Abstract
Conjugate natural convection-conduction heat transfer in a square porous enclosure with a finite-wall thickness is studied numerically in this article. The bottom wall is heated and the upper wall is cooled while the verticals walls are kept adiabatic. The Darcy model is used in the mathematical formulation for the porous layer and the COMSOL Multiphysics software is applied to solve the dimensionless governing equations. The governing parameters considered are the Rayleigh number (100 ≤ Ra ≤ 1000), the wall to porous thermal conductivity ratio (0.44 ≤ K r ≤ 9.90) and the ratio of wall thickness to its height (0.02 ≤ D ≤ 0.4). The results are presented to show the effect of these parameters on the heat transfer and fluid flow characteristics. It is found that the number of contrarotative cells and the strength circulation of each cell can be controlled by the thickness of the bottom wall, the thermal conductivity ratio and the Rayleigh number. It is also observed that increasing either the Rayleigh number or the thermal conductivity ratio or both, and decreasing the thickness of the bounded wall can increase the average Nusselt number for the porous enclosure.
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Abbreviations
- d, D:
-
Wall thickness, dimensionless wall thickness
- g :
-
Gravitational acceleration
- K :
-
Permeability of the porous medium
- K r :
-
Thermal conductivity ratio
- k p :
-
Effective thermal conductivity of porous medium
- k w :
-
Thermal conductivity of wall
- L :
-
Width and height of enclosure
- \({\overline{Nu}}\) :
-
Average Nusselt number
- Ra :
-
Rayleigh number
- T :
-
Temperature
- u, v:
-
Velocity components in the x- and y-directions
- x, y and X, Y:
-
Space coordinates and dimensionless space coordinates
- α :
-
Effective thermal diffusivity
- β :
-
Thermal expansion coefficient
- ψ, Ψ:
-
Stream function, dimensionless stream function
- Θ:
-
Dimensionless temperature
- ν :
-
Kinematic viscosity
- c:
-
Cold
- h:
-
Hot
- max:
-
Maximum
- p:
-
Porous
- w:
-
Wall
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Saleh, H., Saeid, N.H., Hashim, I. et al. Effect of Conduction in Bottom Wall on Darcy–Bénard Convection in a Porous Enclosure. Transp Porous Med 88, 357–368 (2011). https://doi.org/10.1007/s11242-011-9743-8
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DOI: https://doi.org/10.1007/s11242-011-9743-8