Journal of computational fluids engineering (한국전산유체공학회지)

Korean Society of Computational Fluids Engineering (한국전산유체공학회)
권호 표지
DOI QR코드

DOI QR Code

NATURAL CONVECTION BETWEEN TWO HORIZONTAL PLATES WITH SMALL MAGNITUDE NON-UNIFORM TEMPERATURE IN THE LOWER PLATE : Pr=0.7

아래 평판이 미소한 불균일 온도를 갖는 두 수평 평판 사이에서의 자연 대류 : Pr=0.7

  • Yoo, Joo-Sik (Dept. of Mechanical Engineering Education, Andong Nat'l Univ.)
  • 유주식 (안동대학교 기계교육과)
  • Received : 2013.01.01
  • Accepted : 2013.06.14
  • Published : 2013.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

Natural convection of air with Pr=0.7 between two horizontal plates with small magnitude non-uniform temperature distribution[${\in}{\Delta}Tsin({\kappa}X/H)$, H : gap width, X : horizontal coordinate] in the lower plate is numerically(${\in}=0.01$) investigated. In the conduction-dominated regime with $Ra{\leq}1700$, two upright cells are formed over one wave length($2{\pi}/{\kappa}$). For small wave number, the flow becomes unstable with increase of Rayleigh number, and multicellular convection occurs above a critical Rayleigh number. The flow patterns are classified by the number of eddies over one wave length. When ${\kappa}=1$, a transition of $2{\rightarrow}4{\rightarrow}6$ eddy flow occurs with increase of Rayleigh number, and no hysteresis phenomenon is observed. Dual and triple solutions are found for ${\kappa}=1$, and transitions of $10{\rightarrow}8$, $8{\rightarrow}6$, $6{\rightarrow}4{\rightarrow}2$ eddy flow occur with decrease of Rayleigh number.

Keywords

References

  1. 1981, Busse, F.H., "Transition to Turbulence in Rayleigh-Benard Convection," In Topics in Applied Physics, Edited by Swinney, H.L. and Gollub, J.P, Springer-Verlag, Vol.45, pp.97-137.
  2. 1986, Faghri, M. and Asako, Y., "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
  3. 1988, Asako, Y., Hur, N. and Faghri, M., "Heat transfer and pressure drop characteristics in a corrugated duct with rounded corners," Int. J. Heat and Mass Transfer, Vol.31, pp.1237-1245. https://doi.org/10.1016/0017-9310(88)90066-X
  4. 1991, Yoo, J.-S. and Kim, M.-U., "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
  5. 2004, Yoo, J.-S. and Kim Y.-J., "An anomalous bifurcation in natural convection between two horizontal plates with periodic temperatures," (in Korean) Journal of Computational Fluids Engineering, Vol.9, No.4, pp.181-200.
  6. 1984, Poulikakos, D. and Bejan, A., "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
  7. 1996, Bradean, R., Ingham, D.B., Heggs, P.J. and Pop, I., "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
  8. 2003, Yoo, J.-S., "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
  9. 2003, Yoo, J.-S. and Schultz, W.W., "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
  10. 1982, Drazin, P. and Reid, W., Hydrodynamic stability, Cambridge University Press.
  11. 1985, Napolitano, M. and Quartapelle, L., "Block ADI Methods for steady natural convection in two dimensions," in Numerical Methods in Heat and Mass Transfer, Vol.3, John Wiley and Sons.
  12. 1982, Benjamin, T.B. and Mullin, T., "Notes on the multiplicity of flows in the Taylor experiment," J. Fluid Mech., Vol.121, pp.219-230. https://doi.org/10.1017/S0022112082001876
  13. 1985, Nandakumar, K., Masliyah, J.H. and Law, H.S., "Bifurcation in steady laminar mixed convection flow in horizontal ducts," J. Fluid Mech., Vol.152, pp.145-161. https://doi.org/10.1017/S0022112085000611
  14. 1999, Yoo, J.-S., "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.