## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### Combined natural convection and radiation with temperature-dependent properties

**ABSTRACT**

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 (Nr), Rayleigh number (Ra), and optical thickness are discussed. Results show that temperature dependence 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 Nr is decreased or Ra is increased, the effects of temperature dependence of radiative properties become more significant.

**KEYWORDS**

PAPER SUBMITTED: 2016-02-25

PAPER REVISED: 2016-07-17

PAPER ACCEPTED: 2016-07-21

PUBLISHED ONLINE: 2016-08-07

- Kobayashi, T., Reflected Solar Flux for Horizontally Inhomogeneous Atmospheres, J. Atmos. Sci., 48 (1991), pp. 2436-2447
- Galinsky, V. L., 3D Radiative Transfer in Weakly Inhomogeneous Medium. Part II: Discrete Ordinate Method and Effective Algorithm for Its Inversion, J. Atmos. Sci., 57 (2000), pp. 1635-1645
- Yücel, A., et al., Natural Convection and Radiation in a Square Enclosure, Numer. Heat Tranf. A-Appl., 15 (1989), pp. 261-278
- Tan, Z., Howell, J. R., Combined Radiation and Natural Convection in a Two-dimensional Participating Square Medium, Int. J. Heat Mass Transf., 34 (1991), pp. 785-793
- Colomer, G., et al., Three-dimensional Numerical Simulation of Convection and Radiation in a Differentially Heated Cavity Using the Discrete Ordinates Method, Int. J. Heat Mass Transf., 47 (2004), pp. 257-269
- Sangapatnam, S., et al., Radiation and Mass Transfer Effects on MDH Free Convection Flow Past an Impulsively Started Isothermal Vertical Plate with Dissipation, Therm. Sci., 13 (2009), pp. 171-181
- Kolsi, L., et al., Combined Radiation-Natural Convection in Three-Dimensional Verticals Cavities, Therm. Sci., 15 (2011), pp. 383-390
- Tsai, J. R., Özişik, M. N., Radiation in Cylindrical Symmetry with Anisotropic Scattering and Variable Properties, Int. J. Heat Mass Transf., 33 (1990), 12, pp. 2651-2658
- Li, H. Y., et al., Two-dimensional Radiation in a Cylinder with Spatially Varying Albedo, J. Thermophys. Heat Transf., 6 (1992), 1, pp. 180-182
- Farmer, J. T., et al., Monte Carlo Prediction of Radiative Heat Transfer in Inhomogeneous, Anisotropic, Nongray Media, J. Thermophys. Heat Transf., 8 (1994), 1, pp. 133-139
- Ruan, L. M., Tan, H. P., Solutions of Radiative Heat Transfer in Three-Dimensional Inhomogeneous, Scattering Media, Journal of Heat Transfer, 124 (2002), pp. 985-988
- Tseng, C.-L., et al., Numerical analysis of the solar reactor design for a photoelectrochemical hydrogen production system, Int. J. Hydrogen Energy, 37 (2012), pp. 13053-13059
- Ravishankar, M., et al., Application of the Modified Differential Approximation for Radiative Transfer to Arbitrary Geometry, J. Quant. Spectrosc. Radiat. Transf., 111 (2010), 14, pp. 2052-2069
- Muthukumaran, R., et al., Assessment of Signals from a Tissue Phantom Subjected to Radiation Sources of Temporal Spans of the Order of a Nano-, Pico-, and Femto-Second—A Numerical Study, Numer. Heat Tranf. A-Appl., 60 (2011), 2, pp. 154-170
- Chu, H., et al., Calculations of Gas Radiation Heat Transfer in a Two-dimensional Rectangular Enclosure Using the Line-by-line Approach and the Statistical Narrow-band Correlated-k Model, Int. J. Therm. Sci., 59 (2012), C, pp. 66-74
- Jin, Y.Q., An Approach to Two‐dimensional Vector Thermal Radiative Transfer for Spatially Inhomogeneous Random Media, J. Appl. Phys., 69 (1991), 11, pp. 7594-7600
- Meftah, S., et al., Coupled Radiation and Double Diffusive Convection in Nongray Air-CO2 and Air-H2O Mixtures in Cooperating Situations, Numer. Heat Tranf. A-Appl., 56 (2009), pp. 1-19
- Moufekkir, F., et al., Combined Double-diffusive Convection and Radiation in a Square Enclosure Filled with Semitransparent Fluid, Comput. Fluids, 69 (2012), pp. 172-178
- Moradi, A., Rafiee, R., Analytical Solution to Convection-Radiation of a Continuously Moving Fin with Temperature-Dependent Thermal Conductivity, Therm. Sci., 17 (2013), pp. 1049-1060
- Moradi, A., et al., Convection-Radiation Thermal Analysis of Triangular Porous Fins with Temperature-Dependent Thermal Conductivity by DTM, Energy Conv. Manag., 77 (2014), pp. 70-77
- Sun, Y. S., et al., Application of Collocation Spectral Method for Irregular Convective-Radiative Fins with Temperature-Dependent Internal Heat Generation and Thermal Properties, Int. J. Thermophys., 36 (2015), pp. 3133-3152
- Edwards, D. K., Radiation Interchange in a Non Gray Enclosure Containing an Isothermal CO2-N2 Gas Mixture, Journal of Heat Transfer, 84 (1962), pp. 1-11
- Neuroth, N., Der Einfluss der Temperatur auf die spektrale Absorption von Glasern in Ultraroten, I, Glastechnische Berichte, 25 (1952), pp. 242-249.
- Modest, M. F., Radiative Heat Transfer, 2nd ed. Academic Press, San Diego, USA, 2003
- Patankar, S. V., Numerical Heat Transfer and Fluid Flow. McGraw-Hill, New York, USA, 1980