Journal of Advanced Marine Engineering and Technology

The Korean Society of Marine Engineering (한국마린엔지니어링학회)
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Numerical analysis of natural convection heat transfer from a fin in parallel enclosure

  • Bae, Myung-Whan (Engineering Research Institute, Department of Mechanical Engineering for Production, Gyeongsang National University) ;
  • Mochimaru, Yoshihiro (Tokyo Institute of Technology)
  • Received : 2016.03.14
  • Accepted : 2016.06.04
  • Published : 2016.06.30
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Abstract

A fin of finite width with infinitely small thickness is assumed to be placed horizontally between two horizontal parallel plates of infinite extension in the exactly central position. The lower plate and the half of the upper plate are kept at a constant lower temperature, and the remaining upper plate is kept at a constant higher temperature. The fin is also kept at a constant temperature (variable). Steady-state two-dimensional laminar natural convection is analyzed as a problem of boundary value under a boundary-fitted conformal mapping system, using a spectral finite difference scheme, with a condition of doubly-connectedness. The steady-state solution is obtained as a limit of the transient solution.

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References

  1. Y. Mochimaru, "Effectiveness of a spectral finite difference scheme," Computational Fluid Dynamics Review, vol. 1, pp. 379-394, 1998.
  2. L. I. Volkovyskii, G. I. Lints, and I. G. Aramanovich, "A collection of problems on complex analysis," Pergamon Press, 1965.
  3. P. Henrici, Applied and Computational Complex Analysis, vol. 1, Wiley, 1974.
  4. L. N. Trefethen, Numerical Conformal Mapping, North-Holland, 1986.
  5. R. Schinzinger and P. A. A. Laure, Conformal Mapping, Elsevier, 1991.
  6. Y. Mochimaru, "Existence/non-existence of conformal mapping in some family of functions," International Journal of Pure and Applied Mathematics, vol. 49, pp. 497-503, 2008.
  7. Y. Mochimaru, "Analytical treatment of far away field behavior," Computational Fluid Dynamics Journal, vol. 13, pp. 422-426, 2004.
  8. Y. Mochimaru, "Extension of applicability of a spectral finite difference scheme to mixed boundary conditions," Transport Phenomena in Thermal-Fluids Engineering, pp. 315-320, 1996.
  9. I. Catton (Ed. Kankac, Aung, Vskanta), Natural Convection in Horizontally Unbounded Plane Layers, Natural Convection, Fundamentals and Applications, Hemisphere Pub, pp. 97-134, 1985.
  10. F. A. Kulacki and D. E. Richards (Ed. Kankac, Aung, Vskanta), Natural Convection in Plane Layers and Cavities with Volumetric Energy Sources, Natural Convection, Fundamentals and Applications, Hemisphere Pub, pp. 179-255, 1985.
  11. R. Viskanta (Ed. Kankac, Aung, Vskanta), Natural Convection in Melting and Solidification, Natural Convection, Fundamentals and Applications, Hemisphere Pub, pp. 845-877, 1985.
  12. P. G. Simpkins and K. S. Chen (Ed. Kankac, Aung, Vskanta), Natural Convection in Horizontal Containers with Applications to Crystal Growth, Natural Convection, Fundamentals and Applications, Hemisphere Pub, pp. 1010-1032, 1985.
  13. A. G. Bathelt and R. Viskanta, "Heat transfer and interface motion during melting and solidification around a finned heat source/sink," Transactions of ASME, Journal of Heat transfer, vol. 3, pp. 720-726, 1981.
  14. Y. Mochimaru, "A spectral finite difference scheme and its effectiveness," Proceedings of 26th Annual Iranian Mathematics Conference, pp. 245-254, 1995.
  15. Y. Mochimaru, "Global instability of natural convection in an elliptic cavity, Using a fourier spectral difference method," 7th Int. Coll. on Differential Equations, pp. 243-252, 1997.
  16. D. Akita and Y. Mochimaru, "Numerical simulation of a flow past an elliptic cylinder at moderately high reynolds numbers," CMMPG, vol. 1, pp. 1-7, 2015.
  17. Y. Mochimaru and M. W. Bae, "A study on natural convection from two cylinders in a cavity," Journal of Mechanical Science and Technology, vol. 20, no. 10, pp. 1773-1778, 2006. https://doi.org/10.1007/BF02916281
  18. Y. Mochimaru and M. W. Bae, "Natural convection heat transfer in a doubly - connected region, using a spectral finite difference scheme," International Journal of Pure and Applied Mathematics, vol. 32, no. 1, pp. 51-60, 2006.
  19. Y. Mochimaru and M. W. Bae, "Spectral analysis on natural convection heat transfer from a rectangular cylinder partially heated in an infinite extension (Invited Lecture)," International Journal of Pure and Applied Mathematics, vol. 46, no. 2, pp. 237-243, 2008.