Transactions of the Korean Society of Mechanical Engineers B (대한기계학회논문집B)

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지
DOI QR코드

DOI QR Code

Multiple Solutions for Natural Convection Between Two Horizontal Plates with Periodic Temperatures

주기적인 온도를 갖는 두 수평 평판 사이에서 자연 대류에 대한 다중해

  • 유주식 (안동대학교 기계교육과) ;
  • 김용진 (한국기계연구원 열유체환경연구부)
  • Published : 2004.11.01
Download PDF
⟨ Previous Next ⟩

Abstract

Multiple solutions in natural convection of air (Pr=0.7) between two horizontal walls with mean temperature difference and the same periodic nob-uniformities are investigated. An analytical solution is found for small Rayleigh number, and the general solution is investigated by using a numerical method. In the conduction-dominated regime, two upright cells are formed between two walls over one wave length. When the wave number is small, the flow becomes unstable with increase of the Rayleigh number, and multicellular convection occurs above a critical Rayleigh number. The multicellular flows at high Rayleigh numbers consist of approximately square-shape cells. And several kinds of multiple flows classified by the number of cells are found.

Keywords

References

  1. Zandbergen, P. J. and Dijkstra, D., 1987, 'Von Karman Swirling Flows,' Ann. Rev. Fluid Meeh., Vol. 19, pp. 465-491 https://doi.org/10.1146/annurev.fl.19.010187.002341
  2. Nandakurnar, K., and Masliyah, J. H., 1982, 'Bifurcation in Steady Laminar Flow Through Curved Tubes,' J. Fluid Meeh., Vol. 119, pp. 475-490 https://doi.org/10.1017/S002211208200144X
  3. Benjamin, T. B. and Mullin, T., 1982, 'Notes on the Multiplicity of Flows in the Taylor Experiment,' J. Fluid Meeh., Vol. 121, pp. 219-230 https://doi.org/10.1017/S0022112082001876
  4. Nandakumar, K., Masliyah, J. H. and Law, H. S., 1985, 'Bifurcation in Steady Laminar Mixed Convection Flow in Horizontal Ducts,' J. Fluid Meeh., Vol. 152, pp. 145 -161 https://doi.org/10.1017/S0022112085000611
  5. Yoo, J. S., 1999, 'Prandtl Number Effect on Bifurcation and Dual Solutions in Natural Convection in a Horizontal Annulus,' Int. J. Heat and Mass Transfer, Vol. 42, pp. 3275-3286 https://doi.org/10.1016/S0017-9310(98)00384-6
  6. Watson, A. and Poots, G., 1971, 'The Effect of Sinusoidal Protrusions on Laminar Free Convection Between Vertical Walls,' J. Fluid Mech., Vol. 49, pp. 33-48 https://doi.org/10.1017/S0022112071001915
  7. Faghri, M. and Asako, Y., 1986, 'Periodic, Fully Developed, Natural Convection in a Channel with Corrugated Confining Walls,' Int. J. Heat and Mass Transfer, Vol. 29, pp. 1931-1936 https://doi.org/10.1016/0017-9310(86)90011-6
  8. Asako, Y., Nakamura, H. and Faghri, M., 1988, 'Heat Transfer and Pressure Drop Characteristics in a Corrugated Duct with Rounded Comers,' Int. J. Heat and Mass Transfer, Vol. 31, pp. 1237 -1245 https://doi.org/10.1016/0017-9310(88)90066-X
  9. Yoo, J. S. and Kim, M. U., 1991. 'Two-Dimensional Convection in a Horizontal Fluid Layer with Spatially Periodic Boundary Temperatures,' Fluid Dynamics Research, Vol. 7, pp. 181-200 https://doi.org/10.1016/0169-5983(91)90057-P
  10. Poulikakos, D. and Bejan, A., 1984, 'Natural Convection in a Porous Layer Heated and Cooled Along One Vertical Side,' Int. J. Heat and Mass Transfer, Vol. 27, No. 10, pp. 1879-1891 https://doi.org/10.1016/0017-9310(84)90170-4
  11. Bradean, R., Ingham, D. B., Heggs, P. J. and Pop, I., 1996, 'Buoyancy-Induced Flow Adjacent to a Periodically Heated and Cooled Horizontal Surface in Porous Media,' Int. J. Heat and Mass Transfer, Vol. 39, No.3, pp. 615-630 https://doi.org/10.1016/0017-9310(95)00155-3
  12. Yoo, J. S., 2003, 'Thermal Convection in a Vertical Porous Slot with Spatially Periodic Boundary Temperatures: Low Ra Flow,' Int. J. Heat and Mass Transfer, Vol. 46, No.2, pp. 381-384 https://doi.org/10.1016/S0017-9310(02)00293-4
  13. Yoo, J. S. and Schultz, W. W., 2003, 'Thermal Convection in a Horizontal Porous Layer with Spatially Periodic Boundary Temperatures: Small Ra Flow,' Int. J. Heat and Mass Transfer, Vol. 46, No. 24, pp. 4747 -4750 https://doi.org/10.1016/S0017-9310(03)00300-4
  14. Drazin, P. and Reid, W., 1982, Hydrodynamic Stability, Cambridge University Press
  15. Napolitano, M. and Quartapelle, L., 1985, 'Block AD! Methods for Steady Natural Convection in Two Dimensions,' in Numerical Methods in Heat and Mass Transfer, John Wiley and Sons, Vol. 3