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Transient Stability and Convection in Impulsively Heated Porous Layers

[+] Author Affiliations
M. J. Kohl

Intel Corporation, Phoenix, AZ

M. Kristofferson, F. A. Kulacki

University of Minnesota, Minneapolis, MN

Paper No. HT2005-72023, pp. 235-242; 8 pages
doi:10.1115/HT2005-72023
From:
  • ASME 2005 Summer Heat Transfer Conference collocated with the ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems
  • Heat Transfer: Volume 1
  • San Francisco, California, USA, July 17–22, 2005
  • Conference Sponsors: Heat Transfer Division and Electronic and Photonic Packaging Division
  • ISBN: 0-7918-4731-4 | eISBN: 0-7918-3762-9
  • Copyright © 2005 by ASME

abstract

Experiments are reported on initial instability and convection in a porous medium impulsively 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-to-diameter ratio of 1.9. Heating is accomplished with a constant flux lower surface and a constant temperature upper surface. Results include measurement of the initial transition to convection, overall heat transfer coefficient over a range of Rayleigh-Darcy numbers, and temperature profiles. Time-averaged temperature profiles suggest the existence of a unicellular flow over the range of Rayleigh numbers of the present experiments. 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/(1.08η−0.08η2 ) for 0.02 < η < 0.18. Steady convection in terms of the Nusselt and Rayleigh numbers is represented by a new correlation form,

Nu = 0.047 Ra0.91 Pr0.11 μμ00.72,
where Ra is the Rayleigh-Darcy number, 400 < Ra < 5000, and the viscosity ratio is found sufficient to account for strongly temperature-dependent viscosity.

Copyright © 2005 by ASME
Topics: Stability , Convection

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