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The effect of radiation on natural convection of Newtonian fluid contained in an open cavity is investigated in this study. The governing partial differential equations are solved numerically using the Alternate Direct Implicit method together with the Successive Overrelaxation method. The study is focused on studying the flow pattern and the convective and radiative heat transfer rates are studied for different values of radiation parameters, namely, the optical thickness of the fluid, scattering albedo, and the Planck number. It was found that, in the optically thin limit, an increase in the optical thickness of the fluid raises the temperature and radiation heat transfer of the fluid. However, a further increase in the optical thickness decreases the radiative heat transfer rate due to increase in the energy level of the fluid, which ultimately reduces the total heat transfer rate within the fluid.

There are many physical phenomena in which energy exchange due to radiation plays an important role, for instance, heat transfer in furnaces and combustion chambers, solar simulators and the utilization of solar energy, flow of the earth’s mantle, the flow of oxide melts during crystal growth, processing of molten glass, and the solar air receivers. Heat leakage in evacuated spaces, energy dissipation in vacuum tubes, role of air and water as coolant in power plants, and cooling of electronic and optoelectronic devices also involve the energy exchange via radiation. One of the important features of radiation heat transfer is the nature of its dependency on temperature. Review of the radiation models that exist in the literature is given by Siegel and Howell [

In general, the combined mechanism of radiant and convective heat transfer in finite enclosures has received considerable attention. Larson and Viskanta [

Most of the study of natural convection in enclosures has been devoted to the study of streamlines and isotherms. However, the investigation of heat function is also useful in studying the heat transfer characteristics of the phenomenon of natural convection. Kimura and Bejan [

The present study aims to investigate the basic flow pattern and heat transfer characteristics in open ended domain. Since, to author’s knowledge, the study of participating fluids in open ended cavities is not found in literature, such kind of models may have their applications in the situations where heat is rejected via spaces between reflecting surfaces, energy transfer in vacuum tubes, and flow of air and water as coolant in power plants, where heat is mainly rejected via radiation. Thus here we consider the case of combined natural convection and radiation of Newtonian fluid in an open ended cavity, whose left wall is maintained at a higher temperature. The density of fluid with temperature is considered to vary under Boussinesq approximation. Boussinesq approximation is a better choice for laminar case of such fluids. (See also [

Consider two-dimensional flow of a viscous incompressible absorbing/emitting and scattering Boussinesq type fluid confined in an open rectangular cavity formed by the regions between two horizontal planes at

Flow configuration in coordinate system.

Here,

To set up the open end boundary conditions, notice that the velocity component

Heatlines are a measure of the path followed by the heat function across the flow region. Following the formulation of heat function defined by Kimura and Bejan [

The flow is developed by coupling of buoyancy term in (

Average heat transfer rate of the heated wall against time for various grid choices at

Figure

Comparison of (a) streamlines and (b) isotherms. (c) Heat lines with the results of Draoui et al. [

We have considered combined natural convection and radiation phenomena for participating fluid confined in an open square cavity. The left wall is considered at a temperature higher than that of the fluid entering from the ambient region. The effect of relevant radiation parameters, namely, the optical thickness, scattering albedo, and Planck number, on the flow profile and heat transfer rate has been numerically studied. The result is presented graphically in terms of streamlines, isotherms, heatlines, and heat transfer rate for different values of these governing physical parameters.

Figure

Steady state pattern of streamlines for

Isotherms for

Heat lines for

Figure

Average heat transfer rates against various values of optical thickness

Scattering albedo is a measure of radiative participation of the fluid.

Average heat transfer rate against time while

Planck number represents the ratio of conduction to radiation effects on the fluid. The greater the value of

Streamlines for

Heatlines for

Finally Figure

Heat transfer rate as a function of

An investigation of the effect of radiation and natural convection of viscous incompressible fluid in a square open cavity has been carried out. The main focus was the study of flow pattern and heat transfer rates for different values of radiation parameters

It was seen that with the increase in the optical thickness the strength of flow and energy level of the fluid increases, which ultimately results in the negation of heat transfer rate. Convective heat transfer

The total heat transfer is not significantly affected in the range

Both the strength of flow and energy level of the fluid decrease with the increase in Planck number

Aspect ratio

Molar specific heat at constant pressure (JK^{−1})

Acceleration due to gravity (ms^{−2})

Radiant energy Wm^{−2}

Dimensionless radiant energy

Heat function Wm^{−1}

Dimensionless heat function

Mesh spacing

Nodal locations of

The number of grid points in each direction

Coefficient of thermal conductivity (Wm^{−1}K^{−1})

Planck number

Convective Nusselt number

Average convection Nusselt number

Radiation heat transfer

Average radiation heat transfer

Total Nusselt number

Average Nusselt numbers

Fluid pressure (Pa)

Radiant flux Wm^{−2}

Dimensionless radiant flux

Prandtl number

Raleigh number

Dimensional temperature (K)

Maximum and minimum temperature (K)

Average/reference temperature (K)

Dimensional time (s)

Nondimensional time

Velocity components (ms^{−1})

Nondimensional velocity components

Length and height of the cavity (m)

Dimensional coordinate axis (m)

Nondimensional coordinate axis.

Thermal diffusivity

Mean extinction coefficient

Thermal expansion coefficient (K^{−1})

Wall emissivity/absorption

Nondimensional temperature

Dynamic viscosity (m^{−1}s^{−1})

Kinematic viscosity m^{2}s^{−1}Kg^{−1}

Density of fluid (Kgm^{−3})

Stefan-Boltzmann constant Wm^{−2}K^{−4}

Optical thickness

Stream function (m^{2}s^{−1}Kg^{−1})

Nondimensional stream function

Scattering Albedo

Dimensional vorticity function (s^{−1})

Nondimensional vorticity function.

The authors declare that there is no conflict of interests regarding the publication of this paper.

_{1}approximations for modeling buoyant flow of an optically thick fluid