Abstract
The surface tension driven flow induced by the bidirectional temperature differences always exists in various natural processes and phenomena. However, the researchers have mainly focused on the flow resulted from a unidirectional temperature difference. In this paper, combined with a vertical heat transfer, the thermocapillary convection of the silicone oil (Prantal number, Pr = 6.7) in a shallow annular pool is investigated by numerical simulations. We have put emphases on analyzing the effect of the bottom heat flux on the thermocapillary convection driven by a horizontal temperature gradient for three cases, which are divided according to the Marangoni number. The simulation results reveal that a hydrothermal wave coverts into a shorter hydrothermal wave and finally into a chaotic state with the enhancement of the heat flux when an unsteady oscillatory flow takes place in the three cases. The difference lies in the fact that whether the punctate wave and basic flow exist or not, and the details are discussed in this paper. In addition, a small vertical heat transfer can stabilize the thermocapillary convection while the relatively larger bottom heat flux has a negative influence on the stability. This is the first report on this field according to our knowledge, and the obtained results are very different from the ones with unidirectional temperature difference.
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References
Bucchignani, E., Mansutti, D.: Horizontal thermocapillary convection of succinonitrile: Steady state, instabilities, and transition to chaos. Phys. Rev. E 69, 056319 (2004a)
Bucchignani, E.: Numerical characterization of hydrothermal waves in a laterally heated shallow layer. Phys. Fluids 16, 3839–3849 (2004b)
Burguete, J., Mukolobwiez, N., Daviaud, F., Garnier, N., Chiffaudel, A.: Buoyant-thermocapillary instabilities in extended liquid layers subjected to a horizontal temperature gradient. Phys. Fluids. 13, 2773–2787 (2001)
Garnier, N., Chiffaudel, A.: Two dimensional hydrothermal waves in an extended cylindrical vessel. J. Eur. Phys. 19, 87–95 (2001)
Guo, W.D., Narayanan, R.: Onset of Rayleigh-Marangoni convection in a cylindrical annulus heated from below. J. Colloid Interface Sci. 314, 727–732 (2007)
Kim, J., Choi, C. K., Kang, Y. T.: Instability analysis of Marangoni convection for absorption process accompanied by heat transfer. Int. J. Heat Mass Transfer. 47, 2395–2402 (2004)
Kawamura, H., Tagaya, E., Hoshino, Y.: A consideration on the relation between the oscillatory thermocapillary flow in a liquid bridge and the hydrothermal wave in a thin liquid layer. Int. J. Heat Mass Transfer. 50, 1263–1268 (2007)
Kuhlmann, H. C., Albensoeder, S.: Three-dimensional flow instabilities in a thermocapillary-driven cavity. Phys. Rev. E 77, 036303 (2008)
Lebon, G., Dauby, P.C., Regnie, V.C.: Role of interface deformation on Be-Ma instability. ActaAstronautica 48, 617–627 (2001)
Li, Y.R., Peng, L., Wu, S.Y., Imaishi, N., Zeng, D.L.: Thermocapillary-buoyancy flow of silicon melt in a shallow annular pool. Cryst. Res. Technol. 39, 1055–1062 (2004)
Li, Y.R., Quan, X.J., Peng, L., Imaishi, N., Wu, S.Y., Zeng, D.L.: Three-dimensional thermocapillary-buoyancy flow in a shallow molten silicon pool with Cz configuration. Int. J. Heat Mass Transfer 48, 1952–1960 (2005)
Li, Y.R., Peng, L., Wu, S.Y., Imaishi, N.: Bifurcation of thermocapillary convection in a shallow annular pool of silicon melt. Acta Mechan. Sinica 23, 43–48 (2007)
Li, Y.R., Zhang, H.R., Wu, C.M.: Effect of vertical heat transfer on thermocapillary convection in an open shallow rectangular cavity. Heat Mass Transfer 48, 241–251 (2012)
Peng, L., Li, Y.R., Shi, W.Y., Imaishi, N.: Three-dimensional thermocapillary-buoyancy flow of silicone oil in a differentially heated annular pool. Int. J. Heat Mass Transfer 50, 872–880 (2007)
Peng, Z., Li, D., Qi, K.: Transition to chaos in thermocapillary convection. Int. J. Heat Mass Transfer 57, 457–464 (2013)
Riley, R.J., Neitzel, G.P.: Instability of thermocapillary-buoyancy convection in shallow layers. Part 1. Characterization of steady and oscillatory instabilities. J. Fluid Mech. 359, 143–164 (1998)
Schatz, M.F., Vanhook, S.J., McCormick, W.D., Swift, J.B., Swinney, H.L.: Time-independent square patterns in surface-tension-driven Bénard convection. Phys. fluids 11, 2577–2582 (1999)
Shi, W.Y., Imaishi, N.: Hydrothermal waves in differentially heated shallow annular pools of silicone oil. J. Crystal Growth 290, 280–291 (2006)
Siri, Z., Hashim, I.: Control of oscillatory Marangoni convection in a rotating fluid layer. Int. Commun. Heat Mass Transfer 35, 1130–1133 (2008)
Siri, Z., Mustafa, Z., Hashim, I.: Effects of rotation and feedback control on Benard-Marangoni convection. Int. J. Heat Mass Transfer 52, 5770–5775 (2009)
Xu, B., Ai, X., Li, B.Q.: Stabilities of combined radiation and Rayleigh-Benard-Marangoni convection in an open vertical cylinder. Int. J. Heat Mass Transfer 50, 3035–3046 (2007)
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This work was supported by the National Natural Science Foundation of China through the funds (No . 51276203).
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Wang, F., Peng, L., Zhang, Q. et al. Effect of the Vertical Heat Transfer on the Thermocapillary Convection in a Shallow Annular Pool. Microgravity Sci. Technol. 27, 107–114 (2015). https://doi.org/10.1007/s12217-015-9415-3
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DOI: https://doi.org/10.1007/s12217-015-9415-3