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An analytical solution for the stationary behaviour of binary mixtures and pure fluids in a horizontal annular cavity

机译：在水平环形腔中二元混合物和纯流体的稳态行为的解析解

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摘要

This study aims at analysing the characteristics of the two-dimensional flow established by binary mixtures and pure fluids in a horizontal annular cavity isothermally heated inside and cooled outside. Some complications arise considering binary mixtures, as a consequence of thermogravitational diffusion due to the coupling of convection with thermodiffusion. An analytical model has been defined assuming a two-dimensional laminar flow of a visco-elastic fluid, under validity of Boussinesq's assumption and negligible viscous dissipation. For the case of binary mixtures, the buoyancy determined by concentration variations has been ignored, so that momentum equation is independent on concentration and is only coupled with the energy balance equation. The analytical model has been validated, for both cases of binary mixtures and pure fluids, through comparison with numerical results in a wide range of the non-dimensional parameters that govern the problem. In particular, the effect of the geometry and of the boundary conditions on the separation of the mixture compounds due to thermogravitational diffusion has been exploited.
机译：本研究旨在分析由二元混合物和纯流体在内部等温加热并在外部冷却的水平环形腔中建立的二维流动的特征。由于对流与热扩散的耦合而引起的热引力扩散，在考虑二元混合物时会出现一些复杂情况。在Boussinesq假设的有效性和粘性耗散可以忽略不计的前提下，假设粘弹性流体的二维层流已定义了分析模型。对于二元混合物，由浓度变化确定的浮力已被忽略，因此动量方程与浓度无关，仅与能量平衡方程耦合。通过与控制该问题的各种无量纲参数中的数值结果进行比较，已验证了二元混合物和纯流体情况下的分析模型。特别地，已经开发了几何形状和边界条件对由于热引力扩散引起的混合物混合物分离的影响。

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