scholarly journals Error estimates for transport problems with high Péclet number using a continuous dependence assumption

2017 ◽  
Vol 309 ◽  
pp. 267-286 ◽  
Author(s):  
Erik Burman ◽  
Isaac P. Santos
Keyword(s):  
Error Estimates ◽  
Peclet Number ◽  
Continuous Dependence ◽  
Péclet Number ◽  
Transport Problems ◽  
Dependence Assumption

Approximate analysis of the containment of contaminated sites prior to remediation

2000 ◽  
Vol 42 (1-2) ◽  
pp. 319-324 ◽  
Author(s):  
H. Rubin ◽  
A. Rabideau
Keyword(s):  
Steady State ◽  
Peclet Number ◽  
Dimensionless Parameter ◽  
Contaminated Sites ◽  
Unsteady State ◽  
Péclet Number ◽  
Vertical Barrier ◽  
Time Period ◽  
Barrier Performance ◽  
Vertical Barriers

This study presents an approximate analytical model, which can be useful for the prediction and requirement of vertical barrier efficiencies. A previous study by the authors has indicated that a single dimensionless parameter determines the performance of a vertical barrier. This parameter is termed the barrier Peclet number. The evaluation of barrier performance concerns operation under steady state conditions, as well as estimates of unsteady state conditions and calculation of the time period requires arriving at steady state conditions. This study refers to high values of the barrier Peclet number. The modeling approach refers to the development of several types of boundary layers. Comparisons were made between simulation results of the present study and some analytical and numerical results. These comparisons indicate that the models developed in this study could be useful in the design and prediction of the performance of vertical barriers operating under conditions of high values of the barrier Peclet number.

Convective diffusion toward the sphere in laminar flow around the sphere

1979 ◽  
Vol 44 (4) ◽  
pp. 1218-1238
Author(s):  
Arnošt Kimla ◽  
Jiří Míčka
Keyword(s):  
Laminar Flow ◽  
Velocity Profile ◽  
Peclet Number ◽  
Convective Diffusion ◽  
Péclet Number ◽  
Stability Of The Solution

The problem of convective diffusion toward the sphere in laminar flow around the sphere is solved by combination of the analytical and net methods for the region of Peclet number λ ≥ 1. The problem was also studied for very small values λ. Stability of the solution has been proved in relation to changes of the velocity profile.

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.

Modeling temperature rise in multi-track reciprocating frictional sliding

2021 ◽  
pp. 135065012098823
Author(s):  
Thierry A Blanchet
Keyword(s):  
Temperature Rise ◽  
Peclet Number ◽  
Maximum Temperature ◽  
Uniform Heat Flux ◽  
Heat Accumulation ◽  
Stroke Length ◽  
Péclet Number ◽  
Maximum Temperature Rise ◽  
Rectangular Patch ◽  
Accumulation Effect

As in various manufacturing processes, in sliding tests with scanning motions to extend the sliding distance over fresh countersurface, temperature rise during any pass is bolstered by heating during prior passes over neighboring tracks, providing a “heat accumulation effect” with persisting temperature rises contributing to an overall temperature rise of the current pass. Conduction modeling is developed for surface temperature rise as a function of numerous inputs: power and size of heat source; speed and stroke length, and track increment of scanning motion; and countersurface thermal properties. Analysis focused on mid-stroke location for passes of a square uniform heat flux sufficiently far into the rectangular patch being scanned from the first pass at its edge that steady heat accumulation effect response is adopted, focusing on maximum temperature rise experienced across the pass' track. The model is non-dimensionalized to broaden the applicability of the output of its runs. Focusing on practical “high” scanning speeds, represented non-dimensionally by Peclet number (in excess of 40), applicability is further broadened by multiplying non-dimensional maximum temperature rise by the square root of Peclet number as model output. Additionally, investigating model runs at various non-dimensional speed (Peclet number) and reciprocation period values, it appears these do not act as independent inputs, but instead with their product (non-dimensional stroke length) as a single independent input. Modified maximum temperature rise output appears to be a function of only two inputs, increasing with decreasing non-dimensional values of stroke length and scanning increment, with outputs of models runs summarized compactly in a simple chart.

scholarly journals Effect of temperature gradient on the cross-stream migration of a surfactant-laden droplet in Poiseuille flow

2017 ◽  
Vol 835 ◽  
pp. 170-216 ◽  
Author(s):  
Sayan Das ◽  
Shubhadeep Mandal ◽  
Suman Chakraborty
Keyword(s):  
Temperature Field ◽  
Temperature Gradient ◽  
Poiseuille Flow ◽  
Peclet Number ◽  
Marangoni Number ◽  
Stream Velocity ◽  
Small Surface ◽  
Péclet Number ◽  
Surfactant Transport ◽  
The Cross

The motion of a viscous droplet in unbounded Poiseuille flow under the combined influence of bulk-insoluble surfactant and linearly varying temperature field aligned in the direction of imposed flow is studied analytically. Neglecting fluid inertia, thermal convection and shape deformation, asymptotic analysis is performed to obtain the velocity of a force-free surfactant-laden droplet. The droplet speed and direction of motion are strongly influenced by the interfacial transport of surfactant, which is governed by surface Péclet number. The present study is focused on the following two limiting situations of surfactant transport: (i) surface-diffusion-dominated surfactant transport considering small surface Péclet number, and (ii) surface-convection-dominated surfactant transport considering high surface Péclet number. Thermocapillary-induced Marangoni stress, the strength of which relative to viscous stress is represented by the thermal Marangoni number, has a strong influence on the distribution of surfactant on the droplet surface. The present study shows that the motion of a surfactant-laden droplet in the combined presence of temperature and imposed Poiseuille flow cannot be obtained by a simple superposition of the following two independent results: migration of a surfactant-free droplet in a temperature gradient, and the motion of a surfactant-laden droplet in a Poiseuille flow. The temperature field not only affects the axial velocity of the droplet, but also has a non-trivial effect on the cross-stream velocity of the droplet in spite of the fact that the temperature gradient is aligned with the Poiseuille flow direction. When the imposed temperature increases in the direction of the Poiseuille flow, the droplet migrates towards the flow centreline. The magnitude of both axial and cross-stream velocity components increases with the thermal Marangoni number. However, when the imposed temperature decreases in the direction of the Poiseuille flow, the magnitude of both axial and cross-stream velocity components may increase or decrease with the thermal Marangoni number. Most interestingly, the droplet moves either towards the flow centreline or away from it. The present study shows a critical value of the thermal Marangoni number beyond which the droplet moves away from the flow centreline which is in sharp contrast to the motion of a surfactant-laden droplet in isothermal flow, for which the droplet always moves towards the flow centreline. Interestingly, we show that the above picture may become significantly altered in the case where the droplet is not a neutrally buoyant one. When the droplet is less dense than the suspending medium, the presence of gravity in the direction of the Poiseuille flow can lead to cross-stream motion of the droplet away from the flow centreline even when the temperature increases in the direction of the Poiseuille flow. These results may bear far-reaching consequences in various emulsification techniques in microfluidic devices, as well as in biomolecule synthesis, vesicle dynamics, single-cell analysis and nanoparticle synthesis.

Transient Droplet Heating at High Peclet Number

1983 ◽  
Vol 105 (1) ◽  
pp. 83-88 ◽  
Author(s):  
H. A. Dwyer ◽  
R. J. Kee ◽  
P. K. Barr ◽  
B. R. Sanders
Keyword(s):  
Peclet Number ◽  
Good Accuracy ◽  
Reynolds Numbers ◽  
Adaptive Grids ◽  
Transient Heating ◽  
Low Reynolds Numbers ◽  
Péclet Number ◽  
Future Studies ◽  
Transient Period ◽  
Initial Heating

The transient heating of a spherical liquid particle at high Peclet number has been calculated with the use of adaptive grids for low Reynolds numbers. The use of adaptive grids greatly enhances the efficiency of the calculations and allows for the large Peclet numbers to be studied. The results of the calculations show that the transient period of internal isotherm redistribution represents a significant part of the droplet total heating. Even for the Pe = 1600 case, the initial heating period caused more than 50 percent of particle heating, and the asymptotic heating results cannot be used with good accuracy. The methods employed in the study have great potential, and will be applied to unsteady droplet evaporization and burning in future studies.

Sign in / Sign up

Export Citation Format

Share Document