Variational iteration method to solve moving boundary problem with temperature dependent physical properties

Abstract

In this paper, variational iteration method is used to solve a moving boundary problem arising during melting or freezing of a semi infinite egion when physical properties (thermal conductivity and specific heat) of the two regions are temperature dependent. The Result is compared with result obtained by exact method (when thermal conductivity and specific heat in two regions are temperature independent) and semi analytical method (When thermal conductivity and specific heat are temperature dependent) and are in good agreement. We obtain the solution in the form of continuous functions. The method performs extremely well in terms of efficiency and simplicity and effective for solving the moving boundary problem.

Numerical approach to Stefan problem in a two-region and limited space

“…4 and 5. Figure 4 demonstrates the numerical results are coincident closely with the approximate solution which can be obtained by the homotopy perturbation method [10,11] and the variational iteration method [12]. The temperature distribution as a function of time is shown in fig.…”

A Note on Models for Anomalous Phase-Change Processes

“…Free boundary problems involving fractional heat equation (2.4) and fractional Stefan condition (2.5) were considered in several works at dealing with anomalous diffusive-like processes, e.g. [2,3,6,7,16,17,19,25,33,[38][39][40]. A remarkable contribution from Voller, Falcini, and Garra was to identify a definition for the heat flux and a suitable classical global balance leading to a transparent generalization of the classical model to a fractional one.…”

“…Timefractional conservation equations were also considered in [5], where the relation with non-local transport theory with memory effects is discussed. In this way, we provide a new approach to derive some fractional problems that are of interest in pure and applied fields, [2,3,6,7,13,16,17,19,25,33,[38][39][40].…”

Thermal performance of porous fins with temperature-dependent heat generation via the homotopy perturbation method and collocation method

“…Perturbation techniques are too strongly dependent upon the so-called "small parameters" [6]. Many other different methods have been introduced to solve a nonlinear equation such as the δ-expansion method [7], Adomian's decomposition method [8], many homotopy perturbation method (HPM) [9][10][11][12][13][14][15], many variational iteration method (VIM) [16][17][18][19][20][21][22][23][24][25] and many collocation method [26][27][28].…”