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Steady thermocapillary-buoyant convection in a shallow annular pool. Part 2: Two immiscible fluids
Authors:You-Rong Li  Shuang-Cheng Wang  Chun-Mei Wu
Institution:You.-Rong.Li· Shuang.-Cheng.Wang · Chun.-Mei.Wu College of Power Engineering,Chongqing University,400044 Chongqing,China Y.-R.Li Key Laboratory of Low-grade Energy Utilization Technologies and Systems,Ministry of Education,400044 Chongqing,China
Abstract:This work is devoted to the study of steady thermocapillary-buoyant convection in a system of two horizontal superimposed immiscible liquid layers filling a lateral heated thin annular pool. The governing equations are solved using an asymptotic theory for the aspect ratios ɛ → 0. Asymptotic solutions of the velocity and temperature fields are obtained in the core region away from the cylinder walls. In order to validate the asymptotic solutions, numerical simulations are also carried out and the results are compared to each other. It is found that the present asymptotic solutions are valid in most of the core region. And the applicability of the obtained asymptotic solutions decreases with the increase of the aspect ratio and the thickness ratio of the two layers. For a system of gallium arsenide (lower layer) and boron oxide (upper layer), the buoyancy slightly weakens the thermocapillary convection in the upper layer and strengthens it in the lower layer.
Keywords:Thermocapillary-buoyant flow · Asymptotic solution · Shallow annular pool · Two-layer system
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