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ABSTRACT
This paper reports on natural convection heat transfer in a porous annulus between concentric horizontal circular and square cylinders. The heated inner circular cylinder is maintained at the uniform hot temperature Th, whereas the cooled outer square duct is held at the uniform cold temperature Tc. A pressure-based collocated finite-volume method is used to numerically investigate the effects on the total heat transfer of Rayleigh number (Ra), Prandtl number (Pr), Darcy number (Da), porosity (ϵ), and annulus aspect ratio (R/L). Results demonstrate that at low Ra values, conduction is the dominant heat transfer mode. Convection contribution to total heat transfer becomes more important beyond a critical Ra value, which decreases with an increase in Da and/or ϵ. Furthermore, an increase in the enclosure aspect ratio (R/L) leads to an increase in total heat transfer. A similar behavior is obtained with Prandtl number, where predictions indicate higher heat transfer rates at higher Pr values with its effect increasing as Ra increases. Streamlines and isotherms reveal flow separation for some of the reported cases. Limited computations are also performed for natural convection in a porous annulus between two horizontal concentric circular cylinders having the same inner and outer perimeters as the investigated enclosure. Comparison of the predicted average Nusselt number estimates with similar ones obtained in the original enclosure reveals a large percentage difference in values, demonstrating the strong influence of geometry on natural convection in enclosures.
Nomenclature
| cp | = | specific heat of fluid at constant pressure |
| dp | = | pore diameter |
| Da | = | Darcy number |
| F | = | constant in Forchheimer’s extension |
| g | = | gravitational acceleration |
| j | = | unit vector along the y-axis |
| k | = | thermal conductivity of fluid |
| K | = | permeability of the porous media |
| L | = | width of the square duct |
| n | = | unit vector normal to the surface |
| Nu | = | local Nusselt number |
| = | average Nusselt number | |
| p | = | dimensional pressure |
| P | = | dimensionless pressure |
| Pr | = | Prandtl number |
| R | = | radius of the cylinder |
| Ra | = | Rayleigh number |
| Si, So | = | distance along the inner and outer enclosure surfaces |
| T | = | dimensional temperature |
| u, U | = | dimensional and dimensionless x-velocity component |
| v, V | = | dimensional and dimensionless y-velocity component |
| v, V | = | dimensional and dimensionless velocity vector |
| x, y | = | dimensional coordinates |
| X, Y | = | dimensionless coordinates |
| α | = | thermal diffusivity |
| β | = | thermal expansion coefficient |
| μ | = | dynamic viscosity |
| ν | = | kinematic viscosity |
| ρ | = | density |
| θ | = | dimensionless temperature |
| ϵ | = | porosity |
| ψ | = | stream function |
| Subscripts | = | |
| c | = | cold wall |
| h | = | hot wall |
| i | = | condition at inner surface |
| o | = | condition at outer surface |
Nomenclature
| cp | = | specific heat of fluid at constant pressure |
| dp | = | pore diameter |
| Da | = | Darcy number |
| F | = | constant in Forchheimer’s extension |
| g | = | gravitational acceleration |
| j | = | unit vector along the y-axis |
| k | = | thermal conductivity of fluid |
| K | = | permeability of the porous media |
| L | = | width of the square duct |
| n | = | unit vector normal to the surface |
| Nu | = | local Nusselt number |
| = | average Nusselt number | |
| p | = | dimensional pressure |
| P | = | dimensionless pressure |
| Pr | = | Prandtl number |
| R | = | radius of the cylinder |
| Ra | = | Rayleigh number |
| Si, So | = | distance along the inner and outer enclosure surfaces |
| T | = | dimensional temperature |
| u, U | = | dimensional and dimensionless x-velocity component |
| v, V | = | dimensional and dimensionless y-velocity component |
| v, V | = | dimensional and dimensionless velocity vector |
| x, y | = | dimensional coordinates |
| X, Y | = | dimensionless coordinates |
| α | = | thermal diffusivity |
| β | = | thermal expansion coefficient |
| μ | = | dynamic viscosity |
| ν | = | kinematic viscosity |
| ρ | = | density |
| θ | = | dimensionless temperature |
| ϵ | = | porosity |
| ψ | = | stream function |
| Subscripts | = | |
| c | = | cold wall |
| h | = | hot wall |
| i | = | condition at inner surface |
| o | = | condition at outer surface |