## THERMAL SCIENCE

International Scientific Journal

### COMBINED RADIATION-NATURAL CONVECTION IN THREE-DIMENSIONAL VERTICALS CAVITIES

**ABSTRACT**

In this article we studied the effect of radiative transfer and the aspect ratio on the 3D natural convection. Prandtl and Rayleigh numbers are respectively fixed at 13.6 and 105. Equations of natural convection are expressed according the vorticity-stream function formulation. This equations and radiative transfer equation are respectively descritized by volume control method and the FTnFVM. Obtained simulation show that the principal flow structure is considerably modified when the radiation-conduction parameter was varied. However, the peripheral spiraling motion is qualitatively insensitive to these parameters.

**KEYWORDS**

PAPER SUBMITTED: 2010-12-09

PAPER REVISED: 2011-05-01

PAPER ACCEPTED: 2011-07-31

**THERMAL SCIENCE** YEAR

**2011**, VOLUME

**15**, ISSUE

**Supplement 2**, PAGES [S327 - S339]

- Mallinson, G. D., De Vahl Davis, G., Three-dimensional natural convection in a box: a numerical study. J. Fluid Mech. 83 (1977), pp. 1-31.
- Lee, T. S., Son, G. H., Lee, J. S. Numerical predictions of three dimensional natural convection in a box. Proc. 1st KSME-JSME Thermal and Fluid Engineering Conference. 2, (1988), pp. 278-283.
- Hiller, W. J., Koch, S., Kowaleweski, T. A.,. Three-dimensional structures in laminar natural convection in a cubic enclosure. Exp. Thermal. And Fluid Science. 2, (1989), pp. 34-44.
- Hiller, W. J., Koch, S., Kowaleweski, T. A., de Vahl Davis, G., Behnia, M., Experimental and numerical investigation of natural convection in a cube with two heated side walls. Proc. Int. Union of Theoretical and Applied Mechanics Symposium. (1990), pp. 717-726.
- Fusegi, T., Hyun, J. M., Kuwahara, K., Farouk, B., A numerical study of three-dimensional natural convection in a differentially heated cubical enclosure. Int. J. Heat Mass Transfer. 34, (1991), pp. 1543-1557.
- Fusegi, T., Hyun, J. M., Kuwahara, K., A numerical study of 3-D natural convection in a cube: effects of the horizontal thermal boundary conditions. Fluid Dynamics Research. 8, (1991), pp. 221-230.
- Janssen, R. J. A., Henkes, R. A W. M, Hoogendoorn, C. J.,. Transition to time-periodicity of a natural-convection flow in a 3D differentially heated cavity. Int. J. Heat Mass Transfer. 36, (1993), pp. 2927-2940.
- Kowalewski, T. A., Experimental validation of numerical codes in thermally driven flows. Adv. in Computational Heat Transfer, (1998), pp. 1-15.
- Leonardi, E., Kowalewski, T. A., Timchenko, V., De Vahl Davis, G., Effects of finite wall conductivity on flow structures in natural convection. CHMT Cyprus April (1999), pp., 182-188.
- Tric, E., Labrosse, G., Betrouni, M., A first incursion into the 3D structure of natural convection of air in a differentially heated cubic cavity, from accurate numerical solutions. Int. J. Heat Mass Transfer. 43, (2000), pp. 4043-4056.
- Pepper, D. W., Hollands, K. G. T.,. Summary of benchmark numerical studies for 3-D natural convection in an air-filled enclosure. Numerical Heat Transfer, Part A. 42, (2002), 1-11.
- Wakashima, S., Saitoh, T. S., Benchmark solutions for natural convection in a cubic cavity using the high-order time-space method. Int. J. Heat Mass Transfer. 47, (2004), pp. 853-864.
- Le Peutrec, Y., Lauriat, G.,. Effects of the heat transfer at the side walls on natural convection in cavities. J. Heat Transfer. 112, (1990), pp. 370-378.
- Viskanta, R., Kim, D. M., Gau, C., Three-dimensional natural convection heat transfer of a liquid metal in a cavity. Int. J. Heat Mass Transfer. 29, (1986), pp. 475-485.
- Henry, D., Buffat, M., Two and three-dimensional numerical simulations of the transition to oscillatory convection in low-Prandtl fluids. J. of Fluid Mechanics. 374, (1998), pp. 145-171.
- Juel, A., Mulin, T., Ben Hadid, H., Henry, D., Three-dimensional free convection in molten gallium. J. of Fluid Mechanics. 436, (2001), pp. 267-281.
- Piazza, I. D., Ciofalo, M.,. MHD free convection in a liquid-metal filled cubic enclosure. I. Differential heating. Int. J. Heat Mass Transfer. 45, (2002), pp. 1477-1492.
- Kessler, R.,. Nonlinear Transition in Three-Dimensional Convection. J. of Fluid Mechanics. 174, (1987), pp. 357-379.
- Chang, L.C., Yang, K. T., Lioyd, J. R.,. Radiation-natural convection interactions in two-dimensional complex enclosures. J. Heat Transfer.105, (1983), pp. 89-95.
- Yang, K. T., Numerical modelling of natural convection-radiation interactions in enclosures. In Heat Transfer 1986: Proc. Eighth Int. heat Transfer Conf. 1, (1986), pp. 131-140.
- Yucel, A., Acharaya, S., Williams, M. L., Natural convection and radiation in a square enclosure. Numerical. Heat Transfer. 15, (1989), pp. 261-277.
- Fusegi, T., Farouk, B., Laminar and turbulent natural convection-radiation interactions in a square enclosure filled with a nongray gas. Numerical Heat Transfer. 15, (1989), pp. 303-322.
- Tan, Z., Howell, J. R., Combined radiation and natural convection and in a two-dimensional participating square medium. Int. J. Heat Mass Transfer. 34, (1991), pp. 785-793.
- Colomer, G., Costa, M., Cònsul, R., Oliva, A., Three-dimensional numerical simulation of convection and radiation in a differentially heated cavity using the discrete ordinates method. Int. J. Heat Mass Transfer. 47, (2004), pp. 257-269.
- Kobayachi, M., Tsukada, T., Hozawa, M., Effect of internal radiative heat transfer on transition of flow modes in CZ oxide melt, J. Crystal Growth. 208, (2000), pp. 459-465.
- Kim S.H., Huh K. Y. A new angular discretization scheme of the finite volume method for 3-D radiative heat transfer in absorbing, emitting and anisotropically scattering media. Int J Heat Mass Transfer. 43, (2000), pp. 1233-1242.
- Chai J.C., Lee H.S., and Patankar S.V., Finite Volume Method for Radiation Heat Transfer, Journal of Thermophysics and Heat Transfer. 8, (1994), pp. 419-425.