Transport in Porous Media

, Volume 76, Issue 3, pp 363–375 | Cite as

Experimental Study on Oscillatory Natural Convection in a Hele-Shaw Cell due to Unstably Heated Side

  • A. H. AbdelkareemEmail author
  • S. Kimura
  • T. Kiwata
  • N. Komatsu


The oscillatory motion of natural convection in a porous medium has been investigated experimentally using a Hele-Shaw cell technique. The cell has been heated on the lower half and cooled on the upper half along the same vertical sidewall. Flows have been visualized using the pH indicator method. Photographs of natural convection patterns as well as average Nusselt number data have been presented for different Rayleigh numbers. Oscillatory motion of natural convection has been observed for large enough Rayleigh numbers and the critical Rayleigh number has been estimated to be between 120 and 450. Scaling analysis has been conducted to understand the heat transfer and the oscillating mechanism. According to the scaling analysis, it has been found that the average Nusselt number is proportional to the square root of the Rayleigh number, and that the oscillation frequency is proportional to the Rayleigh number. Obtained experimental data support the scaling analysis.


Natural convection Porous media Geothermal energy Hele-Shaw cell Oscillatory convection 



Cross section area of the cell


Specific heat


Cell gap space


Oscillation frequency


Gravitational acceleration


Cell height




Thermal conductivity


Nusselt number


Positive Integer in Eq. 6


Heat transfer


Ratio of the clamp thickness to the contact length with the copper plate; a/b


Rayleigh number


Width of the acrylic clamps






Cell width

Greek symbols


Thermal diffusivity of porous medium


Thermal expansion coefficient


Vertical boundary layer thickness


Thermal boundary layer thickness


Kinematic viscosity of the fluid


Density of the fluid


Dimensionless time







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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • A. H. Abdelkareem
    • 1
    Email author
  • S. Kimura
    • 2
  • T. Kiwata
    • 2
  • N. Komatsu
    • 2
  1. 1.Department of Mechanical Power EngineeringEl-Minia UniversityEl-MiniaEgypt
  2. 2.Department of Mechanical Systems EngineeringKanazawa UniversityKanazawaJapan

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