环形腔内双层薄液层热毛细对流的渐近解

ASYMPTOTIC SOLUTION OF THERMOCAPILLARY CONVECTION OF THIN TWO-LAYER SYSTEM IN AN ANNULAR CAVITY

为了解水平温度梯度作用下环形腔内双层薄液层热毛细对流的基本特性,采用渐近线方法获得了热毛细对流的近似解.环形腔外壁被加热,内壁被冷却,上、下壁面绝热.结果表明,当环形腔宽度与内半径比趋于零时,环形腔退化为矩形腔,所得到的主流区速度场和温度场的表达式演化为Nepomnyashchy等得到的矩形腔内的结果;与数值模拟结果的比较发现,在主流区渐近解与数值解吻合较好.

The convection phenomena in two-layer liquid systems have attracted great attention in the past two decades,mainly owing to their relevance in nature and in many engineering applications.Many works have been carried out to investigate the thermocapillary convection in two-layer liquid systems in rectangular cavities or in infinite horizontal layers.However,few studies focused on the convection phenomena in two-layer liquid systems in the annular cavity.In order to understand the basic characteristics of thermocapillary convection of the thin two superposed horizontal liquid layers subjected to a radial temperature gradient in an annular cavity,an approximate analytical solution is obtained using asymptotical analysis.The cavity is heated from the outer cylindrical wall and cooled at the inner wall.Bottom and top surfaces are adiabatic.Results show that the expressions of velocity and temperature field in the core region are the same as the results obtained by Nepomnyashchy et al（Physics of Fluids,2006,18：032105） when thin annular pool approaches to thin two-dimensional slot.The numerical experiments are also carried out to compare with the asymptotic solution. It is found that there is a good agreement between the asymptotic solution and numerical result in the core region.