Abstract    The interaction of thermal radiation with conduction and laminar natural convection in a vertical circular pin, situated at participating gas, is numerically investigated. An absorbing and emitting gas is considered, and treated to be a gray participating media. Under the idealizing of gray gas, the Rosselan4 approximation is employed to describe the radiative heat flux in the energy equation. The modified box method with unequal grid spacing is used to perform the numerical computation of the coupled boundary layer conservation equations and pin conduction equation. The effects of buoyancy and radiation on the temperature, velocity, heat flux, and Nusselt number are examined in detail. The Nusselt number variation shows that heat transfer is enhanced by thermal radiation. Also, the local Nusselt number is found to be strongly dependent on the temperature ratio YT, radiation-conduction parameter YR, and conventional Gr and Pr numbers. Furthermore, the results are comparable with the available data in the literature for pure natural convection.

Keywords    Natural convection, Conduction, Radiation, Participating Media, Heat Transfer, Finite Difference, Circular Pin

References    1. E. M. Sparrow and S. Acharya, "A Natural Convection Fin with a Solution-Determined Nonmontonically Varying Heat Transfer Coefficient," ASME Journal of Heat Transfer, Vol. 103, (1981), 218-225. 2. Sparrow, E. M. and Chyu, M. K. "Conjugate Forced Convection-conduction Analysis of Heat Transfer in a Plate Fin"; ASME Journal of Heat Transfer, Vol. 104, (1982), 204-206. 3. Samara, P. K. and Subrahmanyam, T. "Turbulent Free Convection from a Radiating Vertical Surface Situated in Air-A Conjugate Problem"; Int. Comm. Heat Mass Transfer, Vol. 16, (1989), 883-894. 4. Hsu, T. H. and Tsai, S. Y. "Thermal Response of a Heated Vertical Plate Fin with Natural Convection-Radiation Interaction," Numerical Heat Transfer, Part A, Vol. 22, (1992), 307-322. 5. Huang, M. J. and Chen, C. K. "Vertical Circular Pin with Conjugate Forced Convection-Conduction Flow"; ASME Journal of Heat Transfer, Vol. 106, (1984), 658-661. 6. Huang, M. J., Chen, C. K. and Cleaver, J. W. "Vertical Circular Pin with Conjugated Natural Convection-Conduction Flow"; ASME Journal of Heat Transfer, Vol. 107, (1985), 242-245. 7. Lee, H. R., Chen, T. S. and Armaly, B. F. "Natural Convection Along Slender Vertical Cylinders with Variable Surface Temperature"; ASME Journal of Heat Transfer, Vol. 110, (1988), 103-108. 8. Tsai, J. R., Ozisik, M. N. "Combined Convection and Radiation in Participating Laminar Flow inside a Parallel-Plate Duct with Flux Boundary Condition"; Int. Comm. Heat Mass Transfer, Vol. 16, (1989), 861-874. 9. Yang, L. K. "Combined Mixed Convection and Radiation in a Vertical Pipe"; Int. Comm. Heat Mass Transfer, Vol. 18, (1991), 419-430. 10.Yang, L. K. "Forced Convection in a Vertical Pipe with Combined Buoyancy and Radiation Effects"; Int. Comm. Heat Mass Transfer, Vol. 19, (1992), 249-262. 11. Yang, G., Ebadian, M. A. and Campo, A. "A Numerical Study of Convective and Radiative Transfer in Ducts of Rectangular and Equilateral Cross Sections"; Int. J. Heat Mass Transfer, Vol. 34, No. 4/5, (1991), 1319-1322. 12. Dong, Z. F. and Ebadian, M. A. "Convective and Radiative Heat Transfer in the Entrance Region of an Elliptic Duct with Fins," Numerical Heat Transfer, Part A, Vol. 21, (1992), 91-107. 13. Balaji, C. and Venkanteshan, S. P. "Natural Convection in L Corners with Surface Radiation and Conduction," ASME Journal of Heat Transfer, Vol. 118, (1996), 222-225. 14. Dehghan, A. A. and Behnia, M. "Combined Natural Convection-Conduction and Radiation Heat Transfer in a Discretely Heated Open Cavity"; ASME Journal of Heat Transfer, Vol. 118, (1996), 56-64. 15. Viskanta, R. "Radiation Heat Transfer: Interaction with Conduction and Convection and Approximate Methods in Radiation"; Proc. 7th Int. Heat Transfer Conf., Grigull, U., Hahne, E., Stephen, K. and J. Straub, eds., Vol. 1, (1982), 103-122.