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 |