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ABSTRACT
A three-dimensional (3D) numerical study has been performed to investigate the effects of non-gray gas radiation on double-diffusive natural convection in a cubic enclosure filled with either air–H2O or air–CO2 mixtures in cooperating situations. Gas radiation was taken into account by the discrete ordinates method (DOM) associated with the spectral line weighted-sum-of-gray-gases (SLW) spectral model. Results obtained for two average concentrations of H2O and CO2 (10% and 20%) show that radiation modifies the temperature and concentration structures by creating oblique stratifications. The heat transfer rate is decreased, whereas mass transfer is not much modified. In addition, a comparison between 2D and 3D results is presented.
Nomenclature
| a | = | weighting coefficient in the SLW model |
| C | = | species concentration, mol/m3 |
| Cabs | = | absorption cross-section m2/mol |
| cp | = | mixture specific heat capacity, J/kg · K |
| D | = | binary mass diffusion coefficient, m2/s |
| g | = | gravitational acceleration, m/s2 |
| I | = | radiation intensity, W/m2 · sr |
| L | = | enclosure length, m |
| Le | = | Lewis number |
| M | = | number of discrete directions |
| N | = | buoyancy ratio |
| Ng | = | number of gray gas |
| Nu | = | Nusselt number |
| P | = | total pressure, Pa |
| qinc | = | incident heat flux at wall, W/m2 |
| qR | = | radiative flux, W/m2 |
| Ra | = | thermal Rayleigh number [ = g βT(TH − TC) L3/(να)] |
| rw | = | given position on the wall |
| s | = | direction of radiation propagation |
| S | = | dimensionless concentration |
| Sh | = | Sherwood number |
| T | = | temperature, K |
| u, v, w | = | velocity components, m/s |
| U, V, W | = | dimensionless velocity components |
| x, y, z | = | space coordinates, m |
| X, Y, Z | = | dimensionless space coordinates |
| xCO2 | = | average molar fraction of CO2 at reference conditions |
| xH2O | = | average molar fraction of H2O at reference conditions |
| α | = | mixture thermal diffusivity, m2/s |
| βC | = | mass expansion coefficient, m3/mol |
| βT | = | thermal expansion coefficient, 1/K |
| ε | = | emissivity of the wall |
| κ | = | absorption coefficient, 1/m |
| λ | = | mixture thermal conductivity, W/m × K |
| θ | = | dimensionless temperature |
| μ,η, ζ | = | direction cosines |
| ν | = | mixture kinematic viscosity, m2/s |
| ρ | = | mixture density, kg/m3 |
| σ | = | Stefan–Boltzmann constant, W/m2 × K4 |
| w | = | weight of angular quadrature |
| Subscript | = | |
| b | = | black body |
| c | = | convective or cold |
| H | = | high |
| h | = | hot |
| i, j, k | = | coordinate indices |
| L | = | low |
| l | = | lth gray gas |
| r | = | radiative quantity |
| t | = | total quantity |
| 0 | = | reference value |
| w | = | wall |
Nomenclature
| a | = | weighting coefficient in the SLW model |
| C | = | species concentration, mol/m3 |
| Cabs | = | absorption cross-section m2/mol |
| cp | = | mixture specific heat capacity, J/kg · K |
| D | = | binary mass diffusion coefficient, m2/s |
| g | = | gravitational acceleration, m/s2 |
| I | = | radiation intensity, W/m2 · sr |
| L | = | enclosure length, m |
| Le | = | Lewis number |
| M | = | number of discrete directions |
| N | = | buoyancy ratio |
| Ng | = | number of gray gas |
| Nu | = | Nusselt number |
| P | = | total pressure, Pa |
| qinc | = | incident heat flux at wall, W/m2 |
| qR | = | radiative flux, W/m2 |
| Ra | = | thermal Rayleigh number [ = g βT(TH − TC) L3/(να)] |
| rw | = | given position on the wall |
| s | = | direction of radiation propagation |
| S | = | dimensionless concentration |
| Sh | = | Sherwood number |
| T | = | temperature, K |
| u, v, w | = | velocity components, m/s |
| U, V, W | = | dimensionless velocity components |
| x, y, z | = | space coordinates, m |
| X, Y, Z | = | dimensionless space coordinates |
| xCO2 | = | average molar fraction of CO2 at reference conditions |
| xH2O | = | average molar fraction of H2O at reference conditions |
| α | = | mixture thermal diffusivity, m2/s |
| βC | = | mass expansion coefficient, m3/mol |
| βT | = | thermal expansion coefficient, 1/K |
| ε | = | emissivity of the wall |
| κ | = | absorption coefficient, 1/m |
| λ | = | mixture thermal conductivity, W/m × K |
| θ | = | dimensionless temperature |
| μ,η, ζ | = | direction cosines |
| ν | = | mixture kinematic viscosity, m2/s |
| ρ | = | mixture density, kg/m3 |
| σ | = | Stefan–Boltzmann constant, W/m2 × K4 |
| w | = | weight of angular quadrature |
| Subscript | = | |
| b | = | black body |
| c | = | convective or cold |
| H | = | high |
| h | = | hot |
| i, j, k | = | coordinate indices |
| L | = | low |
| l | = | lth gray gas |
| r | = | radiative quantity |
| t | = | total quantity |
| 0 | = | reference value |
| w | = | wall |