Asymptotic Solution of Thermocapillary Convection in a Differentially Heated Thin Annular Two-Layer Pool

Abstract

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.