Asymptotic Solution of Thermocapillary Convection in a Differentially Heated Thin Annular Two-Layer Pool
Asymptotic Solution of Thermocapillary Convection in a Differentially Heated Thin Annular Two-Layer Pool
复制标题
DOI：
10.1007/s12217-009-9174-0
复制
发表时间：
2010-04
影响因子：
1.8
通讯作者：
You-Rong Li;Shuang Wang;Shuang-Ying Wu;L. Peng
中科院分区：
文献类型：
--
作者：
You-Rong Li;Shuang Wang;Shuang-Ying Wu;L. Peng
采用渐近分析方法，研究了在径向温度梯度作用下，一个自由面、一个液/液界面的薄环形池中两层非混相液体的二维层状热毛细对流。池从内圆柱形壁加热，在外壁冷却。底部和顶部表面是绝热的。当宽高比（定义为下层厚度与间隙宽度之比）趋于零时，在核心区域内得到渐近解。数值实验也与稳态二维热毛细对流的渐近解进行了比较。结果表明，在小长径比的极限下，核心区的速度场和温度场表达式是有效的。
The steady laminar two-dimensional thermocapillary convection of two immiscible liquid layers in a thin annular pool with one free surface, one liquid/liquid interface subjected to a radial temperature gradient was investigated using asymptotical analysis. The pool is heated from the inner cylindrical wall and cooled at the outer wall. Bottom and top surfaces are adiabatic. The asymptotic solution is obtained in the core region in the limit as the aspect ratio, which is defined as the ratio of the lower layer thickness to the gap width, trends to zero. The numerical experiments are also carried out to compare with the asymptotic solution of the steady two-dimensional thermocapillary convection. The results indicate that the expressions of velocity and temperature fields in the core region are valid in the limit of the small aspect ratio.