Journal of Energy Engineering (에너지공학)

The Korean Society for Energy (한국에너지학회)
권호 표지
DOI QR코드

DOI QR Code

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
Download PDF
⟨ Previous Next ⟩

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

Cited by

  1. Numerical Simulation of Heat Transfer in Chip-in-Board Package vol.37, pp.1, 2013, https://doi.org/10.3795/KSME-B.2013.37.1.075