边界条件随时间变化的热传导问题的一种近似解法An approximate Solution to the Heat Conduction Problem with the Time-dependent Boundary Conditions
袁国静,令锋
摘要(Abstract):
在热平衡积分法和改进的热平衡积分法的基础上,提出了一种求解热传导问题的新方法.应用此方法求解边界条件随时间变化的热传导问题,结果表明:此方法计算过程简单且计算精度高.
关键词(KeyWords): 热传导;固定温度边界条件;线性温度边界条件
基金项目(Foundation): 广东省自然科学基金资助项目(04011600)
作者(Author): 袁国静,令锋
DOI: 10.16393/j.cnki.37-1436/z.2011.02.015
参考文献(References):
- [1]Goodman T R.The heat balance integral and its application to problems involving a change of phase[J].Trans Asme Journal ofHeat Transfer,1958,80:335-342.
- [2]Sadoun N,Si-Ahmed E,Coline T P.On the refined integral method for the one-phase Stefan problem with time-dependentboundary condition[J].Applied Mathematical Modeling,2006,30:531-544.
- [3]Sadoun 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.
- [4]Mosally F,Wood A S,Al-Fhaid A.An Exponential Heat Balance Integral Method[J].Applied Mathematics and Computation,2002,130:87-100.
- [5]Langford D.The Heat Balance Integral Method[J].Int.J.Heat Mass Transfer,1973,16:2424-2428.
- [6]Crank J.The mathematics of Diffusion[M].Oxford:Clarendon Press,1964:310-325.
- [7]Antic A,Hill J M.The double-diffusivity heat transfer model for grain stores incorporating microwave heating[J].Appl MathModel,2003,27:629–647.
- [8]Myers T G.Optimal exponent heat balance and refined integral methods applied to Stefan problems[J].Heat Mass Transfer,2010,53:1119-1127
- [9]Carslaw H S,Jaeger J C.Heat in solids[M].Oxford:Clarendon Press,1959:50-91.