Abstract
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.
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Abbreviations
- A :
-
Cross section area of the cell
- C :
-
Specific heat
- d :
-
Cell gap space
- f :
-
Oscillation frequency
- g :
-
Gravitational acceleration
- H :
-
Cell height
- K :
-
Permeability
- k :
-
Thermal conductivity
- Nu :
-
Nusselt number
- n :
-
Positive Integer in Eq. 6
- q :
-
Heat transfer
- r :
-
Ratio of the clamp thickness to the contact length with the copper plate; a/b
- Ra :
-
Rayleigh number
- w :
-
Width of the acrylic clamps
- T :
-
Temperature
- t :
-
Time
- Y :
-
Cell width
- α :
-
Thermal diffusivity of porous medium
- β :
-
Thermal expansion coefficient
- δ :
-
Vertical boundary layer thickness
- ε :
-
Thermal boundary layer thickness
- ν :
-
Kinematic viscosity of the fluid
- ρ :
-
Density of the fluid
- τ :
-
Dimensionless time
- f:
-
Fluid
- w:
-
Wall
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Abdelkareem, A.H., Kimura, S., Kiwata, T. et al. Experimental Study on Oscillatory Natural Convection in a Hele-Shaw Cell due to Unstably Heated Side. Transp Porous Med 76, 363–375 (2009). https://doi.org/10.1007/s11242-008-9251-7
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DOI: https://doi.org/10.1007/s11242-008-9251-7