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Neumann问题热平衡积分法细化解的收敛性 被引量：5

Convergence Properties of the Refined Heat Balance Integral Solution for the Neumann Problem
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摘要 本文应用热平衡积分法及其细化方法求得了Neumann问题的分段线性近似解。在参数S充分大的条件下,应用伽玛函数及不完全伽玛函数的性质,证明了Neumann问题的热平衡积分细化解的收敛性,并求得各相的收敛速度分别为O(n-1)、O(n-1/2)。本文推广了热平衡积分细化解收敛性分析中的一些已知结论。 A piecewise linear approximate solution for the Neumann problem is presented by using the heat balance integral method and its refined method. It is proved that the approximate solution converges formally to the exact solution at large values of the parameter S and the convergence rate in each phase is O（n-1） and O（n-1/2）, respectively, by using the properties of the Gamma function and incomplete Gamma function. The methods used in this paper can be applied to two-phase and multi-phase heat conduction problems. The present work generalizes the former results in convergence analysis to the refined heat balance integral solution.
作者 徐湘田 令锋
机构地区 内蒙古工业大学理学院 肇庆学院计算机科学与软件学院
出处 《工程数学学报》 CSCD 北大核心 2010年第3期503-512,共10页 Chinese Journal of Engineering Mathematics
基金 广东省自然科学基金(04011600) 教育部留学回国人员科研启动基金([2005]55)~~
关键词 热平衡积分法 近似解 NEUMANN问题 收敛速度 heat balance integral method approximate solution Neumann problem convergence rate
分类号 O175.29 [理学—基础数学]
  • 相关文献

参考文献11

  • 1Goodman T R. The heat-balance integral and its application to problems involving a change of phase[J]. Tran ASMEJ Heat Transfer, 1958, 80:335-342.
  • 2Langford D. The heat balance integral method[J]. Int J Heat Mass Transfer, 1973, 16:2424-2428.
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  • 5Bell G E. Solidification of a liquid about a cylindrical pipe[J]. Int J Heat Mass Transfer, 1979, 22:1681-1686.
  • 6Bell G E, Abbas S K. Convergence properties of the heat balance integral method[J]. Numer Heat Transfer, 1985, 8:373-382.
  • 7Mosally F, Wood A S, AL-Fhaid A. On the convergence of the heat balance integral method[J]. Applied Mathematical Modelling, 2005,29:903-912.
  • 8徐湘田,令锋.单相融化问题热平衡积分细化解的收敛性[J].内蒙古大学学报（自然科学版）,2009,40(2):128-131. 被引量：7
  • 9Lunadini V J. Heat Transfer in Cold Climate[M]. New York: Van Nostrand Reinhold Company, 1981.
  • 10Wood A S. A new look at the heat balance integral method[J]. Applied Mathematical Modelling, 2001, 25: 815-824.

二级参考文献9

  • 1Goodman T R. The heat-balance integral and its application to problems involving a change of phase [J]. Trans. ASME Journal of Heat Transfer, 1958,80 : 335 -342.
  • 2Wood A S. A new look at the heat balance integral method [J].Applied Mathematical Modelling. 2001.25: 815 -824.
  • 3Langford D. The Heat Balance Integral Method [J]. Int. J. Heat Mass Transfer, 1973,16 : 2 424-2428.
  • 4Crank J. The mathematics of Diffusion [M]. Oxford: Clarendon Press. 1964. 310- 325.
  • 5Noble B. Heat balance methods in melting problems [A]. Ockendon J R ,Hodgkins W R.eds. Moving Boundary Problems in Heat Flow and Diffusion[C]. Oxford: Clarendon Press,1975,208-209.
  • 6Bell G E. A refinement of the Heat Balance Integral Method applied to a Melting Problem [J] Int. J. Heat Mass Transfer, 1978.21 : 1357-1362.
  • 7Bell G E. Solidification of a Liquid about a Cylindrical Pipe [J]. Int. J. Heat Mass Transfer, 1979,22:1 681-1686.
  • 8Bell G E. Abbas S K. Convergence properties of the heat balance integral method [J]. Numerical Heat Transfer, 1985,8: 373-382.
  • 9Mosally F, Wood A S, AL-Fhaid A. On the convergence of the heat balance integral method [J]. Applied Mathematical Modelling, 2005,29 : 903 -12.

共引文献6

同被引文献40

  • 1GOODMAN T R.The heat balance integral and its application to problems involving a change of phase[J].Trans ASME Journal of Heat Transfer,1958,80:335-342.
  • 2WOOD A S.A new look at the heat balance integral method[J].Applied Mathematical Modeling,2001,25(10):815-824.
  • 3MITCHELL S L,MYERS T G.Application of standard and refined heat balance integral methods to one-dimensional Stefan problem[J].SIAM Review,2010,52(1):57-86.
  • 4MOSALLY F,WOOD A S,AL-FHAID A.On the convergence of the heat balance integral method[J].Applied Mathematical Modeling,2005,29(10):903-912.
  • 5SADOUN N,SI-AHMED E,COLINET P.On the refined integral method for the one-phase Stefan problem with time-dependent boundary condition[J].Applied Mathematical Modeling,2006,30:531-544.
  • 6SADOUN N,SI-AHMED E.A new analytical expression of the freezing constant in the Stefan problem with initial superheat[J].Numer Meth Therm Probl,1995,9:843-854.
  • 7LANGFORD D.The heat balance integral method[J].Int J Heat Mass Transfer,1973,16(12):2424-2428.
  • 8MYERS T G.Optimizing the exponent in the heat balance and refined integral methods[J].International Communications in Heat and Mass Transfer,2009,36:143-147.
  • 9MYERS T G.Optimal exponent heat balance and refined integral methods applied to Stefan problems[J].International Journal of Heat and Mass Transfer,2010,53:1119-1127.
  • 10Goodman. The heat balance integral and its application to problem involving a change of phase[ J]. Trans ASME Journal of Heat Transfer, 1985,80:335 - 342.

引证文献5

二级引证文献9

工程数学学报
2010年 第3期

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