一类马兰哥尼对流问题的同伦解析解

Homotopyic Analytical Solutions for a Kind of Marangoni Convection Problem

马兰哥尼对流对金属的晶体生长过程具有重要影响。研究附加材料流过初始熔体的马兰哥尼对流模型,用一种解析的方法——同伦分析方法和数值逼近法求解了该问题的非线性常微分方程组,求得了与数值解接近的近似解析解,并给出了无量纲速度分布的图形。

The Marangoni Convection is of significant effects on crystal growth of metals. In this paper, Marangoni t Convection model in which the additional material spreads on the initial smelting body has been studied. Homotopic analysis method, a kind of analytical method and a numerical approximation technique are applied to solve the ordinary differential equations. The results agree well with the numerical ones. The profiles of the dimensionless velocity distribution are shown in the paper.