0
Research Papers

Squeezing Flow of a Power Law Fluid Between Grooved Plates

[+] Author and Article Information
Drew A. Davidson

Department of Mechanical Engineering, State University of New York at Binghamton, Binghamton, NY 13902-6000

Bahgat G. Sammakia

Department of Mechanical Engineering, State University of New York at Binghamton, Binghamton, NY 13902-6000bahgat@binghamton.edu

J. Electron. Packag 131(3), 031007 (Jun 23, 2009) (13 pages) doi:10.1115/1.3144158 History: Received December 08, 2008; Revised March 15, 2009; Published June 23, 2009

Surface microchannels can accelerate squeezing flow of a fluid in a thin gap between parallel plates. Using a computational model and restricting attention to power law fluid, a parametric study is made of the influence of channel size for a certain family of channel patterns, with results tabulated for general use. An approximate heat conduction model is used to estimate the effect of channel size and pattern on resistance to heat flow normal to the fluid layer.

Copyright © 2009 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Fluid flow domain (with simplest surface microchannel pattern shown) showing the geometric nomenclature and the direction of squeezing (indicated by velocity vector V)

Grahic Jump Location
Figure 2

Schematic of surface microchannel pattern

Grahic Jump Location
Figure 3

Schematic of modified Poiseuille flow model of a surface microchannel

Grahic Jump Location
Figure 4

Schematic showing cross section (along line GH in Fig. 3) of a surface microchannel

Grahic Jump Location
Figure 5

Comparison of a numerical solution of Poiseuille flow in a surface microchannel (Eq. 10), with the plane channel limit (Eq. 11) and the analytical solution for a round pipe having diameter equal to the hydraulic diameter of the surface microchannel (Eq. 12)

Grahic Jump Location
Figure 6

Approximate fraction of chip area covered by surface microchannels (β) for the channel pattern diagrammed at lower right

Grahic Jump Location
Figure 7

Pressure contours (one-eighth symmetry domain) given by a numerical solution of squeezing flow of power law fluid between a flat plate and a plate with surface microchannels (channel pattern diagrammed at top left; L/H={1520, 8670, 13,400, 20,700, 76,200}, w/H={1.2,6.8,10.5,16.3,60}, β=.006, and n=.95)

Grahic Jump Location
Figure 8

Contours of wall shear rate (one-eighth symmetry domain) given by a numerical solution of squeezing flow of power law fluid between a flat plate and a plate with surface microchannels (channel pattern diagrammed at top left; L/H={1520, 8670, 13,400, 20,700,76,200}, w/H={1.2,6.8,10.5,16.3,60}, β=.006, and n=.95)

Grahic Jump Location
Figure 9

Magnitude of volumetric flowrate in each surface microchannel (one-eighth symmetry domain shown; the channel pattern is diagrammed at the right) divided by the product of squeezing speed V and chip area (L/H=76,200, w/H=600, β=.06, and n=.95)

Grahic Jump Location
Figure 10

Pressure contours (one-eighth symmetry domain) given by a numerical solution of squeezing flow of power law fluid between a flat plate and a plate with surface microchannels (channel pattern visible as straight black lines in the top left image; L/H={164,403,1604}, w/H={1.3,3.2,12.6}, β=.364, and n=.95)

Grahic Jump Location
Figure 11

Contours of wall shear rate (one-eighth symmetry domain) given by a numerical solution of squeezing flow of power law fluid between a flat plate and a plate with surface microchannels (channel pattern visible as straight black lines in top left image; L/H={164,403,1604}, w/H={1.3,3.2,12.6}, β=.364, and n=.95)

Grahic Jump Location
Figure 12

Magnitude of volumetric flowrate in each surface microchannel (one-eighth symmetry domain shown; the channel pattern is diagrammed at right) divided by the product of squeezing speed V and chip area (L/H=6350, w/H=50, β=.364, and n=.4)

Grahic Jump Location
Figure 13

Dimensionless squeezing force given by a numerical solution of squeezing flow of power law fluid between a flat plate and a plate with surface microchannels. Predictions are shown for six distinct geometries corresponding to two different channel patterns (diagrammed at the upper right), and three different channel sizes (with d=w). For comparison, predictions are also shown for two flat plates and for an appropriate sum of pairs of 45 deg right-triangular flat plates (isolated subplate limit). Power law index n is .4.

Grahic Jump Location
Figure 14

Dimensionless time history of constant-force squeezing flow of power law fluid (Eq. 14) between a flat plate and a plate with surface microchannels, given by a numerical model. Predictions are shown for six distinct geometries corresponding to two different channel patterns (diagrammed at lower right), and three different channel sizes (with d=w). For comparison, predictions are also shown for two flat plates and for an appropriate sum of pairs of 45 deg right-triangular flat plates (isolated subplate limit, Eq. 19). Power law index n is .4.

Grahic Jump Location
Figure 15

Dimensionless squeezing force given by a numerical solution of squeezing flow of power law fluid between a flat plate and a plate with surface microchannels. Predictions are shown for three distinct geometries corresponding to three different channel patterns (diagrammed at the right), each having channel size (with d=w) selected such that channel area fraction β is identical for the three. For comparison, predictions are also shown for two flat plates and for an appropriate sum of pairs of 45 deg right-triangular flat plates (isolated subplate limit). Power law index n is .3.

Grahic Jump Location
Figure 16

Dimensionless time history of constant-force squeezing flow of power law fluid (Eq. 14) between a flat plate and a plate with surface microchannels, given by a numerical model. Predictions are shown for three distinct geometries corresponding to three different channel patterns (diagrammed at the right), each having channel size (with d=w) selected such that channel area fraction β is identical for the three. For comparison, predictions are also shown for two flat plates and for an appropriate sum of pairs of 45 deg right-triangular flat plates (isolated subplate limit, Eq. 19). Power law index n is .3.

Grahic Jump Location
Figure 17

Dimensionless time history of thermal resistance (Eq. 15) for a constant-force squeezing flow of power law fluid between a flat plate and a plate with surface microchannels. Predictions are shown for three distinct geometries corresponding to one channel pattern (diagram at the right) and three different channel sizes (with w=d). For comparison, predictions are also shown for two flat plates and for an isolated subplate limit. Power law index n is .4.

Grahic Jump Location
Figure 18

Dimensionless time history of thermal resistance (Eq. 15) for a constant-force squeezing flow of power law fluid between a flat plate and a plate with surface microchannels. Predictions are shown for three distinct geometries corresponding to one channel pattern (diagram at right) and three different channel sizes (with w=d). For comparison, predictions are also shown for two flat plates and for an isolated subplate limit. Power law index n is .4.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In