Application of the variational iteration method to nonlinear non-Fourier conduction heat transfer equation with variable coefficient

2011 ◽  
Vol 40 (6) ◽  
pp. 513-523 ◽  
Author(s):  
Seyfolah Saedodin ◽  
Hessameddin Yaghoobi ◽  
Mohsen Torabi
Keyword(s):  
Heat Transfer ◽  
Iteration Method ◽  
Transfer Equation ◽  
Variable Coefficient ◽  
Variational Iteration Method ◽  
Heat Transfer Equation ◽  
Conduction Heat Transfer ◽  
Variational Iteration

He's Variational Iteration Method

2017 ◽  
pp. 62-76
Keyword(s):  
Heat Transfer ◽  
Problem Solving ◽  
Iteration Method ◽  
Transfer Equation ◽  
Iterative Scheme ◽  
Variational Iteration Method ◽  
Heat Transfer Equation ◽  
Variational Iteration ◽  
Nonlinear Heat Transfer ◽  
He’S Variational Iteration Method

In this chapter, a variational iteration method (VIM) has been applied to nonlinear heat transfer equation. The concept of the variational iteration method is introduced briefly for applying this method for problem solving. The proposed iterative scheme finds the solution without any discretization, linearization, or restrictive assumptions. The results reveal that the VIM is very effective and convenient in predicting the solution of such problems.

scholarly journals He's fractional derivative for non-linear fractional heat transfer equation

2016 ◽  
Vol 20 (3) ◽  
pp. 793-796 ◽  
Author(s):  
Kang-Le Wang ◽  
San-Yang Liu
Keyword(s):  
Heat Transfer ◽  
Fractional Derivative ◽  
Iteration Method ◽  
Transfer Equation ◽  
Variational Iteration Method ◽  
Heat Transfer Equation ◽  
Fractional Complex Transform ◽  
Non Linear ◽  
He’S Variational Iteration Method ◽  
Fractional Equation

This paper adopts He's fractional derivative for non-linear fractional heat transfer equation. The fractional complex transform and He's variational iteration method are used to solve the fractional equation.

scholarly journals Temperature distribution in the three-layered upper mantle beneath a continent

2021 ◽  
Vol 2119 (1) ◽  
pp. 012006
Author(s):  
A G Kirdyashkin ◽  
A A Kirdyashkin ◽  
A V Borodin ◽  
V S Kolmakov
Keyword(s):  
Heat Transfer ◽  
Temperature Distribution ◽  
Convective Heat Transfer ◽  
Upper Mantle ◽  
Lower Mantle ◽  
Transfer Equation ◽  
Horizontal Layer ◽  
Heat Transfer Equation ◽  
Continental Lithosphere ◽  
Conduction Heat Transfer

Abstract Temperature distribution in the upper mantle underneath the continent, as well as temperature distribution in the lower mantle, is obtained. In the continental lithosphere, the solution to the heat transfer equation is obtained in the model of conduction heat transfer with inner heat within the crust. To calculate the temperature distribution in the upper and lower mantle, we use the results of laboratory and theoretical modeling of free convective heat transfer in a horizontal layer heated from below and cooled from above.

scholarly journals A variational iteration method integral transform technique for handling heat transfer problems

2017 ◽  
Vol 21 (suppl. 1) ◽  
pp. 55-61 ◽  
Author(s):  
Yuejin Zhou ◽  
Shun Pang ◽  
Guo Chong ◽  
Xiaojun Yang ◽  
Xiaoding Xu ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Iteration Method ◽  
Integral Transform ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Excess Temperature ◽  
Variational Iteration ◽  
Transfer Equations ◽  
Transfer Problems ◽  
Integral Transform Technique

In this paper, we consider the heat transfer equations at the low excess temperature. The variational iteration method integral transform technique is used to find the approximate solutions for the problems. The used method is accurate and efficient.

scholarly journals Fractal heat conduction problem solved by local fractional variation iteration method

2013 ◽  
Vol 17 (2) ◽  
pp. 625-628 ◽  
Author(s):  
Xiao-Jun Yang ◽  
Dumitru Baleanu
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Iteration Method ◽  
Heat Conduction Equation ◽  
Heat Conduction Problem ◽  
Variational Iteration Method ◽  
Conduction Equation ◽  
Variational Iteration ◽  
Fractional Heat Conduction ◽  
Variation Iteration Method

This paper points out a novel local fractional variational iteration method for processing the local fractional heat conduction equation arising in fractal heat transfer.

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