Combined natural convection and radiation with temperature-dependent properties
This paper investigates the effects of temperature dependence of radiative properties of a medium on radiation and natural convection interaction in a rectangular enclosure. The radiative transfer equation is solved using the discrete ordinates method, and the momentum, continuity, and energy equations are solved by the finite volume method. Effects of the conduction-to-radiation parameter, Rayleigh number, and optical thickness are discussed. Results show that temperature dependence of
... pendence of radiative properties affects the temperature gradient, and hence the energy transport even in relatively weak radiation condition. On the other hand, temperature dependence of radiative properties has relatively insignificant effects on convection characteristics, even though it does affect the way that energy transfers into the system. As conduction-to-radiation parameter is decreased or Rayleigh number is increased, the effects of temperature dependence of radiative properties become more significant. Sangapatnam et al.  discussed radiation and mass transfer effects on a MHD free convection problem. The Rosseland approximation were used to handle thermal radiation. Kolsi et al.  studied the effect of the radiation on a transverse spiraling flow in a 3-D vertical cavity. A gray, emitting-absorbing and isotropic scattering fluid was assumed in the cavity. Tsai and Ozisiki  found that the inhomogeneity of a medium greatly affects radiative transfer in a 1-D domain by using the discrete ordinates method. Li et al.  extended their analysis to 2-D cylindrical domain filled with inhomogeneous medium. Farmer and Howell  investigated an anisotropic scattering, non-gray, and inhomogeneous medium in a 3-D rectangular cavity using the Monte-Carlo method. They found the maximum radiative heat flux occurred in the central part near the cold wall. Ruan and Tan  also used the Monte-Carlo method to study the effects of property inhomogeneity due to location and proposed an average method to improve computation speed. Tseng et al.  investigated convection and radiation transfer characteristics in a solar hydrogen production reactor. Ravishankar et al.  solved an inhomogeneous medium problem using modified differential approximation method and compared results with other algorithms. They also studied the effects of inhomogeneity caused by variation of optical thickness. Muthukumaran et al.  numerically analyzed a short-pulse laser on a human tissue phantom. Radiative properties of human tissue was assumed to vary with location. Chu et al.  used the line-by-line approach and the statistical narrow-band correlated-k model to predict the radiative properties of gases. Five test cases were carried out, for an inhomogeneous problem caused by a mixture of different gaseous species. The properties of a mixture do change with its composition. Jin  assumed that the radiative properties varied with the concentration of particle distribution in air and calculated its radiative transfer in a 2-D domain. Meftah et al.  considered real gas properties, and they analyzed the interaction of radiation and double diffusive natural convection with air-CO 2 and air-H 2 O mixtures. Moufekkir et al.  studied combined double-diffusive convection and radiation. In the study, the absorption coefficient is a linear function of local dimensionless concentration. These literatures show that inhomogeneity caused by concentration also affect system thermal characteristics. More recently, Moradi and Rafiee  set-up an 1-D steady-state energy equation to express a fin system with constant moving speed and losing heat. Convection and radiation were considered simultaneously, and a temperature-dependent thermal conductivity was assumed. Moradi et al.  analyzed a triangular porous fin with temperature-dependent thermal conductivity in a convection-radiation system. They used Rosseland approximation to simplify the radiative heat transfer. Sun et al.  studied an irregular fin heat transfer with temperature-dependent internal heat generation and thermal properties. In past studies, the inhomogeneity of a medium was usually assumed to vary with geometry or composition of species. However, the radiative properties may also change with other physical properties like temperature. For a gaseous mixture of CO 2 and N 2 , the absorption of the mixture increases with temperature, although its spectral distribution remains approximately the same  . In addition to gases, solid materials such as glass, have absorption coefficient changing with temperature without changing the spectral distribution characteristics  . The objective of this work is to investigate the effects of inhomogeneity of radiative properties due to temperature variation on thermal and heat transfer characteristics. A rectangular enclosure will be considered and the discrete ordinates method will be employed. Effects of the conduction-to-radiation parameter, Rayleigh number, and optical thickness will also be discussed.