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Abstract
This paper reports on the effect of buoyancy ratio due to both heat and mass transfer on natural convection in a porous enclosure between two isothermal concentric cylinders of rhombic cross sections. For negative values of the buoyancy ratio, buoyancy forces due to heat and mass transfer are in opposite directions (opposing mode), while for positive values they are in the same direction (aiding mode). Numerical results demonstrate that the flow strength increases as the absolute value of the buoyancy ratio increases. In the opposing mode, the eye of the vortex flow is located in the lower half of the enclosure, while in the aiding mode it is positioned in the upper part of the annulus. The average Nusselt and Sherwood number values increase as the absolute value of the buoyancy ratio moves away from 1, with values obtained in the aiding mode being higher than corresponding values achieved in the opposing mode. A comparison is also made between the computed average Nusselt and Sherwood number values and similar ones obtained in a circular annulus having the same inner and outer perimeters as the rhombic enclosure. Predictions indicate large percent difference in values, demonstrating that circular geometries cannot be exploited to accurately predict heat and mass transfer in complex geometries.
NOMENCLATURE
| A | = | wall area |
| cp | = | specific heat at constant pressure |
| dp | = | pores diameter |
| D | = | mass diffusion coefficient |
| Di | = | length of inner pipe's main diagonal |
| Do | = | length of outer pipe's main diagonal |
| Da | = | Darcy number |
| Eg | = | enclosure gap ratio (Eg = 1 − Di/Do) |
| F | = | constant in Forchheimer's extension |
| g | = | gravitational acceleration |
| k | = | fluid thermal conductivity |
| K | = | permeability of the porous media |
| Le | = | Lewis number |
| n | = | unit vector normal to surface |
| N | = | buoyancy ratio |
| Nu | = | local Nusselt number |
| = | average Nusselt number | |
| p | = | dimensional pressure |
| P | = | dimensionless pressure |
| Pr | = | Prandtl number |
| Ra | = | Rayleigh number |
| S | = | dimensional solute concentration |
| Sh | = | local Sherwood number |
| = | average Sherwood number | |
| T | = | dimensional temperature |
| u, U | = | dimensional and dimensionless x-velocity component |
| v, V | = | dimensional and dimensionless y-velocity component |
| x, y | = | dimensional coordinates |
| X, Y | = | dimensionless coordinates |
Greek Symbols
| α | = | thermal diffusivity |
| β | = | volumetric expansion coefficient |
| ϵ | = | porosity |
| θ | = | dimensionless temperature |
| μ | = | dynamic viscosity |
| ρ | = | density |
| σ | = | dimensionless solute concentration |
| ψ | = | stream function |
| Ω | = | rhombus angle |
Subscripts
| c | = | cold wall or convection heat transfer |
| h | = | hot wall |
| i | = | condition at inner pipe |
| o | = | condition at outer pipe |
| S | = | refers to concentration |
| T | = | refers to temperature |
| ∞ | = | refers to a reference value |
Additional information
Notes on contributors
Fadl Moukalled
Fadl Moukalled is a professor of mechanical engineering at the American University of Beirut, Lebanon. He received his Ph.D. in 1987 from Louisiana State University, Baton Rouge, LA. His main research interests are computational fluid dynamics, numerical heat transfer, and finite-time thermodynamics.
Marwan Darwish
Marwan Darwish is currently a professor in the Mechanical Engineering Department of the American University of Beirut, Lebanon. His research interest is in computational fluid dynamics, where he has worked on the development of high-resolution schemes, and in the development of pressure–velocity coupling algorithms for all-speed and multifluid flows.