Thermal Convection in an Annular Two-Layer System Under Combined Action of Buoyancy and Thermocapillary Forces

Linear-stability Analysis of Thermocapillary Flow in an Annular Two-layer System with Upper Rigid Wall

“…For other configurations with different fluid layer thickness, the same procedure of grid convergence tests was performed before the data are adopted in this paper. The validation of the method in this work could be confirmed by comparing the results with the numerical simulation obtained by Li et al (2010) at ε = 0.5, h = 4 mm and Γ = 0.2 with the presence of gravity. It could be found that the critical Marangoni numbers of flow transition are 1.61 × 10 6 and 1.54 × 10 6 , respectively.…”

“…Liu et al (1998) performed numerical simulations in cavities with different aspect ratios for coupled thermocapillary and buoyancy-driven convection. Recently, Li et al (2008Li et al ( , 2009Li et al ( , 2010 investigated the stable and unstable thermal convection of two superposed horizontal liquid layers in a shallow annular cavity subjected to a radial temperature gradient by using asymptotical analysis and numerical simulation. In this paper, the results of a set of linear-stability analysis for the thermocapillary flow in an annular two-layer system are thoroughly presented.…”

Linear-stability analysis of thermocapillary-buoyancy convection in annular two-layer system with a radial temperature gradient

“…In the numerical simulation for the basic flow and the linear stability analysis, non-uniform staggered grids of 100 R × 40 Z are used. The grid convergence was verified in our previous work [13,14,16]. In order to validate the current code, a linear-stability analysis was performed for the thermocapillary convection in a single liquid pool (r o = 40 mm and r i = 20 mm) filled with 0.65cSt silicone oil.…”

“…The velocity and temperature fields are obtained by two-dimensional direct numerical simulation, as shown in Refs. [13,14]. This flow is called as the basic flow.…”

“…Furthermore, a linear perturbative analysis revealed that depending on the relative height of both liquids, three kinds of patterns exist: either wave propagation from cold to the hot region, or waves propagating in the opposite direction or still stationary longitudinal rolls. Recently, Li et al [12][13][14] investigated the thermal convection of two superposed horizontal liquid layers in a shallow annular pool subjected to a radial temperature gradient by using asymptotical analysis and numerical simulations. The velocity and temperature fields were obtained for a sufficiently small Marangoni number in the core region in the limit as the aspect ratio goes to zero.…”