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Research Papers: Porous Media

Stability and Convection in Impulsively Heated Porous Layers

[+] Author and Article Information
M. J. Kohl1

Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455

M. Kristoffersen2

Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455mkristoffersen@mmm.com

F. A. Kulacki3

Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455kulacki@me.umn.edu

1

Present address: Intel Corporation, Chandler, AZ 85226.

2

Present address: 3M Company, St. Paul, MN.

3

Corresponding author.

J. Heat Transfer 130(11), 112601 (Aug 28, 2008) (9 pages) doi:10.1115/1.2957484 History: Received June 21, 2007; Revised April 13, 2008; Published August 28, 2008

Experiments are reported on initial instability, turbulence, and overall heat transfer in a porous medium heated from below. The porous medium comprises either water or a water-glycerin solution and randomly stacked glass spheres in an insulated cylinder of height:diameter ratio of 1.9. Heating is with a constant flux lower surface and a constant temperature upper surface, and the stability criterion is determined for a step heat input. The critical Rayleigh number for the onset of convection is obtained in terms of a length scale normalized to the thermal penetration depth as Rac=83/(1.08η0.08η2) for 0.02<η<0.18. Steady convection in terms of the Nusselt and Rayleigh numbers is Nu=0.047Ra0.91Pr0.11(μ/μ0)0.72 for 100<Ra<5000. Time-averaged temperatures suggest the existence of a unicellular axisymmetric flow dominated by upflow over the central region of the heated surface. When turbulence is present, the magnitude and frequency of temperature fluctuations increase weakly with increasing Rayleigh number. Analysis of temperature fluctuations in the fluid provides an estimate of the speed of the upward moving thermals, which decreases with distance from the heated surface.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Determination of transition to convection for water and 6 mm DIA glass spheres. Applied heat flux is q0m=683.9 W/m2. (—) Conduction solution; (- - -) regression fit.

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Figure 2

Transition Rayleigh numbers in terms of normalized penetration depth. Thermal conductivity is evaluated as kA, and viscosity is evaluated at the porous medium average temperature. (◼) water-glass; (▲) glycerin-water-glass; (–––) Eq. 4; (- - -) Eq. 1.

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Figure 3

Transition Rayleigh numbers scaled to penetration depth with uncertainty band on average value of 83. (●) water-glass; (▲) glycerin-water-glass; (- - -) linear stability theory.

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Figure 4

Steady state Nusselt numbers and correlation, Eq. 5

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Figure 5

Temperature traces for the water-glass porous medium along the centerline for the first 5000 s after the start of heating. Ra≈2700.

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Figure 6

Radial temperature distribution for steady convection with glycerin-water solution and an applied heat flux of ∼900 W/m2. Measurements are made at z=3 cm(z/H=0.078). Properties are evaluated at 293 K. (◼) Ra=414. (●) Ra=429.

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Figure 7

Radial temperature distribution for steady convection with water and an applied heat flux of 1550 W/m2. Measurements are made 3 cm above lower surface, z/H=0.078. Properties are evaluated at 293 K. (◻) Ra=512. (○) Ra=525.

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Figure 8

Centerline temperatures averaged over 5000 s intervals at Ra≈2700. For 0<t<5000 s, flow develops from initial conduction transient to turbulent flow. For t>60,000 s, steady turbulent flow is observed. Temperatures profiles generally exhibit a reversal at midheights for t>35,000 s.

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Figure 9

rms fluctuating temperatures at z/H=0.078. (a) (●) r/r0=0 and (–––) regression line. (b) (●) r/r0=0.366 and (–––) regression line. (◼) r/r0=0.070 and (- - -) regression line.

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