Modified Homotopy Perturbation Transform Method: A Paradigm for Nonlinear Boundary Layer Problems

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2014-02-01 DOI:10.1515/ijnsns-2011-0065

Y. Khan, M. Usman

引用次数: 15

Abstract

Abstract This paper suggests a novel modified homotopy perturbation transform method (MHPTM) for a nonlinear boundary layer problem by suitable choice of an initial solution. The steady Navier–Stokes equations are reduced to nonlinear ordinary differential equations by using similarity variables. The governing nonlinear differential equations are solved by means of MHPTM. The equations are Laplace transformed and the nonlinear terms represented by He's polynomials. The series solution of the nonlinear boundary layer problem is obtained. For such a boundary layer problem, the second derivative at zero is an important point of function, so we have computed f″(0) and compared it with other results. An excellent agreement between the MHPTM and HPM is achieved. Such flow analysis is even not available yet for the hydrodynamic fluid. The series solution for MHD boundary layer problem with slip condition by means of MHPTM is yet not available in the literature

查看原文本刊更多论文

修正同伦摄动变换方法:非线性边界层问题的一种范式

提出了一种新的修正同伦摄动变换方法(MHPTM)，该方法通过选择合适的初始解来求解非线性边界层问题。利用相似变量将稳态Navier-Stokes方程化为非线性常微分方程。利用MHPTM方法求解了控制非线性微分方程。方程是拉普拉斯变换的，非线性项由何氏多项式表示。得到了非线性边界层问题的级数解。对于这样的边界层问题，零点处的二阶导数是函数的一个重要点，因此我们计算了f″(0)，并与其他结果进行了比较。MHPTM和HPM之间达成了良好的协议。这种流动分析甚至还不能用于水动力流体。用MHPTM方法求解具有滑移条件的MHD边界层问题的级数解，目前还没有文献报道

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.