Influence of the Prandtl number on the location of recirculation eddies in thermocapillary flows
The authors consider a two-dimensional thermocapillary-driven flow in a rectangular cavity filled with a fluid whose top surface, open to ambient air, has surface tension acting on it. It is assumed that a horizontal temperature gradient is applied, by differentially heating two of the opposite vertical walls confining the fluid laterally. The authors study the influence of Prandtl number \(Pr\) on the location of recirculation eddies observed either near the hot or the cold sidewalls in thermocapillary-driven flows. The analysis is performed by solving the coupled conservation equations for mass, momentum and energy. Two regions in the fluid are distinguished, the core region where the velocity has only one component \(u = U(z)\) in the horizontal \(x\)-direction, and two end regions where the vertical component of the velocity \(w\) cannot neglected. The influence of the end regions on the core flow is described by the superposition of spatial disturbances on core flow solution. The stability analysis of this perturbed state leads to an eigenvalue problem for the complex wave number of disturbances. This analysis is made for a wide range of Prandtl numbers, from very small to very large ones. The authors show that, depending on the Prandtl number, recirculation eddies can exist either near the hot wall \((Pr \gg 1)\) or the cold wall \((Pr \ll 1).\) They also find that their results are in agreement with previous experimental and numerical findings. In addition, these results provide a direct interpretation of different behaviours observed in previous experimental and numerical studies.
two-dimensional thermocapillary-driven flow
scientific article; zbMATH DE number 1750711