Investigation of thermal adiabatic boundary condition on semitransparent wall in combined radiation and natural convection

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 $(q_c=0)$ or combined conductive and radiative adiabatic $(q_c+q_r=0).$ 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 $W/m^2$ 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 $W/m^{2}K.$ 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.

Keywords:

• Collimated beam irradiation
• semitransparent window
• symmetrical cooling
• thermal adiabatic boundaries
• natural convection
• OpenFOAM

Nomenclature

Acronyms

Cp	=	Specific heat capacity ($J/kg-K$)
g	=	Acceleration due to gravity ($m/s^2$)
G	=	Irradiation ($W/m^2$)
H	=	Height (m)
I	=	Intensity ($W/m^2$)
Ib	=	Black body intensity ($W/m^2$)
k	=	Thermal conductivity (W/mK)
L	=	Length of the domain of study (m)
N	=	Conduction-radiation parameter
Nu	=	Nusselt number
p	=	Pressure ($N/m^2$)
Pl	=	Planck number
Pr	=	Prandtl number
q	=	Flux ($W/m^2$)
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 ($1/K$)
ϵ	=	Emissivity
κa	=	Absorption coefficient ($1/m$)
ρ	=	Density of the fluid ($kg/m^3$)
τ	=	Optical thickness
θ	=	Polar angle
$\varphi$	=	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.