Effect of Peclet Number in Thermo-Mechanical Cracking Due to High-Speed Friction Load

1988 ◽  
Vol 110 (2) ◽  
pp. 217-221 ◽  
Author(s):  
F. D. Ju ◽  
J. C. Liu
Keyword(s):  
Tensile Stress ◽  
Peclet Number ◽  
High Speed ◽  
Property Values ◽  
Critical Depth ◽  
Two Dimensional ◽  
Péclet Number ◽  
Parametric Effects ◽  
The Relationship ◽  
Thermal Tensile Stress

The present paper discussed the critical depth, i.e., the depth at which the thermal tensile stress reaches a maximum, caused by the frictional excitation of a fast moving asperity. In the study, the critical depth was computed directly by maximizing the thermal tensile stress with respect to positions under the asperity inside the material. The relationship between critical depth and Peclet number for all materials in the two-dimensional formulation may be simplified to satisfy the exponential form R(ηcr)2.275=20.4368. Stellite III was chosen as the indicator material. Other parametric effects including mechanical properties and thermal properties were tested with materials having diverse property values. These tests confirmed that for the two-dimensional formulation, the Peclet number is the only one which dominates the critical depth.

Numerical Analysis of Heat Transfer Enhancement in a Micro-Channel Due to Mechanical Stirrers

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
M. Sreejith ◽  
S. Chetan ◽  
S. N. Khaderi
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Heat Transfer Enhancement ◽  
Peclet Number ◽  
Periodic Case ◽  
Two Dimensional ◽  
Transfer Enhancement ◽  
Fluidic Channel ◽  
Enhancement Of Heat Transfer ◽  
Péclet Number

Abstract Using two-dimensional numerical simulations of the momentum, mass, and energy conservation equations, we investigate the enhancement of heat transfer in a rectangular micro-fluidic channel. The fluid inside the channel is assumed to be stationary initially and actuated by the motion imparted by mechanical stirrers, which are attached to the bottom of the channel. Based on the direction of the oscillation of the stirrers, the boundary conditions can be classified as either no-slip (when the oscillation is perpendicular to the length of the channel) or periodic (when the oscillation is along the length of the channel). The heat transfer enhancement due to the motion of the stirrers (with respect to the stationary stirrer situation) is analyzed in terms of the Reynolds number (ranging from 0.7 to 1000) and the Peclet number (ranging from 10 to 100). We find that the heat transfer first increases and then decreases with an increase in the Reynolds number for any given Peclet number. The heat transferred is maximum at a Reynolds number of 20 for the no-slip case and at a Reynolds number of 40 for the periodic case. For a given Peclet and Reynolds number, the heat flux for the periodic case is always larger than the no-slip case. We explain the reason for these trends using time-averaged flow velocity profiles induced by the oscillation of the mechanical stirrers.

Steady Temperature in a Rotating Cylinder Subject to Surface Heating and Convective Cooling

1984 ◽  
Vol 106 (1) ◽  
pp. 120-126 ◽  
Author(s):  
B. Gecim ◽  
W. O. Winer
Keyword(s):  
Heat Source ◽  
Peclet Number ◽  
High Speed ◽  
Integral Transform ◽  
The Body ◽  
Cooling Zone ◽  
Dimensionless Numbers ◽  
Péclet Number ◽  
Heating And Cooling ◽  
Simultaneous Heating

This study utilizes an integral transform technique in order to solve the heat conduction equation in cylindrical coordinates. The major assumption is the high speed (i.e., large Peclet number) assumption. The boundary value problem is governed by the parabolic form of the heat equation representing the quasi-stationary state. The boundary conditions are a combination of Neumann and mixed type due to simultaneous heating and cooling on the surface of the cylinder. The surface temperature reaches a peak value over the heat source and gradually decreases to a nearly constant level over the cooling zone. Thermal penetration in the radial direction is shown to be only a few percent of the radius, leaving the bulk of the body at a uniform temperature. The width of the heat source and the total heat input are shown to be effective on the level of temperature whereas the input distribution is shown to be unimportant. The dimensionless numbers involved are the Biot and the Peclet numbers where the solution is governed by the ratio of the Biot number to the square root of the Peclet number.

Laminate Mixing in Micro-Scale Fractal-Like Merging Channel Networks

2003 ◽  
Author(s):  
Kent E. Enfield ◽  
Jeremy J. Siekas ◽  
Deborah V. Pence
Keyword(s):  
Peclet Number ◽  
Concentration Profiles ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Total Flow ◽  
Initial Flow ◽  
Flow Network ◽  
Péclet Number ◽  
Flow Length ◽  
Two Dimensional Model

A two-dimensional model was developed to predict concentration profiles resulting from passive, or diffusive, mixing of laminated layers formed in a fractal-like merging flow network. Both uniform and parabolic velocity profiles were considered in the model. Concentration profiles were experimentally acquired near the top surface of the flow network using laser induced fluorescence. The degree of mixing was assessed from concentration profiles at the end of each channel. Although the degree of mixing from the two-dimensional model well predicts the trend of the experimental degree of mixing, the numerical model under predicts the experimental values by approximately 25 percent. This may be due in part to the presence of top and bottom walls in the experimental device. These walls tend to slow the flow in this region, thereby increasing the residence time and improving the mixing. These top and bottom walls are neglected in the two-dimensional model. For the existing flow network, the degree of mixing is provided as a function of Peclet number. The degree of mixing is further investigated by varying the number of branching levels, the width of the initial flow channels, and the total flow length for a fixed Peclet number. A nondimensional parameter is established that serves as a design tool for predicting an optimum number of branching levels for fixed values of the total flow length, initial branch width and channel depth.

Estimation of capillary reflection coefficients and unique PS products in dog paw

1989 ◽  
Vol 257 (3) ◽  
pp. H1037-H1041 ◽  
Author(s):  
R. K. Reed ◽  
M. I. Townsley ◽  
A. E. Taylor
Keyword(s):  
Total Protein ◽  
Peclet Number ◽  
Reflection Coefficients ◽  
Plasma Protein Concentration ◽  
Linear Portion ◽  
Péclet Number ◽  
Capillary Membrane ◽  
Permeability Surface ◽  
The Relationship ◽  
Ig G

Lymphatic protein flux (Js) obtained in canine hindpaws at low lymph flows were used to determine the capillary osmotic reflection coefficients (sigma d) and unique permeability surface area (PS) products for total proteins, albumin, immunoglobulin (Ig)G, and IgM. This new analysis is based on the phenomenon that when maximal diffusion occurs across the capillary membrane, the Peclet number [x = Jv(1 - sigma d)/PS] attains a unique value defined only by sigma d. The diffusive flux is maximal when the relationship between protein flux and transcapillary fluid flux (Jv) changes from a curvilinear to a linear relationship. The slope of the linear portion of this protein flux relationship was used to determine sigma d as (1 - sigma d) = delta Js/(delta JvCp), where Cp is the plasma protein concentration. With the use of sigma d, the Jv at which the maximal diffusion occurred, and the corresponding Peclet number, a unique value is obtained for the PS product. Experiments performed using lymph from canine hindpaws (n = 6) yielded sigma d's (mean +/- SD) of 0.91 +/- 0.03, 0.83 +/- 0.11, 0.96 +/- 0.03, and virtually 1 for total protein, albumin, IgG, and IgM, respectively. The corresponding PS products for total protein, albumin, and IgG were 25.0 +/- 13.2, 28.4 +/- 6.6, and 14.0 +/- 7.9 microliters.min-1.100 g-1, respectively; PS for IgM was almost zero.(ABSTRACT TRUNCATED AT 250 WORDS)

scholarly journals Optimal mixing in two-dimensional plane Poiseuille flow at finite Péclet number

2014 ◽  
Vol 748 ◽  
pp. 241-277 ◽  
Author(s):  
D. P. G. Foures ◽  
C. P. Caulfield ◽  
P. J. Schmid
Keyword(s):  
Scalar Field ◽  
Poiseuille Flow ◽  
Peclet Number ◽  
Passive Scalar ◽  
Two Dimensional ◽  
Plane Poiseuille Flow ◽  
Péclet Number ◽  
Dimensional Plane ◽  
Scalar Variance ◽  
Optimal Mixing

AbstractWe consider the nonlinear optimisation of the mixing of a passive scalar, initially arranged in two layers, in a two-dimensional plane Poiseuille flow at finite Reynolds and Péclet numbers, below the linear instability threshold. We use a nonlinear-adjoint-looping approach to identify optimal perturbations leading to maximum time-averaged energy as well as maximum mixing in a freely evolving flow, measured through the minimisation of either the passive scalar variance or the so-called mix-norm, as defined by Mathew, Mezić & Petzold (Physica D, vol. 211, 2005, pp. 23–46). We show that energy optimisation appears to lead to very weak mixing of the scalar field whereas the optimal mixing initial perturbations, despite being less energetic, are able to homogenise the scalar field very effectively. For sufficiently long time horizons, minimising the mix-norm identifies optimal initial perturbations which are very similar to those which minimise scalar variance, demonstrating that minimisation of the mix-norm is an excellent proxy for effective mixing in this finite-Péclet-number bounded flow. By analysing the time evolution from initial perturbations of several optimal mixing solutions, we demonstrate that our optimisation method can identify the dominant underlying mixing mechanism, which appears to be classical Taylor dispersion, i.e. shear-augmented diffusion. The optimal mixing proceeds in three stages. First, the optimal mixing perturbation, energised through transient amplitude growth, transports the scalar field across the channel width. In a second stage, the mean flow shear acts to disperse the scalar distribution leading to enhanced diffusion. In a final third stage, linear relaxation diffusion is observed. We also demonstrate the usefulness of the developed variational framework in a more realistic control case: mixing optimisation by prescribed streamwise velocity boundary conditions.

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