Korean Journal of Air-Conditioning and Refrigeration Engineering (설비공학논문집)

The Society of Air-Conditioning and Refrigerating Engineers of Korea (대한설비공학회)
권호 표지
DOI QR코드

DOI QR Code

The Effect of Variation in Angle of the Elliptic Cylinder on Natural Convection in a Square Enclosure

타원형 실린더의 각도 변화가 사각 밀폐계 내부의 자연대류 현상에 미치는 영향

  • Son, Yong Jin (School of Mechanical Engineering, Pusan National University) ;
  • Ha, Man Yeong (School of Mechanical Engineering, Pusan National University)
  • Received : 2017.09.19
  • Accepted : 2017.12.07
  • Published : 2018.02.10
Download PDF
⟨ Previous Next ⟩

Abstract

This study investigated the effect of variation in the angle of the elliptic cylinder as well as the presence of circular cylinder on natural convection inside a square enclosure. The Rayleigh number was varied between $10^3$ and $10^6$, and the Prandtl number was fixed to 0.7. In the present study, the angle of the elliptic cylinder was changed from $0^{\circ}$ to $90^{\circ}$, and the perimeter of the elliptic cylinder was same as that of the circular cylinder. The immersed boundary method was used to capture the virtual wall boundary of the inner cylinder. With the increasing angle of the elliptic cylinder, the surface-averaged Nusselt numbers on the cylinder and the enclosure increased. In the Rayleigh number range considered in the present study, the surface-averaged Nusselt number on the elliptic cylinder over = $45^{\circ}$ was higher than that of the circular cylinder. The effect of elliptic cylinder's angle on natural convection in the enclosure was analyzed according to the flow and thermal fields, and the distributions of the Nusselt number.

Keywords

References

  1. Angeli, D., Levoni, P., and Barozzi, G. S., 2008, Numerical predictions for stable buoyant regimes within a square cavity containing a heated horizontal cylinder, International Journal of Heat and Mass Transfer, Vol. 51, pp. 2015-1108.
  2. Kim, B. S., Lee, D. S., Ha, M. Y., and Yoon, H. S., 2008, A numerical study of natural convection in a square enclosure with a circular cylinder at different vertical locations, International Journal of Heat and Mass Transfer, Vol. 51, pp. 1888-1906. https://doi.org/10.1016/j.ijheatmasstransfer.2007.06.033
  3. Moukalled, F. and Acharya, S., 2007, Natrual convection in the annulus between concentric horizontal circular and square cylinders, Journal of Thermophysics and Heat Transfer, Vol. 10, No. 3, pp. 524-531. https://doi.org/10.2514/3.820
  4. Ghaddar, N. K., 1992, Natural convection heat transfer between a uniformly heated cylindrical element and its rectangular enclosure, International Journal of Heat and Mass Transfer, Available online.
  5. Kang, D. H., Ha, M. Y., Yoon, H. S., and Choi, C., 2013, Bifurcation to unsteady natural convection in square enclosure with a circular cylinder at Rayleigh number of 107, International Journal of Heat and Mass Transfer, Vol. 64, pp. 926-944. https://doi.org/10.1016/j.ijheatmasstransfer.2013.05.002
  6. Yoon, H. S., Ha, M. Y., Kim, B. S., and Yu, D. H., 2009, Effect of the position of a circular cylinder in a square enclosure on natural convection at Rayleigh number of 107, Physics of Fluids, pp. 1-11.
  7. Lee, H. J., Doo, J. H., Ha, M. Y., and Yoon, H. S., 2013, Effect of thermal boundary conditions on natural convection in a square enclosure with an inner circular cylinder locally heated from the bottom wall, International Journal of Heat and Mass Transfer, Vol. 65, pp. 435-450. https://doi.org/10.1016/j.ijheatmasstransfer.2013.06.031
  8. Bararnia, H., Soleimani, S., and Ganji, D. D., 2011, Lattice Boltzmann simulation of natural convection around a horizontal elliptic cylinder inside a square enclosure, International Communications in Heat and Mass Transfer, Vol. 38, pp. 1436-1442. https://doi.org/10.1016/j.icheatmasstransfer.2011.07.012
  9. Sheikholeslami, M., Ellahi, R., Hassan, M., and Soleimani, S., 2014, A study of natural convection heat transfer in a nonofluid filled enclosure with elliptic inner cylinder, International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 24, pp. 1906-1927. https://doi.org/10.1108/HFF-07-2013-0225
  10. Zhang, P., Zhang, X., Deng, J., and Song, L., 2016, A numerical study of natural convection in an induced square enclosure with an elliptic cylinder using variation multiscale element free Galerkin method, International Journal of Heat and Mass Transfer, Vol. 99, pp. 721-737. https://doi.org/10.1016/j.ijheatmasstransfer.2016.04.011
  11. Kalyana Raman, S., Arul Prakash, K., and Vengadesen, S., 2012, Natural Convection from a Heated Elliptic Cylinder with a Different Axis Ratio in a Square Enclosure, Numerical Heat Transfer, Part, Vol. 62, pp. 639-658. https://doi.org/10.1080/10407782.2012.707058
  12. Liao, C.-C. and Lin, C.-A., 2012, Influences of a confined elliptic cylinder at different aspect ratios and inclinations on the laminar natural and mixed convection flows, International Journal of Heat and Mass Transfer, Vol. 55, pp. 6638-6650. https://doi.org/10.1016/j.ijheatmasstransfer.2012.06.073
  13. Gray, D. D. and Giorgini, A., 1976, The Validity of the Boussinesq Approximation for Liquids and Gases, International Journal of Heat and Mass Transfer, Vol. 19, pp. 545-551. https://doi.org/10.1016/0017-9310(76)90168-X
  14. Kim, J., Kim, D., and Choi, H., 2001, An immersed-boundary finite volume method for simulations of flow in complex geometries, Journal of Computational Physics, Vol. 171, pp. 132-150. https://doi.org/10.1006/jcph.2001.6778
  15. Kim, J. and Choi, H., 2004, An immersed-boundary finite-volume method for simulation of heat transfer in complex geometries, KSME Int, Vol. 18, pp. 1026-1035. https://doi.org/10.1007/BF02990875