Effect of Drop Deformation on Heat Transfer to a Drop Suspended in an Electrical Field

1998 ◽  
Vol 120 (3) ◽  
pp. 682-689 ◽  
Author(s):  
M. A. Hader ◽  
M. A. Jog
Keyword(s):  
Nusselt Number ◽  
Steady State ◽  
Heat Transport ◽  
Peclet Number ◽  
Drop Deformation ◽  
Dielectric Fluid ◽  
Electrical Field ◽  
Drop Shape ◽  
Péclet Number ◽  
Internal Problem

Heat transfer to a drop of a dielectric fluid suspended in another dielectric fluid in the presence of an electric field is investigated. We have analyzed the effect of drop deformation on the heat transport to the drop. The deformed drop shape is assumed to be a spheroid and is prescribed in terms of the ratio of drop major and minor diameter. Results are obtained for both prolate and oblate shapes with a range of diameter ratio b/a from 2.0 to 0.5. The internal problem where the bulk of the resistance to the heat transport is in the drop, as well as the external problem where the bulk of the resistance is in the continuous phase, are considered. The electrical field and the induced stresses are obtained analytically. The resulting flow field and the temperature distribution are determined numerically. Results indicate that the drop shape significantly affects the flow field and the heat transport to the drop. For the external problem, the steady-state Nusselt number increases with Peclet number for all drop deformations. For a fixed Peclet number, the Nusselt number increases with decreasing b/a. A simple correlation is proposed to evaluate the effect of drop deformation on the steady-state Nusselt number. For the internal problem, for all drop deformations, the maximum steady-state Nusselt number becomes independent of the Peclet number at high Peclet number. The maximum steady-state Nusselt numbers for an oblate drop are significantly higher than that for a prolate drop.

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.

Analysis of Laminar Slip-Flow Thermal Transport in Microchannels With Transverse Rib and Cavity Structured Superhydrophobic Walls at Constant Heat Flux

2011 ◽  
Author(s):  
D. Maynes ◽  
B. W. Webb ◽  
V. Soloviev
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Laminar Flow ◽  
Thermal Transport ◽  
Peclet Number ◽  
Average Nusselt Number ◽  
Slip Flow ◽  
Constant Heat Flux ◽  
Constant Heat ◽  
Péclet Number

This paper presents an analytical investigation of the thermally developing and periodically fully-developed flow in a parallel-plate channel comprised of superhydrophobic walls. The superhydrophobic walls considered in this paper exhibit alternating micro-ribs and cavities positioned perpendicular to the flow direction and the transport scenario analyzed is that of constant wall heat flux through the rib surfaces with negligible thermal transport through the vapor cavity interface. Axial conduction is neglected in the analysis and the problem is one of Graetz flow with apparent slip-flow and periodicity of constant heating. Closed form solutions for the local Nusselt number and wall temperature are presented and are in the form of infinite series expansions. Previously it has been shown that significant reductions in the overall frictional pressure drop can be expected relative to the classical smooth channel laminar flow. The present results reveal that the overall thermal transport is markedly influenced by the relative cavity region (cavity fraction), the relative rib/cavity module width, and the flow Peclet number. The following conclusions can be made regarding thermal transport for a constant heat flux channel exhibiting the superhydrophobic surfaces considered: 1) Increases in the cavity fraction lead to decreases in the average Nusselt number; 2) Increasing the relative rib/cavity module length yields a decrease in the average Nusselt number; and 3) as the Peclet number increases the average Nusselt number increases. For all parameters explored, the limiting upper bound on the fully-developed average Nusselt number corresponds to the limiting case scenario of classical laminar flow through a smooth-walled channel with constant heat flux.

scholarly journals Particle-size and -density segregation in granular free-surface flows

2015 ◽  
Vol 779 ◽  
pp. 622-668 ◽  
Author(s):  
J. M. N. T. Gray ◽  
C. Ancey
Keyword(s):  
Particle Size ◽  
Steady State ◽  
Parameter Space ◽  
Peclet Number ◽  
Particle Density ◽  
Critical Concentration ◽  
Free Surface Flows ◽  
Size Segregation ◽  
Péclet Number ◽  
Concentration Changes

When a mixture of particles, which differ in both their size and their density, avalanches downslope, the grains can either segregate into layers or remain mixed, dependent on the balance between particle-size and particle-density segregation. In this paper, binary mixture theory is used to generalize models for particle-size segregation to include density differences between the grains. This adds considerable complexity to the theory, since the bulk velocity is compressible and does not uncouple from the evolving concentration fields. For prescribed lateral velocities, a parabolic equation for the segregation is derived which automatically accounts for bulk compressibility. It is similar to theories for particle-size segregation, but has modified segregation and diffusion rates. For zero diffusion, the theory reduces to a quasilinear first-order hyperbolic equation that admits solutions with discontinuous shocks, expansion fans and one-sided semi-shocks. The distance for complete segregation is investigated for different inflow concentrations, particle-size segregation rates and particle-density ratios. There is a significant region of parameter space where the grains do not separate completely, but remain partially mixed at the critical concentration at which size and density segregation are in exact balance. Within this region, a particle may rise or fall dependent on the overall composition. Outside this region of parameter space, either size segregation or density segregation dominates and particles rise or fall dependent on which physical mechanism has the upper hand. Two-dimensional steady-state solutions that include particle diffusion are computed numerically using a standard Galerkin solver. These simulations show that it is possible to define a Péclet number for segregation that accounts for both size and density differences between the grains. When this Péclet number exceeds 10 the simple hyperbolic solutions provide a very useful approximation for the segregation distance and the height of rapid concentration changes in the full diffusive solution. Exact one-dimensional solutions with diffusion are derived for the steady-state far-field concentration.

THE STABILITY OF SPATIALLY NONHOMOGENEOUS STEADY STATES IN A TUBULAR CHEMICAL REACTOR

1993 ◽  
Vol 03 (06) ◽  
pp. 1477-1486
Author(s):  
JAMES M. ROTENBERRY ◽  
ANTONMARIA A. MINZONI
Keyword(s):  
Steady State ◽  
Peclet Number ◽  
Chemical Reactor ◽  
Higher Order ◽  
Steady States ◽  
Complex Conjugate ◽  
Heat Of Reaction ◽  
Péclet Number ◽  
The Stability ◽  
Steady State Solutions

We study the axial heat and mass transfer in a highly diffusive tubular chemical reactor in which a simple reaction is occurring. The steady state solutions of the governing equations are studied using matched asymptotic expansions, the theory of dynamical systems, and by calculating the solutions numerically. In particular, the effect of varying the Peclet and Damköhler numbers (P and D) is investigated. A simple expression for the approximate location of the transition layer for large Peclet number is derived and its accuracy tested against the numerical solution. The stability of the steady states is examined by calculating the eigenvalues and eigenfunctions of the linearized equations. It is shown that a Hopf bifurcation of the CSTR model (i.e., the limit as the P approaches zero) can be continued up to order 1 in the Peclet number. Furthermore, it is shown numerically that for appropriate values of the Peclet number, the Damköhler number, and B (the heat of reaction) these Hopf bifurcations merge with the limit points of an "S–shaped" bifurcation curve in a higher order singularity controlled by the Bogdanov–Takens normal form. Consequently, there must exist a finite amplitude, nonuniform, stable periodic solution for parameter values near this singularity. The existence of higher order degeneracies is also explored. In particular, it is shown for D ≪ 1 that no value of P exists where two pairs of complex conjugate eigenvalues of the steady state solutions can cross the imaginary axis simultaneously.

Heat transport into a shear flow at high Peclet number

1990 ◽  
Vol 427 (1872) ◽  
pp. 25-30
Keyword(s):  
Thermal Diffusivity ◽  
Temperature Distribution ◽  
Shear Flow ◽  
Heat Transport ◽  
Peclet Number ◽  
Asymptotic Form ◽  
Convex Region ◽  
Heated Region ◽  
Péclet Number ◽  
Special Case

Heat transport from a heated convex region on an otherwise insulating plane, into a fluid in shear flow along the plane, is considered. The asymptotic form of the temperature distribution is determined for large values of the Peclet number sL 2 / k where s is the shear rate of the flow, L is a typical dimension of the heated region and k is the thermal diffusivity of the fluid. From it the asymptotic form of the total heat transport is obtained. Although the shape of the region is arbitrary, the solution is constructed by using previous results for the special case of a heated strip with its edges normal to the flow.

scholarly journals Heat transfer from a moving fluid sphere with internal heat generation

2014 ◽  
Vol 18 (4) ◽  
pp. 1213-1222
Author(s):  
Silvia Alexandrova ◽  
Maria Karsheva ◽  
Abdellah Saboni ◽  
Christophe Gourdon
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Heat Generation ◽  
Peclet Number ◽  
Average Nusselt Number ◽  
Viscosity Ratio ◽  
Fluid Sphere ◽  
Péclet Number ◽  
Convection Equation

In this work, we solve numerically the unsteady conduction-convection equation including heat generation inside a fluid sphere. The results of a numerical study in which the Nusselt numbers from a spherical fluid volume were computed for different ranges of Reynolds number (0<Re<100), Peclet number (0<Pe<10000) and viscosity ratio (0<k<10), are presented. For a circulating drop with Re?0, steady creeping flow is assumed around and inside the sphere. In this case, the average temperatures computed from our numerical analysis are compared with those from literature and a very good agreement is found. For higher Reynolds number (0<Re<100), the Navier-Stokes equations are solved inside and outside the fluid sphere as well as the unsteady conduction-convection equation including heat generation inside the fluid sphere. It is proved that the viscosity ratio k (k = ?d/?c) influences significantly the heat transfer from the sphere. The average Nusselt number decreases with increasing k for a fixed Peclet number and a given Reynolds number. It is also observed that the average Nusselt number is increasing as Peclet number increases for a fixed Re and a fixed k.

Low Knudsen Number Heat Transfer From Two Spheres in Contact

1974 ◽  
Vol 96 (4) ◽  
pp. 478-482 ◽  
Author(s):  
F. A. Morrison ◽  
L. D. Reed
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Knudsen Number ◽  
Peclet Number ◽  
Temperature Jump ◽  
Péclet Number

Heat transfer from an acrosol aggregate composed of two touching spheres is investigated analytically. In the range of interest, the Knudsen number is small and the Peclet number negligible. The Nusselt number of a sphere is found to be reduced by the presence of a neighbor and by temperature jump. Expressions for the Nusselt number are obtained.

Effect of Plate Characteristics on Axial Dispersion and Heat Transfer in Plate Heat Exchangers

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
K. Shaji ◽  
Sarit K. Das
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Heat Exchangers ◽  
Peclet Number ◽  
Axial Dispersion ◽  
Outlet Temperature ◽  
Plate Heat ◽  
Péclet Number ◽  
Back Mixing ◽  
Two Fluid

A new mathematical model of single-blow transient testing technique is proposed for the determination of heat transfer and dispersion coefficients in plate heat exchangers (PHEs) in which the flow maldisrtibution effects are separated from the fluid back-mixing. The fluid axial dispersion is used to characterize the back-mixing and other deviations from plug flow. Single-blow experiments are carried out with different number of plates for various flow rates with three different plate geometries of 30 deg, 60 deg, and mixed (30 deg/60 deg) chevron angles. The outlet temperature response to an exponential inlet temperature variation is solved numerically using finite difference method. In the present work, the whole curve matching technique is used to determine the values of Nusselt number and dispersive Peclet number. Since the maldistribution effects are separated, these data are independent of test conditions and hence using a regression analysis, general correlations are developed for Nusselt number and Peclet number of the present plate heat exchangers. The applicability of the single-blow test data is validated using a two-fluid experiment. Two-fluid experiments are conducted on the same plate heat exchanger with smaller and larger number of plates and the results have been compared with its simulation which used the Nusselt number and Peclet number correlations developed by the new model of single-blow test as the inputs.

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