An approximate analytical solution of one-dimensional phase change problems in a finite domain

Das, S.; Rajeev, .

doi:10.1016/j.amc.2010.10.032

Cited by 4 publications

(4 citation statements)

References 12 publications

(11 reference statements)

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“…Solidification of a pure metal can be modeled as a twophase Stefan problem [1,2,18,24], which is a system of ordinary PDEs with an unknown moving boundary. The temperature distribution in the metal liquid phase, ( , ), and the solid phase, V( , ), and the moving interface at which solidification occurs, = ( ), are unknown functions for the model.…”

Section: The Two-phase Stefan Problemmentioning

confidence: 99%

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Approximate Analytic Solutions for the Two-Phase Stefan Problem Using the Adomian Decomposition Method

Qin

Yue-xing

Yin

2014

Journal of Applied Mathematics

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An Adomian decomposition method (ADM) is applied to solve a two-phase Stefan problem that describes the pure metal solidification process. In contrast to traditional analytical methods, ADM avoids complex mathematical derivations and does not require coordinate transformation for elimination of the unknown moving boundary. Based on polynomial approximations for some known and unknown boundary functions, approximate analytic solutions for the model with undetermined coefficients are obtained using ADM. Substitution of these expressions into other equations and boundary conditions of the model generates some function identities with the undetermined coefficients. By determining these coefficients, approximate analytic solutions for the model are obtained. A concrete example of the solution shows that this method can easily be implemented in MATLAB and has a fast convergence rate. This is an efficient method for finding approximate analytic solutions for the Stefan and the inverse Stefan problems.

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Section: The Two-phase Stefan Problemmentioning

confidence: 99%

“…Substituting (24) and 25into (17) and 18, respectively, and choosing the initial items 0 and V 0 yield the following recursive relations:…”

Section: Approximate Analytic Solutions By Admmentioning

confidence: 99%

Approximate Analytic Solutions for the Two-Phase Stefan Problem Using the Adomian Decomposition Method

Qin

Yue-xing

Yin

2014

Journal of Applied Mathematics

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“…McCue et al [10] analysed the two-phase problem for spheres by applying the method of matched asymptotic expansions. Das and Rajeev [11] derived an analytical solution of the two-phase problem in a finite domain by using the finite sine transform technique. An and Su [12] developed a lumped parameter model and analysed the melting of a finite slab with volumetric heat generation.…”

Section: Introductionmentioning

confidence: 99%

A Series Solution for Heat Conduction Problem with Phase Change in a Finite Slab

Chiba

2014

Abstract and Applied Analysis

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A two-dimensional differential transform method is applied to solve one-dimensional phase change problems in a slab of finite thickness, which is subjected to convective thermal loading at one surface and a constant prescribed temperature at the other. In the problems, the initial temperature of the slab does not necessarily have to be the same as the fusion temperature. A series solution is derived for the temperature profile in the melting or solidifying slab with temperature-dependent thermal conductivity and volumetric heat capacity. The latent heat effect of the phase change is incorporated into the temperature-dependent heat capacity. Numerical results demonstrate the effects of the temperature-dependent parameters on the transient temperature profile of the slab.

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“…The same procedure is used in paper [16] for solution of 1-D moving boundary problem with periodic boundary conditions. Furthermore, Das and Rajeev in paper [19] have introduced an approximate analytic solution of 1-D Stefan problem. Furthermore, Das and Rajeev in paper [19] have introduced an approximate analytic solution of 1-D Stefan problem.…”

Section: Introductionmentioning

confidence: 99%

A certain analytical method used for solving the Stefan problem

et al. 2013

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The paper presents an analytic method applied for finding the approximate solution of Stefan problem reduced to the one-phase solidification problem of a plate with the unknown a priori, varying in time boundary of the region in which the solution is sought. Proposed method is based on the known formalism of initial extension of a sought function describing the field of temperature into the power series, some coefficients of which can be determined with the aid of boundary conditions, and on the approximation of a function defining the freezing front location with the broken line, parameters of which can be obtained by solving the appropriate differential equations. Results received by applying the proposed procedure will be compared with the results obtained with the aid of a classical numerical method served for solving the Stefan problem

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An approximate analytical solution of one-dimensional phase change problems in a finite domain

Cited by 4 publications

References 12 publications

Approximate Analytic Solutions for the Two-Phase Stefan Problem Using the Adomian Decomposition Method

Approximate Analytic Solutions for the Two-Phase Stefan Problem Using the Adomian Decomposition Method

A Series Solution for Heat Conduction Problem with Phase Change in a Finite Slab

A certain analytical method used for solving the Stefan problem

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