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ABSTRACT
In this paper, the effects of surface radiation on turbulent natural convection and heat transfer in an enclosure partially filled with a porous medium have been studied numerically. The governing equations for the momentum and thermal energy in both free fluid and porous medium were solved by the finite element method. Effects of thermal radiation on natural convection and heat transfer in both free fluid and porous media were analyzed. It was found that with the increase of Rayleigh number, the convective Nusselt number at the interface between the free fluid and the porous medium increases, and the mean temperature at the interface decreases. Surface thermal radiation can significantly change the temperature fields of free flow. With the increase of surface emissivity, the mean convective Nusselt number at the interface decreases slightly, and the radiative and total Nusselt numbers at the interface increase. The thickness of the porous medium also has a significant effect on heat transfer in the region of free flow, and the convective Nusselt number at the interface decreases with the increase of the ratio of thickness between the porous media and free flow until the ratio is 0.25. Comparing the enclosure with the adiabatic upper wall, the mean temperature at the interface is higher, and the convective Nusselt number at the interface is lower when the upper wall is nonadiabatic.
Nomenclature
| cf | = | specific heat of air, J · kg−1 · K |
| cp | = | specific heat of porous medium, J · kg−1 · K |
| d | = | thickness of porous medium, m |
| Ebi | = | blackbody radiation intensity |
| Fij | = | radiation heat transfer angle coefficients of the ith and jth surfaces |
| g | = | gravity vector, m · s−2 |
| K | = | permeability of porous medium, m2 |
| keff | = | effective thermal conductivity of porous medium, W · m−1 · K−1 |
| kf | = | effective thermal conductivity of air, W · m−1 · K−1 |
| k | = | turbulent kinetic energy, m2 · s−2 |
| p | = | pressure, Pa |
| Pr | = | Prandtl number of air |
| Q | = | surface heat flux |
| Ra | = | Rayleigh number |
| t | = | time, s |
| T | = | temperature, K |
| To | = | reference temperature, K |
| ui | = | component of air velocity in the i th direction, m · s−1 |
| uj | = | component of air velocity in the j th direction, m · s−1 |
| upi | = | component of air velocity in the porous medium in the i th direction, m · s−1 |
| upj | = | component of air velocity in the porous medium in the j th direction, m · s−1 |
| X | = | dimensionless horizontal distance |
| xi, xj | = | Cartesian coordinates, m |
| Greek symbols | = | |
| β | = | volumetric expansion coefficient, K−1 |
| ε | = | dissipation of turbulent kinetic energy, m2 · s−3 |
| εi | = | emissivity of the ith surface |
| θ | = | dimensionless temperature |
| ϕ | = | porosity of the porous medium |
| μ | = | dynamic viscosity, Pa · s |
| ρ | = | density, kg · m−3 |
| ρo | = | air density at To, kg · m−3 |
| Subscripts | = | |
| c | = | cold wall |
| f | = | fluid |
| h | = | hot wall |
| int | = | interface between free fluid and porous medium |
| p | = | porous medium |
Nomenclature
| cf | = | specific heat of air, J · kg−1 · K |
| cp | = | specific heat of porous medium, J · kg−1 · K |
| d | = | thickness of porous medium, m |
| Ebi | = | blackbody radiation intensity |
| Fij | = | radiation heat transfer angle coefficients of the ith and jth surfaces |
| g | = | gravity vector, m · s−2 |
| K | = | permeability of porous medium, m2 |
| keff | = | effective thermal conductivity of porous medium, W · m−1 · K−1 |
| kf | = | effective thermal conductivity of air, W · m−1 · K−1 |
| k | = | turbulent kinetic energy, m2 · s−2 |
| p | = | pressure, Pa |
| Pr | = | Prandtl number of air |
| Q | = | surface heat flux |
| Ra | = | Rayleigh number |
| t | = | time, s |
| T | = | temperature, K |
| To | = | reference temperature, K |
| ui | = | component of air velocity in the i th direction, m · s−1 |
| uj | = | component of air velocity in the j th direction, m · s−1 |
| upi | = | component of air velocity in the porous medium in the i th direction, m · s−1 |
| upj | = | component of air velocity in the porous medium in the j th direction, m · s−1 |
| X | = | dimensionless horizontal distance |
| xi, xj | = | Cartesian coordinates, m |
| Greek symbols | = | |
| β | = | volumetric expansion coefficient, K−1 |
| ε | = | dissipation of turbulent kinetic energy, m2 · s−3 |
| εi | = | emissivity of the ith surface |
| θ | = | dimensionless temperature |
| ϕ | = | porosity of the porous medium |
| μ | = | dynamic viscosity, Pa · s |
| ρ | = | density, kg · m−3 |
| ρo | = | air density at To, kg · m−3 |
| Subscripts | = | |
| c | = | cold wall |
| f | = | fluid |
| h | = | hot wall |
| int | = | interface between free fluid and porous medium |
| p | = | porous medium |
Acknowledgments
The authors also wish to express their appreciation to Shandong Provincial Key Laboratory of Building Energy-Saving Technique and Key Laboratory of Renewable Energy Utilization Technologies in Buildings of the National Education Ministry for providing support for this study.