Convective diffusion to a slowly rotating spherical electrode; The effect of axial diffusion in the bulk liquid for Re 10

1985 ◽  
Vol 50 (4) ◽  
pp. 806-827
Author(s):  
Pavel Mitschka ◽  
Ondřej Wein
Keyword(s):  
Mathematical Model ◽  
Convective Diffusion ◽  
Creeping Flow ◽  
Bulk Liquid ◽  
Axially Symmetric ◽  
Flow Conditions ◽  
Transfer Coefficients ◽  
Axial Diffusion ◽  
Spherical Electrode ◽  
Method Of Solution

A complete mathematical model has been solved of the steady axially symmetric convective diffusion toward the surface of a spherical electrode of radius R rotating at an angular velocity Ω under the creeping flow conditions Re ≡ ΩR2ρ/η < 10 and Pe ≡ Ω2R4ρ/(12Dη) > 10 by the method of singular perturbations. For Pe > 300 the effect of axial diffusion has been found entirely negligible; for 10 < Pe < 300 it causes an increase of local transfer coefficients by 1-10%. For Pe < 10 the applied asymptotic method of solution, assuming Pe >> 1 is no longer applicable.

Convective diffusion to a slowly rotating spherical electrode; Basic model for Re → O, Pe → ∞

1983 ◽  
Vol 48 (6) ◽  
pp. 1571-1578 ◽  
Author(s):  
Ondřej Wein
Keyword(s):  
Boundary Layer ◽  
Flow Regime ◽  
Peclet Number ◽  
Convective Diffusion ◽  
Creeping Flow ◽  
Péclet Number ◽  
Spherical Electrode ◽  
Basic Model ◽  
Boundary Layer Solution ◽  
Layer Solution

Theory has been formulated of a convective rotating spherical electrode in the creeping flow regime (Re → 0). The currently available boundary layer solution for Pe → ∞ has been confronted with an improved similarity description applicable in the whole range of the Peclet number.

Modelling of experiments with colloidal organic matter in biofilm reactors

1994 ◽  
Vol 29 (10-11) ◽  
pp. 479-486 ◽  
Author(s):  
T. A. Larsen ◽  
P. Harremoës
Keyword(s):  
Mathematical Model ◽  
Organic Matter ◽  
Bulk Liquid ◽  
Native Starch ◽  
Trickling Filters ◽  
Biofilm Reactors ◽  
Removal Capacity

A mathematical model for the degradation of colloidal organic matter in biofilm reactors has been developed. Contradictory to existing theories, the model includes bulk liquid hydrolysis as the first important step in the degradation sequence. This leads to unexpected effects of different reactor configurations. The model was successfully verified with native starch as a model substrate. Observed differences in colloid removal capacity between trickling filters and RBC-reactors are well explained by the model.

Modeling of aerated upflow fixed bed reactors for nitrification

1999 ◽  
Vol 39 (4) ◽  
pp. 85-92 ◽  
Author(s):  
J. Behrendt
Keyword(s):  
Mathematical Model ◽  
Mass Transfer ◽  
Liquid Phase ◽  
Gas Phase ◽  
Fixed Bed ◽  
Fixed Bed Reactor ◽  
Bulk Liquid ◽  
Initial Value ◽  
Fixed Bed Reactors ◽  
Number Of Cells

A mathematical model for nitrification in an aerated fixed bed reactor has been developed. This model is based on material balances in the bulk liquid, gas phase and in the biofilm area. The fixed bed is divided into a number of cells according to the reduced remixing behaviour. A fixed bed cell consists of 4 compartments: the support, the gas phase, the bulk liquid phase and the stagnant volume containing the biofilm. In the stagnant volume the biological transmutation of the ammonia is located. The transport phenomena are modelled with mass transfer formulations so that the balances could be formulated as an initial value problem. The results of the simulation and experiments are compared.

On the convective diffusion under partial slip at wall

1989 ◽  
Vol 54 (4) ◽  
pp. 967-980 ◽  
Author(s):  
Ondřej Wein ◽  
Petr Kučera
Keyword(s):  
Mass Transfer ◽  
Numerical Solution ◽  
Analytic Solution ◽  
Convective Diffusion ◽  
Linear Velocity ◽  
Partial Slip ◽  
Accurate Calculation ◽  
Transfer Coefficients ◽  
Empirical Formulas ◽  
Mass Transfer Coefficients

Extended Leveque problem is studied for linear velocity profiles, vx(z) = u + qz. The existing analytic solution is reconsidered and shown to be inapplicable for the accurate calculation of mean mass-transfer coefficients. A numerical solution is reported and its accuracy is checked in detail. Simple but fairly accurate empirical formulas are suggested for the calculating of local and mean mass-transfer coefficients.

scholarly journals Heat Transfer Measurements for Rotating Turbine Discs

1989 ◽  
Author(s):  
G. Qureshi ◽  
M. H. Nguyen ◽  
N. R. Saad ◽  
R. N. Tadros
Keyword(s):  
Heat Transfer ◽  
Coolant Flow ◽  
Flow Conditions ◽  
Transfer Coefficients ◽  
Rotating Disc ◽  
Heat Transfer Coefficients ◽  
Nusselt Numbers ◽  
Rotating Discs ◽  
Turbine Disc ◽  
State Technique

To optimise the turbine disc weight and coolant flow requirements, the aspect of improving thermal analysis was investigated. As a consequence, an experimental investigation was undertaken to measure the rates of convective heat transfer. The constant temperature steady state technique was used to determine the local and average heat transfer coefficients on the sides of rotating discs. The effects of coolant flow rates, CW (3000 ≤ CW ≤ 18600) with two types of cavity in-flow conditions and of the rotational speeds, Reθ (from 4×105 to 1.86×106) on the disc heat transfer were studied and correlations developed. For a rotating disc in confined cavities with superimposed coolant flows, Nusselt numbers were found to be higher than those for the free rotating disc without confinement.

Correlation Between LDA and Ultrasound Heart Catheter Measurements in a Stenosed Arterial Model

1995 ◽  
Vol 117 (1) ◽  
pp. 103-106 ◽  
Author(s):  
D. Liepsch ◽  
A. Poll ◽  
R. Blasini
Keyword(s):  
Cross Section ◽  
Laser Doppler Anemometry ◽  
Water Solution ◽  
Maximum Velocity ◽  
Symmetric Model ◽  
Axially Symmetric ◽  
Flow Conditions ◽  
Future Studies ◽  
Glycerine Water ◽  
Arterial Model

Ultrasound heart catheters are used to measure the velocity in coronary arteries. However, the act of introducing a catheter into the vessel disturbs the very flow being measured. We used laser Doppler anemometry to measure the velocity distribution in an axially symmetric model, both with and without a catheter inserted. The catheter reduced the center-line velocity by as much as 60 percent at a distance of 2 mm downstream from the catheter, and by as much as 25 percent at a distance of 10 mm. This means the velocity measured with an ultrasound catheter does not show the maximum velocity of the undisturbed flow in the tube center. In the constriction, however, the measured velocities with the LDA and ultrasound catheter are almost the same. Thus, catheter measurements in the stenosis achieve accurate results. The velocity profile in the stenosed areas is flattened over nearly the whole cross section. The velocity is extremely reduced only close to the wall. The measurements outside of the stenosis lead to large differences which need to be studied carefully in the future. The disturbed flow finally disappeared 15 mm downstream of the catheter. The measurements were done at steady flow using a glycerine water solution with a dynamic viscosity of 4.35m Pas. In future studies, these experiments will be repeated for pulsatile flow conditions using non-Newtonian blood-like fluids.

scholarly journals Interpolation of Boundary Condition at Time-Interval of Unknown Lenghth for the Problem of Convective Diffusion in a Three-Layered Water Filter

2019 ◽  
pp. 25-28
Author(s):  
Olha Chernukha ◽  
Yurii Bilushchak
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Mass Transfer ◽  
Boundary Condition ◽  
Boundary Value Problem ◽  
Convective Diffusion ◽  
Lower Boundary ◽  
Time Interval ◽  
Water Filter ◽  
The Right

On the basis of mathematical model of convectivediffusion in a three-layered filter it is formulated a contactinitial-boundary value problem for description of mass transferof pollution accompanying the sorption processes. It is proposedthe algorithm for establishing the estimation of values of soughtfunction (concentration of pollution) at the lower boundary of thefilter on the basis of the interpolation of experimental data. It istaken into account that the right end of the interpolation segmentis unknown. It is determined the exact solutions of contact-initialboundaryvalue problems of mass transfer with provision forboth diffusive and convective mechanisms of transfer as well assorption processes, which is based on integral transformationsover space variables in the contacting regions. Is it designedsoftware and established regularities of convective diffusionprocess in the three-layered filter.

scholarly journals DETERMINATION OF CHARACTERISTICS AND SMOKE EXHAUSTERS PARAMETERS IN CONDITIONS OF INDEPENDED AND JOINT WORK WITH OTHER DEVICES BASED ON MATHEMATICAL MODEL

2018 ◽  
Vol 1 (2) ◽  
pp. 10-17
Author(s):  
A Kodryk ◽  
O Titenko ◽  
V Prysiazhniuk ◽  
S Semychaievskyi
Keyword(s):  
Mathematical Model ◽  
Aerodynamic Resistance ◽  
Exhaust System ◽  
Axially Symmetric ◽  
Axial Fan ◽  
Joint Work ◽  
Mixture Flow ◽  
Operating Modes ◽  
Table Data ◽  
Independent Work

The principle of construction and examples of implementation of the developed mathematical model of the smoke exhaust system designed for operational use in case of fire for the elimination of gas pollution and lowering the temperature in the premises. Estimated target features of the installation are based on existing experience, namely: expected aerodynamic airway resistance: 80 Pa and volumetric air mixture flow rate of 3.3 m3/s. The specified characteristics and parameters necessary for the design, or modernization of existing axial fans, and their choice for three operating modes: independent work, joint work with the supply of finely divided water, joint work with the foam generating plant. Simplifications were used in the development of a mathematical model: scheme of the design of the axial fan, which does not involve the presence of a guiding apparatus; it is assumed that the flow in the operating cavity of the pump is axially symmetric; it is assumed that the thermodynamic process taking place in the pump cavity is isothermal; simplified formula of the lifting factor and drag coefficient of the grid is used on the basis of known table data. The mathematical model takes into account: the dimensions of the smoke exhaust system, the number and size of the blades, the angle of attack of the blade, the frequency of rotation, the amount of aerodynamic resistance of the airway, the density and the amount of supply of finely divided water or foam. The examples of the implementation of the developed mathematical model of the smoke exhaust system are illustrated in the form of diagrams of the location of the working points (volume flow of air mixture, m3/s, pressure, Pa; power of the engine of the smoke exhaust system, W) at operation of a smoke exhaust system in the conditions of the average airway for the three above-mentioned operating modes.

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