scholarly journals Comparative Analysis of Power-Law Fin-Type Problems Using Variational Iteration Method and Finite Element Method

2008 ◽  
Vol 2008 ◽  
pp. 1-9 ◽  
Author(s):  
Mehmet Tarık Atay ◽  
Safa Bozkurt Coşkun
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Power Law ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Solution Technique ◽  
Variational Iteration ◽  
Nonlinear Heat Conduction Equation ◽  
Different Levels ◽  
Element Method

Variational iteration method is applied to examine the temperature distribution within a single fin with a one-dimensional steady-state nonlinear heat conduction equation. Variation of temperature due to different levels of nonlinearities is analyzed. The results obtained by means of variational iteration method are compared with the results obtained from finite element method. A fourth iteration variational iteration solution is used in all cases considered. An error analysis is also conducted to evaluate the performance of proposed solution technique. The results have shown that variational iteration method is a powerful solution technique in the analysis of power-law fin-type problems.

scholarly journals Analysis of Convective Straight and Radial Fins with Temperature-Dependent Thermal Conductivity Using Variational Iteration Method with Comparison with Respect to Finite Element Analysis

2007 ◽  
Vol 2007 ◽  
pp. 1-15 ◽  
Author(s):  
Safa Bozkurt Coşkun ◽  
Mehmet Tarik Atay
Keyword(s):  
Thermal Conductivity ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Large Temperature ◽  
Temperature Dependent ◽  
Element Analysis ◽  
Variational Iteration ◽  
Temperature Dependent Thermal Conductivity

In order to enhance heat transfer between primary surface and the environment, radiating extended surfaces are commonly utilized. Especially in the case of large temperature differences, variable thermal conductivity has a strong effect on performance of such a surface. In this paper, variational iteration method is used to analyze convective straight and radial fins with temperature-dependent thermal conductivity. In order to show the efficiency of variational iteration method (VIM), the results obtained from VIM analysis are compared with previously obtained results using Adomian decomposition method (ADM) and the results from finite element analysis. VIM produces analytical expressions for the solution of nonlinear differential equations. However, these expressions obtained from VIM must be tested with respect to the results obtained from a reliable numerical method or analytical solution. This work assures that VIM is a promising method for the analysis of convective straight and radial fin problems.

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