Effect of the horizontal aspect ratio on thermocapillary convection stability in annular pool with surface heat dissipation. (February 2020)

• Record Type: Journal Article
• Authors: López-Núñez, E.; Pérez-Quiles, M.J.; Fajardo, P.; Hoyas, S.
• Is Part Of: International journal of heat and mass transfer. Volume 148(2020)
• Publication Date: 2020-02
• Subjects: Thermocapillary convection -- Linear stability -- Flow perturbations -- Bond number; Heat -- Transmission -- Periodicals; Mass transfer -- Periodicals; Chaleur -- Transmission -- Périodiques; Transfert de masse -- Périodiques; Electronic journals; 621.4022
• DOI: 10.1016/j.ijheatmasstransfer.2019.119140
• Languages: English
• ISSNs: 0017-9310

Abstract

Highlights: Up to 3 different thermo-convective perturbations (SR, LR & HWI) for large Bond. For the lower Bond numbers only two appear (LR & HWI). Strong dependency of the co-dimension two boundaries with the Bond number. Horizontal aspect ratio influences the number of structures in the perturbations. Abstract: A linear stability analysis of the thermoconvective problem of a thin liquid film contained in an annular domain has been conducted. The influence of the horizontal aspect ratio on the solution has been considered by keeping a fixed external wall while the internal radius of the annular domain was modified. The parameter used in the study, Γ h, has been defined as the ratio of the internal radius to the domain depth. The other control parameter of the study is the Prandtl number ranging from 0.7 to 50, i.e. characteristic of fluids as air to n − butanol. The study has been performed for different Bond (Bo) regimes ranging from 0.0 for surface tension dominated flows to 67 for buoyancy dominated ones. Three different kind of bifurcations are found in the Γ h − Pr plane for large Bonds, while for low Bonds only two of them appear. In the case of pure buoyancy or surface tension flows, for every Γ h there exists a Prandtl number such that oscillatory and stationary coexist in a co-dimension two bifurcation point. These transitions show a strong dependency with the Bond number. Indeed, the lower transition disappears for low Bo and the upper one disappears with intermediate Bo values. Furthermore, there is a non-linear dependency of the number of structures of the growing bifurcation with Γ h . These co-dimension two lines show a strong dependency with Bo. Firstly, looking at the frontier between HWI and LR regions, for large Bo numbers, Pr increases with Γ h, while for low Bo the trend is reversed. Additionally, this transition only appears in the extreme Bo cases, for the central values of the considered, no transition is found. Similarly, the second transition found only appears for Bo larger than 30.