Abstract
Using asymptotical analysis, we investigate the characteristics of the coupled thermal and solutal capillary convection with the radial temperature and solute concentration gradients in a shallow annular pool with the free surface. The pool is heated from the outer cylinder with high solutal concentration and cooled at the inner cylinder with low solutal concentration. The asymptotic solution is obtained in the core region in the limit as the aspect ratio, which is defined as the ratio of the depth to the width of the pool, goes to zero. The comparison with the previous work certifies that the asymptotic solution is right and believable. The influences of the solutal capillary force, the buoyant force, the Soret effect and the geometric parameters on the fluid flow are analyzed.
Similar content being viewed by others
References
Schwabe D, Scharmann A, Preisser F, et al. Experiments on surface tension driven flow in floating zone melting. J Cryst Growth, 1978, 43: 305–312
Cröll A, Mitric A, Aniol O, et al. Solutocapillary convection in germanium-silicon melts. Cryst Res Technol, 2009, 44: 1101–1108
Wang J S, Yan J J, Hu S H, et al. Marangoni condensation heat transfer of water-ethanol mixtures on a vertical surface with temperature gradients. Int J Heat Mass Transfer, 2009, 52: 2324–2334
Bergman T L. Numerical simulation of double-diffusive Maragnoni convection. Phys Fluids, 1986, 29: 2103–2108
Arafune K, Hirata A. Interactive solutal and thermal Marangoni convection in a rectangular open boat. Num Heat Transf, 1998, Part A 34: 421–429
Arafune K, Yamamoto K, Hirata A. Interactive solutal and thermal Marangoni convection during compound semiconductor growth in a rectangular open boat. Int J Heat Mass Transf, 2001, 44: 2405–2411
Chan C L, Chen C F. Salt finger convection generated by thermal and solutal capillary motion in a stratified fluid. Int J Heat Mass Transf, 1999, 42: 2143–2159
Chen C F, Chan C L. Stability of buoyancy and surface tension driven convection in a horizontal double-diffusive fluid layer. Int J Heat Mass Transf, 2010, 53: 1563–1569
Li Y S, Chen Z W, Zhan J M. Double-diffusive Marangoni convection in a rectangular cavity: transition to chaos. Int J Heat Mass Transf, 2010, 53: 5223–5231
Chen Z W, Li Y S, Zhan J M. Double-diffusive Marangoni convection in a rectangular cavity: Onset of convection. Phys Fluids, 2010, 22: 0341006
Zhan J M, Chen Z W, Li Y S, et al. Three-dimensional double-diffusive Marangoni convection in a cubic cavity with horizontal temperature and concentration gradients. Phys Rev E, 2010, 82: 066305
Li Y R, Zhao X X, Wu S Y, et al. Asymptotic solution of thermocapillary convection in a thin annular pool of silicon melt. Phys Fluids, 2008, 20: 082107
Li Y R, Wang S C, Wu S Y, et al. Asymptotic solution of thermocapillary convection in a differentially heated thin annular two-layer pool. Microgr Sci Technol, 2010, 22: 193–203
Li Y R, Wang S C, Wu S Y, et al. Asymptotic solution of thermocapillary convection in two immiscible liquid layers in a shallow annular cavity. Sci China Tech Sci, 2010, 53: 1655–1665
Sen A K, Davis S H. Steady thermocapillary flows in two-dimensional slots. J Fluid Mech, 1982, 121: 163–186
Leppinen D M. Natural convection in a shallow cylindrical annuli. Int J Heat Mass Transf, 2002, 45: 2967–2981
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Li, Y., Gong, Z., Wu, C. et al. Steady thermal-solutal capillary convection in a shallow annular pool with the radial temperature and concentration gradients. Sci. China Technol. Sci. 55, 2176–2183 (2012). https://doi.org/10.1007/s11431-012-4924-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11431-012-4924-4