Asymptotic solution of thermocapillary convection of thin two-layer system in an annular cavity

The convection phenomena in two-layer liquid systems haveattracted great attention in the past two decades, mainly owing to theirrelevance in nature and in many engineering applications. Many works havebeen carried out to investigate the thermocapillary convection in two-layerliquid systems in rectangular cavities or in infinite horizontal layers.However, few studies focused on the convection phenomena in two-layer liquidsystems in the annular cavity. In order to understand the basiccharacteristics of thermocapillary convection of the thin two superposedhorizontal liquid layers subjected to a radial temperature gradient in anannular cavity, an approximate analytical solution is obtained usingasymptotical analysis. The cavity is heated from the outer cylindrical walland cooled at the inner wall. Bottom and top surfaces are adiabatic. Resultsshow that the expressions of velocity and temperature field in the coreregion are the same as the results obtained by Nepomnyashchy et al (Physicsof Fluids, 2006, 18: 032105) when thin annular pool approaches to thin two-dimensional slot.The numerical experiments are also carried out to compare with theasymptotic solution. It is found that there is a good agreement between theasymptotic solution and numerical result in the core region.