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ABSTRACT
A numerical study of natural convection with surface and air/H2O mixture radiation in a differentially heated cubic square cavity is presented. The coupled flow and heat transfers in the cavity are predicted by coupling a finite volume method with a spectral line weighted sum of gray gase model to describe gas radiative properties. The radiative transfer equation is solved by means of the discrete ordinate method. Simulations are performed at Ra = 106, considering different combinations of passive wall and/or gas radiation properties and different cavity length. It was found that in presence of a participative medium representative of building, cavity length has a strong influence on temperature and velocity fields which affect the global circulation and heat transfers in the cavity. For each steady-state solution, the convective and radiative contributions to the global heat transfer are discussed. More specifically, boundary layer thickness, thermal stratification parameter, and three-dimensional effects are compared to pure convective case results. The results suggest that radiative effects, often considered as negligible in view of the relatively low optical thickness, may not be neglected when trying to predict regime transitions.
Nomenclature
| aj | = | weighting coefficient associated with the jth fictitious gray gas |
| Cabs | = | absorption cross section (m2/mol) |
| Cp | = | heat capacity (J/kg.K) |
| F | = | black body distribution function |
| = | gravitational field (m/s2) | |
| Gλ | = | spectral incident radiation (W/m2) |
| Iλ | = | spectral intensity (W/m2.sr) |
| Ibλ | = | spectral black body intensity (W/m2.sr) |
| L | = | cubic cavity length (m) |
| Ng | = | total number of fictitious gases |
| = | incident radiative heat flux (W.m2) | |
| R | = | ideal gas constant, R = 8.3144621 (J/K.mol) |
| T0 | = | mean temperature, |
| Uref | = | reference velocity, |
| = | molar fraction of water vapor | |
| Dimensionless numbers | = | |
| Nuc | = | convective Nusselt number, |
| Nur | = | radiative Nusselt number, |
| Pr | = | Prandtl number, |
| Ra | = | Rayleigh number, |
| S | = | dimensionless stratification parameter, |
| T* | = | dimensionless temperature, |
| u*, v*, w* | = | dimensionless velocity components along x, y, and z axis, e.g., |
| x*, y*, z* | = | dimensionless coordinate, e.g., |
| Greek symbols | = | |
| α | = | thermal diffusivity (m2/s) |
| β | = | thermal expansion coefficient, |
| ε | = | emissivity |
| μ, η, ξ | = | direction cosines |
| κj | = | absorption coefficient associated with the jth fictitious gray gas (1/m) |
| λ | = | wavelength (μm) |
| ρ | = | fluid density (kg/m3) |
| σ | = | StefanBoltzmann constant, σ = 5.670367 × 10−8 (W/m2.K4) |
| Ω | = | propagation direction, Ω ∈ [0,4π] |
| Subscripts | = | |
| b | = | black body |
| m | = | number of direction cosine under consideration, m ∈ [1, M] |
| j | = | number of gray gas under consideration, j ∈ [0, Ng] |
| w | = | wall |
Nomenclature
| aj | = | weighting coefficient associated with the jth fictitious gray gas |
| Cabs | = | absorption cross section (m2/mol) |
| Cp | = | heat capacity (J/kg.K) |
| F | = | black body distribution function |
| = | gravitational field (m/s2) | |
| Gλ | = | spectral incident radiation (W/m2) |
| Iλ | = | spectral intensity (W/m2.sr) |
| Ibλ | = | spectral black body intensity (W/m2.sr) |
| L | = | cubic cavity length (m) |
| Ng | = | total number of fictitious gases |
| = | incident radiative heat flux (W.m2) | |
| R | = | ideal gas constant, R = 8.3144621 (J/K.mol) |
| T0 | = | mean temperature, |
| Uref | = | reference velocity, |
| = | molar fraction of water vapor | |
| Dimensionless numbers | = | |
| Nuc | = | convective Nusselt number, |
| Nur | = | radiative Nusselt number, |
| Pr | = | Prandtl number, |
| Ra | = | Rayleigh number, |
| S | = | dimensionless stratification parameter, |
| T* | = | dimensionless temperature, |
| u*, v*, w* | = | dimensionless velocity components along x, y, and z axis, e.g., |
| x*, y*, z* | = | dimensionless coordinate, e.g., |
| Greek symbols | = | |
| α | = | thermal diffusivity (m2/s) |
| β | = | thermal expansion coefficient, |
| ε | = | emissivity |
| μ, η, ξ | = | direction cosines |
| κj | = | absorption coefficient associated with the jth fictitious gray gas (1/m) |
| λ | = | wavelength (μm) |
| ρ | = | fluid density (kg/m3) |
| σ | = | StefanBoltzmann constant, σ = 5.670367 × 10−8 (W/m2.K4) |
| Ω | = | propagation direction, Ω ∈ [0,4π] |
| Subscripts | = | |
| b | = | black body |
| m | = | number of direction cosine under consideration, m ∈ [1, M] |
| j | = | number of gray gas under consideration, j ∈ [0, Ng] |
| w | = | wall |