictates maximum salt rejection. On a mis au point un modèle électrocinétique pour un capillaire onduleux. Les équations de Poisson-Nernst-Planck et de Navier-Stokes constituent le modèle qui gouverne le fluide et les flux ioniques ainsi que la distribution de potentiel électrique dans le capillaire. Dans le présent article, on analyse par la méthode des éléments finis un capillaire cylindrique onduleux fini possédant un grand réservoir aux deux extrémités du capillaire. Le modèle sert principalement à examiner l'influence de l'ondulation de la surface capillaire sur les comportements de transport électrocinétiques. On prend en compte différentes fréquences et amplitudes de la surface onduleuse pour étudier l'influence de l'ondulation de surface sur le transport électrocinétique. Les fluctuations dans la distribution de concentration potentielle et ionique augmentent l'amplitude ou la fréquence d'ondulation de surface capillaire. Toutefois, pour des fréquences plus élevées, la fluctuation diminue pour toutes les amplitudes d'ondulation de surface. On a observé que toute irrégularité dans la surface capillaire entraîne un plus grand rejet de sel. On a trouvé que le rejet de sel était dépendant de la longueur axiale de capillaire ainsi que de la vitesse d'écoulement. Un nombre de Peclet critique, au-delà duquel le rejet de sel atteint une valeur stable constante, dicte le rejet de sel maximum. [source]

Radioisotope tracer study in trickle bed reactors

THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 6 2001
Krishna Deo Prasad Nigam
Abstract The residence time distribution (RTD) of liquid phase in trickle bed reactors has been measured for air-water system using radioisotope tracer technique. Experiments were carried out in a glass column of internal diameter of 0.152 m packed with glass beads and actual catalyst particles of two different shapes. From the measured RTD curves, mean residence time of liquid was calculated and used to estimate liquid holdup. The axial dispersion model was used to simulate the experimental data and estimate mixing index, ie. Peclet number. The effect of liquid and gas flow rates on total liquid holdup and Peclet number has been investigated. Results of the study indicated that shape of the packing has significant effect on holdup and axial dispersion. Bodenstein number has been correlated to Reynolds number, Galileo number, shape and size of the packing. La distribution de temps de séjour (DTS) de la phase dans des réacteurs a lits ruisselants a été measurée pour le système air-eau à d'une technique par traceurs radio-isotopes. Des expériences ont été menées dans une colonne de verre de 0,152 m de diamètre intérieur garnie de billes de verre et de particules de catalyseur réelles de deux formes différentes. à partir des courbes de DTS mesurées, ie temps de séjour moyen du liquide a été calculé puls utilisé pour l'estimation de la rétention de liquide. On a utilisé. On a utilisé le modèl de dispersion axiale afin de simuler les données expérimentales et d'estimer l'indice de mélange, soit le nombre de Peclet. On a étudié l'effet des débits de liquide et de gaz sur la rétention de liquide totale et le nombre de Peclet. Les résultats de l'étude indiquent que la forme du garnissage a un effet significatif sur la rétention et la dispersion axiale. Le nombre de Bodenstein a été corrélé au nombre de Reynolds, au nombre de Galilée, ainsi qu'à la forme et à la taille du garnissage. [source]

Influence of Iron Ore Indirect Reduction on the Transfer Process in Porous Media

ASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING, Issue 3-4 2006
Ming-Chun Li
The solid material used in most metallurgical reactions can be considered as porous media consisting of the accumulated pellets. When the fluid flows through the porous media, various chemical reactions may occur between the fluid and solid matrix which have a significant effect on the transfer process in the porous media. Based on derivation of the overall rate formulation of the representative elementary volume (REV), a mathematical model describing the transfer process in the porous media was established. The model was tested numerically by applying the implicit formulation finite volume method. The predictions were validated by comparison with the experimental results and literature data. For the indirect reduction of iron ores, the influence of the flow rate, the particle size, reaction rate, the dimension of the reactor, and the ratio of the Thielet number to the Peclet number on the distribution of gas concentration and the solid conversion degree were analyzed. [source]

Efficiency of boundary element methods for time-dependent convective heat diffusion at high Peclet numbers

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 4 2005
M. M. Grigoriev
Abstract A higher-order boundary element method (BEM) recently developed by the current authors (Comput Methods Appl Mech Eng 2003; 192: 4281,4298; 4299,4312; 4313,4335) for time-dependent convective heat diffusion in two-dimensions appears to be a very attractive tool for efficient simulations of transient linear flows. However, the previous BEM formulation is restricted to relatively small time step sizes (i.e. ,t,4,/V2) owing to the convergence issues of the time series for the kernel representation within a time interval. This paper extends the boundary element formulation in a way to allow time step sizes several orders of magnitude larger than in the previous approach. We consider an example problem of thermal propagation, and investigate the accuracy and efficiency of BEM formulations for Peclet numbers in the range from 103 to 105. Copyright © 2005 John Wiley & Sons, Ltd. [source]

A transmission line modelling (TLM) method for steady-state convection,diffusion

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2007
Alan Kennedy
Abstract This paper describes how the lossy transmission line modelling (TLM) method for diffusion can be extended to solve the convection,diffusion equation. The method is based on the correspondence between the convection,diffusion equation and the equation for the voltage on a lossy transmission line with properties varying exponentially over space. It is unconditionally stable and converges rapidly to highly accurate steady-state solutions for a wide range of Peclet numbers from low to high. The method solves the non-conservative form of the convection,diffusion equation but it is shown how it can be modified to solve the conservative form. Under transient conditions the TLM scheme exhibits significant numerical diffusion and numerical convection leading to poor accuracy, but both these errors go to zero as a solution approaches steady state. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Quasi-dual reciprocity boundary-element method for incompressible flow: Application to the diffusive,advective equation

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2003
C. F. Loeffler
Abstract This work presents a new boundary-element method formulation called quasi-dual reciprocity formulation for heat transfer problems, considering diffusive and advective terms. The present approach has some characteristics similar to those of the so-called dual-reciprocity formulation; however, the mathematical developments of the quasi-dual reciprocity approach reduces approximation errors due to global domain interpolation. Some one- and two-dimensional examples are presented, the results being compared against those obtained from analytical and dual-reciprocity formulations. The method convergence is evaluated through analyses where the mesh is successively refined for various Peclet numbers, in order to assess the effect of the advective term. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Second-law analysis and optimization of microchannel flows subjected to different thermal boundary conditions

INTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 3 2005
Kuan Chen
Abstract Entropy generation and transfer in microchannel flows were calculated and analyzed for different thermal boundary conditions. Due to the small flow cross-sectional area, fluid temperature variation in the lateral direction was neglected and a laterally lumped model was developed and used in the first- and second-law analyses. Since the Peclet numbers of microchannel flows are typically low, heat conduction in the flow direction was taken into consideration. Computed fluid temperature and entropy generation rate were cast into dimensionless forms, thus can be applied to different fluids and channels of different sizes and configurations. Local entropy generation rate was found to be only dependent upon the temperature gradient in the flow direction. The optimization results of microchannel flows exchanging heat with their surroundings indicate the optimal fluid temperature distribution is a linear one. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Effect of gas evolution on mixing and conversion in a flow-through electrochemical reactor

AICHE JOURNAL, Issue 9 2009
Matthew A. Petersen
Abstract Flow-through electrolytic reactors (FTER) emplaced below the subsurface may be used to control the migration of groundwater contamination away from source zones. During prior studies with FTERs, water electrolysis and associated gas generation have occurred concurrently with contaminant degradation. Gas evolution-induced mixing within the electrode assembly has the potential to impact system performance. A mathematical model of the system was developed to capture the impact of mixing on transport processes in the system. Corresponding transient and steady-state tracer experiments using ferricyanide as a model contaminant were conducted to quantify mixing-dependent parameters and verify modeling results. Over a range of relevant groundwater flowrates, Peclet numbers were between 0.1 and 10, indicating that mixing was a important process under low-flow conditions. Comparison of experiments and model calculations demonstrated that incorporating gas evolution into the model was necessary for accurate performance prediction. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source]