Application of variational iteration method and homotopy-perturbation method for nonlinear heat diffusion and heat transfer equations

Ganji DD; Afrouzi GA; Talarposhti RA

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Application of variational iteration method and homotopy-perturbation method for nonlinear heat diffusion and heat transfer equations

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

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Perturbation methods depend on a small parameter which is difficult to be found for real-life nonlinear problems. To overcome this shortcoming, two new but powerful analytical methods are introduced to solve nonlinear heat transfer problems in this Letter; one is He's variational iteration method (VIM) and the other is the homotopy-perturbation method (HPM). Nonlinear convective-radiative cooling equations are used as examples to illustrate the simple solution procedures. These methods are useful and practical for solving the nonlinear heat diffusion equation, which is associated with variable thermal conductivity condition. Comparison of the results obtained by both methods with exact solutions reveals that both methods are tremendously effective. (c) 2007 Elsevier B.V. All tights reserved.

机译：摄动方法取决于一个很小的参数，对于实际的非线性问题很难找到。为了克服这个缺点，在本文中介绍了两种新的但功能强大的分析方法来解决非线性传热问题。一种是He的变分迭代方法（VIM），另一种是同伦摄动方法（HPM）。以非线性对流辐射冷却方程为例来说明简单的求解过程。这些方法对于求解与可变热导率条件相关的非线性热扩散方程是有用且实用的。通过两种方法获得的结果与精确解的比较表明，两种方法都非常有效。（c）2007年Elsevier B.V.版权所有。

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《Physics Letters, A》 |2007年第6期|共8页
作者
Ganji DD; Afrouzi GA; Talarposhti RA;
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正文语种 eng
中图分类物理学;
关键词
heat transfer; heat diffusion; nonlinear equation; variational iteration equation (VIM); homotopy-perturbation method (HPM); VARIABLE THERMAL PARAMETERS; POROUS-MEDIA; FINS; CONDUCTIVITY; BIFURCATION; FLOW;

机译：传热;热扩散;非线性方程;变分迭代方程（VIM）;同摄摄动法（HPM）;可变热参数;多孔介质;鳍;电导率;分岔;流动;

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专利

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. Application of variational iteration and homotopy-perturbation methods to nonlinear heat transfer equations with variable coefficients [J] . Khaleghi H, Ganji DD, Sadighi A Numerical Heat Transfer, Part A. Application: An International Journal of Computation and Methodology . 2007,第1期

机译：变分迭代和同伦摄动方法在变系数非线性传热方程中的应用
3. Application on Homotopy-perturbation and Variational Iteration Methods for Heat Equation [J] . Gholamreza Jandaghi, Hasan Zarei Matin Australian Journal of Basic and Applied Sciences . 2009,第2期

机译：热方程的同伦摄动和变分迭代方法的应用
4. Variational Iteration Method and Homotopy-Perturbation Method for Solving Second-Order Non-Linear Wave Equation [C] . A. Barari, M. Omidvar, S. Gholitabar, International Conference on Numerical Analysis and Applied Mathematics . 2007

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5. Integral equation method for radiative transfer and its application in combined heat transfer enhancement analysis. [D] . Zhang, Jianmin. 1995

机译：辐射传递积分方程方法及其在强化传热分析中的应用。
6. Colloquium PaperNonlinear partial differential equations and applications: Crystalline variational methods [O] . Jean E. Taylor 2007

机译：非线性偏微分方程及其应用：结晶变分法
7. Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations [O] . Ganji D.D., Sadighi A. 2007

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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

Application of variational iteration method and homotopy-perturbation method for nonlinear heat diffusion and heat transfer equations

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