The Asymptotic Solution of a Kind of Stefan Problem

Liu Zheng-rong

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1983 > 4(6): 801-808

Liu Zheng-rong. The Asymptotic Solution of a Kind of Stefan Problem[J]. Applied Mathematics and Mechanics, 1983, 4(6): 801-808.

Citation:

Liu Zheng-rong. The Asymptotic Solution of a Kind of Stefan Problem[J]. Applied Mathematics and Mechanics, 1983, 4(6): 801-808.

Citation:

Liu Zheng-rong. The Asymptotic Solution of a Kind of Stefan Problem[J]. Applied Mathematics and Mechanics, 1983, 4(6): 801-808.

PDF( 439 KB)

The Asymptotic Solution of a Kind of Stefan Problem

Liu Zheng-rong

Anhui University, Hefei, Anhui

Received Date: 1982-10-07
Publish Date: 1983-12-15

Abstract

Abstract

In this paper, a kind of Stefan problem subject to general initial condition is studied. The slab considered is divided into three regions. There is a different time scale in each one. By means of PLK method or like multi-scales method, the asymptotic solution of each one is obtained. Finally we discuss the asymptotic solution and draw some conclusions.

FullText(HTML)

References(14)

References

[1]	Sherman,B.,A general one-phase Stefan problem,Quart.Appl.Math.,Vol.28,(1970),377-382.
[2]	Kyner,Walter.T.,On a free boundary value problem for the heat equations,Quart.Appl.Math.,Vol.17,(1959),305-310.
[3]	Miranker,W.L.,A free boundary value problem for the heat equation,Quart.Appl.Math.,Vol.16,(1958),121-130.
[4]	Meyer,G.H.,One-dimensional parabolic free boundary problem,SIAM Review,Vol.19,(1977),17-34.
[5]	Evans,G.W.,E.Isaacson and I.Macdonald,Stefan-like problem,Quart.Appl.Math.,Vol.8,(1950),312-319.
[6]	Boley,Bruns.A.,A method of heat conduction analysis of melting and solidi-fication problem,J.Math.and Phys.,Vol.40,(1961),300-313.
[7]	Pedroso,R.I.,and G.A.Domoto,Perturbation solutions for spherical solidification of saturated liquid,ASME.J.Heat Transfer,Vol 95,(1973),42-46.
[8]	Weimbaum,S.and L.M.Jiji,Singular perturbation theory for melting or freezing in finite domains initially not at the fusion temperature,J.Appl.Mech.,Vol.44,(1977),25-30.
[9]	Rubinsky,B.and E.G.Cravalho,The determination of the thermal history in a one-dimensional freezing sysytem by perturbation method,ASME.J.Heat Transfer,Vol.101,(1979),326-330.
[10]	Tiji,Latif M.and Sheldon Weibaum,Perturbation solution for melting of freezing in annular regions initially not at the fusion temperature,Inter.J.Heat Mass Transfer,Vol.21,(1978),581-590.
[11]	Predroso,R.I.and G.A.Domoto,Exact solution by perturbation method for planar solidification of a saturated liquid with convection at the wall,Inter.J.Heat Mass Transfer,Vol.16,(1973),1816-1819.
[12]	刘曾荣,一维熔解与凝固问题的摄动解,(尚未发表).
[13]	陈则靓、葛新石,相变热传导问题,混合法近似解(尚大发表).
[14]	Nayfeh,A.H.,Perturbation Methods,Wiley-Interscience,New York,Chap.3,(1973).