Abstract
Two thermal adiabatic boundary conditions arise on the semitransparent window (wall made of glass material) owing to the fact that whether semitransparent window allows the energy to leave the system by radiation mode of heat transfer or not. It is assumed that the energy does not leave by the conduction mode of heat transfer, due to the low thermal conductivity of semitransparent material. This does mean that the semitransparent window may behave as only conductive adiabatic or combined conductive and radiative adiabatic In the present work, the above two thermal adiabatic boundary conditions have been investigated for natural convection in a cavity, whose left vertical wall has been divided into upper and lower parts in the ratio 4:6. The upper section is a semitransparent window, while the lower section is an isothermal wall at a temperature of 296 K. A collimated beam is irradiated on the semitransparent window with values 0, 100, 500, and 1,000 at an azimuthal angle 135°. The cavity is heated from the bottom by convective heating with free stream temperature 305 K and heat transfer coefficient 50 While the right wall is also isothermal at the same temperature as of lower left wall and the upper wall is adiabatic. All walls are opaque for radiation except the semitransparent window. The results reveal that the dynamics of both the vortices inside the cavity change drastically with irradiation values and also with the boundary conditions on the semitransparent window. The temperature and Nusselt numbers increase many folds inside the cavity for combined conductive and radiative adiabatic condition than only conductive adiabatic condition on the semitransparent window.
Nomenclature
Acronyms
Cp | = | Specific heat capacity () |
g | = | Acceleration due to gravity () |
G | = | Irradiation () |
H | = | Height (m) |
I | = | Intensity () |
Ib | = | Black body intensity () |
k | = | Thermal conductivity (W/mK) |
L | = | Length of the domain of study (m) |
N | = | Conduction-radiation parameter |
Nu | = | Nusselt number |
p | = | Pressure () |
Pl | = | Planck number |
Pr | = | Prandtl number |
q | = | Flux () |
Ra | = | Rayleigh number |
U | = | Velocity (m) |
bBSF | = | buoyantBoussinesqSimpleFoam |
CAW | = | Conductive adiabatic wall |
CCRAW | = | Combined conductive and radiative adiabatic wall |
Greek symbols
βT | = | Thermal expansion coefficient () |
ϵ | = | Emissivity |
κa | = | Absorption coefficient () |
ρ | = | Density of the fluid () |
τ | = | Optical thickness |
θ | = | Polar angle |
= | Azimuthal angle | |
δ | = | Kronecker delta |
ζ | = | Direction cosine |
Subscripts
C | = | Conduction |
c | = | Cold wall |
co | = | collimated beam |
conv | = | Convection |
f | = | Face center |
free | = | Free stream |
i, j | = | Tensor indices |
nb | = | Neighbour cell |
p | = | Cell center |
R | = | Radiation |
ref | = | Reference |
t | = | Total |
w | = | Wall |
Acknowledgments
The authors greatly acknowledge the financial support provided by Science and Engineering Research Board (SERB) (Statutory Body of the Government of India) via Grant. No: ECR/2015/000327 to carry out the present work
Declaration of interest
The authors declare that they have no known financial interests or personal relationships that could have appeared to influence the work reported in this paper.