Optimal Perturbation Iteration Method for Solving Nonlinear Heat Transfer Equations

Sinan Deniz

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Optimal Perturbation Iteration Method for Solving Nonlinear Heat Transfer Equations

机译：求解非线性传热方程的最优摄动迭代法

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摘要

In this paper, the new optimal perturbation iteration method (OPIM) is introduced and applied for solving nonlinear differential equations arising in heat transfer. The effectiveness of the proposed method will be tested by considering two specific applications: the temperature distribution equation in a thick rectangular fin radiation to free space and cooling of a lumped system with variable specific heat. Comparing different methods shows that the results obtained by optimal perturbation iteration method are very good agreement with the numerical solutions and perform better than the most existing analytic methods.

机译：本文介绍了一种新的最优摄动迭代方法（OPIM），并将其应用于求解传热中的非线性微分方程。将通过考虑两个特定的应用来测试所提出方法的有效性：在厚矩形散热片向自由空间的辐射中的温度分布方程式以及具有可变比热的集总系统的冷却。对不同方法的比较表明，最优扰动迭代方法获得的结果与数值解非常吻合，并且比大多数现有的分析方法具有更好的性能。

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来源
《Journal of Heat Transfer》 |2017年第7期|074503.1-074503.4|共4页
作者
Sinan Deniz;
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作者单位

Department of Mathematics, Faculty of Art and Sciences, Manisa Celal Bayar University, Manisa 45140, Turkey;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
optimal perturbation iteration method; heat transfer; perturbation methods;

机译：最优摄动迭代法;传播热量;摄动法;

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1. Application of variational iteration method and homotopy-perturbation method for nonlinear heat diffusion and heat transfer equations [J] . Ganji DD, Afrouzi GA, Talarposhti RA Physics Letters, A . 2007,第6期

机译：变分迭代法和同伦摄动法在非线性热扩散和传热方程中的应用
2. Analytical solutions to nonlinear equations arising in heat transfer by variational iteration, homotopy perturbation, and adomian decomposition methods [J] . Ganji D.D., Gorji M., Alipanah M., Numerical Methods for Partial Differential Equations: An International Journal . 2010,第6期

机译：通过变分迭代，同伦摄动和阿德曼分解方法求解传热中产生的非线性方程的解析解
3. Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations [J] . Ganji DD, Sadighi A Journal of Computational and Applied Mathematics . 2007,第1期

机译：同伦摄动和变分迭代方法在非线性传热和多孔介质方程中的应用
4. Assessment of perturbation and homotopy-perturbation methods for solving nonlinear oscillator equations [C] . Maziar Ramezani, Thomas Neitzert International Conference onechanical, Automotive and Materials Engineering . 2013

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5. A high -order finite difference method for solving bioheat transfer equations in three-dimensional triple -layered skin structure [D] . Yu, Haofeng 2004

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6. On Generalization Based on Bi et al. Iterative Methods with Eighth-Order Convergence for Solving Nonlinear Equations [O] . Taher Lotfi, Alicia Cordero, Juan R. Torregrosa, -1

机译：基于Bi等人的概论。八阶收敛迭代法求解非线性方程
7. Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations [O] . Ganji D.D., Sadighi A. 2007

机译：同伦摄动和变分迭代方法在非线性传热和多孔介质方程中的应用
8. Comparison of Methods for Solving Nonlinear Finite-Element Equations in Heat Transfer [R] . Cort, G. E., Graham, A. L., Johnson, N. L. 1981

机译：传热非线性有限元方程求解方法的比较

Optimal Perturbation Iteration Method for Solving Nonlinear Heat Transfer Equations

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