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Natural Convection Heat Transfer in Inclined Rectangular Enclosures

경사진 사각형 공간내의 자연대류 열전달

  • 장병훈 (인천대학교 공과대학 기계시스템공학부)
  • Received : 2010.06.30
  • Accepted : 2011.01.25
  • Published : 2011.03.31

Abstract

The laminar natural convection of air in 2-D rectangular enclosure in which two opposing isothermal walls were kept at different temperatures is investigated numerically for Rayleigh number up to $10^6$. Computations were performed for the width-to-height ratios of 1, 2, and 4, and for the inclination angle range of $0^{\circ}{\leq}{\theta}{\leq}90^{\circ}$. For each aspect ratio, the influence of the inclination angle on the flow patterns and heat transfer rates were examined for $10^3{\leq}Ra{\leq}10^6$. It is found that the growth of secondary flow in the corners led to the decrease in overall heat transfer for small aspect ratio case, and the transition from a three-cell structure to a unicell flow pattern in large aspect ratio led to a step-like change in heat transfer. A new correlation of mean Nusselt number is presented for the vertical case of ${\theta}=90^{\circ}$.

본 논문에서는 마주보는 두 벽면들이 서로 다른 온도로 유지되는 2차원 사각형 공간 내 공기의 층류 자연대류를 수치해석 방법을 사용하여 $10^6$의 Rayleigh 수까지 조사하였다. 사각공간의 폭과 높이의 비가 1, 2, 4인 경우와 $0^{\circ}{\leq}{\theta}{\leq}90^{\circ}$의 경사각도 범위에서 계산을 수행하였다. $10^3{\leq}Ra{\leq}10^6$의 범위에서 공간의 경사각도가 유동 구조와 열전달에 미치는 영향을 각 종횡비에 대하여 조사하였다. 작은 종횡비의 경우에는 공간 구석에서 발달되는 2차 유동 셀들이 총괄 열전달의 감소를 초래하는 것으로 나타났으며, 큰 종횡비의 경우에는 3개의 유동 셀이 1개로 전이되는 과정에서 스텝모양과 비슷한 열전달의 급 감소가 일어났다. 수직의 경우인 ${\theta}=90^{\circ}$에 대해서 새로운 평균 Nusselt 수 상관식이 제공되었다.

Keywords

References

  1. Dropkin, D., Somerscales, E.: "Heat transfer by natural convection in liquids confined by two parallel plates which are inclined at various angles with respect to the horizontal", J. Heat Transfer, 77-84, (1965).
  2. Emery, A., Chu, N.C.: "Heat transfer across vertical layers", J. Heat Transfer, 110-116, (1965).
  3. Eckert, E.R.G., Carlson, W.O.: "Natural convection in an air layer enclosed between two vertical plates with different temperatures", Int. J. Heat Mass Transfer, V.2, No.2, 106-120, (1961). https://doi.org/10.1016/0017-9310(61)90019-9
  4. Arnold, J.N., Catton, I., Edwards, D.K.: "Experimental investigation of natural convection in inclined rectangular regions of differing aspect ratio", J. Heat Transfer, 67-70, (1976).
  5. Ozoe, H., Sayama, H., Churchill, S.W.: "Natural convection in an inclined rectangular channel at various aspect ratios and angles-experimental measurements", Int. J. Heat Mass Transfer, V.18, 1425-1431, (1975). https://doi.org/10.1016/0017-9310(75)90256-2
  6. Inaba, H.: "Experimental study of natural convection in an inclined air layer", Int. J. Heat Mass Transfer, V.27, No.8, 1127-1139, (1984). https://doi.org/10.1016/0017-9310(84)90040-1
  7. Hamady, F.J., Lloyd, J.R., Yang, H.Q., Yang, K.T.: "Study of local natural convection heat transfer in a inclined enclosure", Int. J. Heat Mass Transfer, V.32, No.9, 1697-1708, (1989). https://doi.org/10.1016/0017-9310(89)90052-5
  8. Soong, C.Y., Tzeng, P.Y., Chinag, D.C., Sheu, T.S.: "Numerical study on mode-transition of natural convection in differentially heated inclined enclosures", Int. J. Heat Mass Transfer, V.39, No.14, 2869-2882, (1996). https://doi.org/10.1016/0017-9310(95)00378-9
  9. D'Orazio, M.C., Cianfrini, C., Corcione, M.: "Rayleigh-Benard convection in tall rectangular enclosures", Int. J. Thermal Sciences, V.43, 135-144, (2004). https://doi.org/10.1016/j.ijthermalsci.2003.05.002
  10. Corcione, M.: "Effects of the thermal boundary conditions at the sidewalls upon natural convection in rectangular enclosures heated from below and cooled from above", V.42, 199-208, (2003). https://doi.org/10.1016/S1290-0729(02)00019-4
  11. Wang, H., Hamed, M.S.: "Flow mode-transition of natural convection in inclined rectangular enclosures subjected to bidirectional temperature gradients", Int. J. Thermal Sciences, V.45, 782-792, (2006). https://doi.org/10.1016/j.ijthermalsci.2005.07.008
  12. Bairi, A., Laraqi, N., de Maria, J.M.G.: "Numerical and experimental study of natural convection in tilted parallelepipedic cavities for large Raleigh numbers", Experimental Thermal and Fluid Science, V.31, 309-324, (2007). https://doi.org/10.1016/j.expthermflusci.2006.04.017
  13. Ozoe, H., Yamamoto, K., Sayama, H., Churchill, S.: "Natural convection patterns in a long inclined rectangular box heated from below", Int. J. Heat Mass Transfer, V.20, 131-139, (1977). https://doi.org/10.1016/0017-9310(77)90005-9
  14. Concentration, Heat and Momentum Limited, Bakery House, 40 High Street, Wimbledon Village, London SW19 5AU, England.
  15. Spalding, D.B.: "Mathematical modelling of Fluid-mechanics, Heat-transfer and Chemical-reaction Processes", CFDU Report HTS/80/1, Imperial College, London, (1980).
  16. Barakos, G., Mitsoulis, E., Assimacopoulos, D.: "Natural convection flow in a square cavity revisited: laminar and turbulent models with wall functions", Int. J. for Numerical Methods in Fluids, V.18, 695-719, (1994). https://doi.org/10.1002/fld.1650180705
  17. Khanafer, K., Vafai, K., Lightstone, M.: "Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids", Int. J. Heat Mass Transfer, V.46, 3639-3653, (2003). https://doi.org/10.1016/S0017-9310(03)00156-X
  18. De Vahl Davis, G.: "Natural convection of air in a square cavity, a bench-mark numerical solution", Int. J. Numerical Methods in Fluids, V.3, 249-264, (1983). https://doi.org/10.1002/fld.1650030305
  19. Kuyper, R.A., Van der Meer, Th.H., Hoogendoorn, C.J., Henkes, R.A.W.M.: "Numerical study of laminar and turbulent natural convection in an inclined square cavity", Int. J. Heat Mass Transfer, V.36, No.11, 2899-2911, (1993). https://doi.org/10.1016/0017-9310(93)90109-J
  20. Van Leer, B:, "Towards the ultimate conservative difference scheme II", J. Comp. Phys. V.14, 361-370, (1974). https://doi.org/10.1016/0021-9991(74)90019-9
  21. Linthorst, S.J.M., Schinkel, W.M.M., Hoogendoorn, C.J.: "Flow structure with natural convection in inclined air-filled enclosures", J. Heat Transfer, V.103, 535-539, (1981). https://doi.org/10.1115/1.3244498

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