# Double-diffusive natural convection in a vertical porous annulus

## Abstract

Double-diffusive convection in porous media has been extensively investigated in recent years, owing to its relevance in varied applications. Examples include the dispersion of chemical contaminants through water-saturated soil, the migration of moisture through the air contained in fibrous insulation and grain-storage installations, and the exploitation of continental geothermal reservoirs. Here, a numerical study is carried out on double-diffusive natural convection in a vertical annular porous layer whose vertical walls are at constant temperatures and concentrations. The investigation covers the range 10 {le} R{sub T} {le} 500, 1 {le} Le {le} 10, {minus}50 {le} N {le} 50, 1 {le}A {le} 5, 1 {le} {kappa} {le} 10, where R{sub T}, Le, N, A, and {kappa} are the thermal Rayleigh number, Lewis number, buoyancy ratio, aspect ratio, and radius ratio of the enclosure, respectively. The two extreme cases of heat-driven and solute-driven natural convection correlations, valid in the boundary layer regime, are derived to calculate the average Nusselt and Sherwood numbers in terms of the governing parameters of the problem. In order to investigate the effects of the combined thermal and solutal buoyancy forces on the average heat and mass transfer, results have been obtained for a large range of buoyancy ratiosmore »

- Authors:

- Lab. Materiaux et Sciences des Constructions, Neuville sur Oise (France)
- Univ. of Montreal, Quebec (Canada). Ecole Polytechnique

- Publication Date:

- OSTI Identifier:
- 687452

- Resource Type:
- Journal Article

- Journal Name:
- Numerical Heat Transfer. Part A, Applications

- Additional Journal Information:
- Journal Volume: 36; Journal Issue: 2; Other Information: PBD: 13 Aug 1999

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING NOT INCLUDED IN OTHER CATEGORIES; NATURAL CONVECTION; ANNULAR SPACE; POROUS MATERIALS; NUMERICAL ANALYSIS; ENVIRONMENTAL TRANSPORT; THERMAL INSULATION; GEOTHERMAL SYSTEMS

### Citation Formats

```
Beji, H., Bennacer, R., Duval, R., and Vasseur, P.
```*Double-diffusive natural convection in a vertical porous annulus*. United States: N. p., 1999.
Web.

```
Beji, H., Bennacer, R., Duval, R., & Vasseur, P.
```*Double-diffusive natural convection in a vertical porous annulus*. United States.

```
Beji, H., Bennacer, R., Duval, R., and Vasseur, P. Fri .
"Double-diffusive natural convection in a vertical porous annulus". United States.
```

```
@article{osti_687452,
```

title = {Double-diffusive natural convection in a vertical porous annulus},

author = {Beji, H. and Bennacer, R. and Duval, R. and Vasseur, P.},

abstractNote = {Double-diffusive convection in porous media has been extensively investigated in recent years, owing to its relevance in varied applications. Examples include the dispersion of chemical contaminants through water-saturated soil, the migration of moisture through the air contained in fibrous insulation and grain-storage installations, and the exploitation of continental geothermal reservoirs. Here, a numerical study is carried out on double-diffusive natural convection in a vertical annular porous layer whose vertical walls are at constant temperatures and concentrations. The investigation covers the range 10 {le} R{sub T} {le} 500, 1 {le} Le {le} 10, {minus}50 {le} N {le} 50, 1 {le}A {le} 5, 1 {le} {kappa} {le} 10, where R{sub T}, Le, N, A, and {kappa} are the thermal Rayleigh number, Lewis number, buoyancy ratio, aspect ratio, and radius ratio of the enclosure, respectively. The two extreme cases of heat-driven and solute-driven natural convection correlations, valid in the boundary layer regime, are derived to calculate the average Nusselt and Sherwood numbers in terms of the governing parameters of the problem. In order to investigate the effects of the combined thermal and solutal buoyancy forces on the average heat and mass transfer, results have been obtained for a large range of buoyancy ratios N. Streamlines, isotherms, and isosolutes in the system are produced to illustrate the flow structure transition from mass species dominated opposing to thermal dominated and mass species dominated aiding flows, respectively. The thermal Rayleigh and Lewis numbers and the radius ratio are found to influence the buoyancy ratio at which flow transition and flow reversal occurs.},

doi = {},

journal = {Numerical Heat Transfer. Part A, Applications},

number = 2,

volume = 36,

place = {United States},

year = {1999},

month = {8}

}