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In order to understand the characteristics of the coupled thermal and solutal capillary convection with the radial temperature gradient in a slowly rotating shallow annular pool with the free surface, the asymptotic solution is obtained in the core region using asymptotical analysis in the limit as the aspect ratio, which is defined as the ratio of the layer thickness to the gap width, goes to zero. The influences of the rotating, Soret effect, solute diffusion coefficient, buoyant force and geometric parameters on fluid flow are analyzed. The results show that when the rotating and the solutal capillary force and the buoyancy induced by the ununiform distribution of solute concentration are not considered, the asymptotic solution is the same as that of the previous work. The influences of the rotating, the buoyancy, solute diffusion coefficient and the geometric parameters on the fluid flow are all small and the coupled thermal and solutal capillary forces play a dominant role in the convection. When the coupled forces are in the same direction, the flow is reinforced, otherwise, the flow is suppressed.
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Keywords:
- rotating /
- shallow annular pool /
- coupled thermal and solutal capillary convection /
- asymptotic solution
[1] Schwabe D, Scharmann A, Preisser F, Oeder R 1978 J. Cryst. Growth 43 305
[2] Cröll A, Mitric A, Aniol O, Schtt S, Simon P 2009 Cryst. Res. Technol. 44 1101
[3] Wang J S, Yan J J, Hu S H, Liu J P 2009 Int. J. Heat Mass Transfer 52 1533
[4] Bergman T L 1986 Phys. Fluids 29 2103
[5] Bergeon A, Henry D, Benhadid L H, Tuckerman L S 1998 J. Fluid Mech. 375 143
[6] Arafune K, Hirata A 1998 Numerical Heat Transfer A 44 421
[7] Arafune K, Yamamoto K, Hirata A 2001 Int. J. Heat Mass Transfer 44 2405
[8] Chen C F, Chan C L 2010 Int. J. Heat Mass Transfer 53 1563
[9] Li Y S, Chen Z W, Zhan J M 2010 Int. J. Heat Mass Transfer 53 5223
[10] Chen Z W, Li Y S, Zhan J M 2010 Phys. Fluids 22 0341006
[11] Zhan J M, Chen Z W, Li Y S, Nie Y H 2010 Phys. Rev. E 82 066305
[12] Li Y R, Wu C M, Wu S Y, Peng L 2009 Phys. Fluids 21 084102
[13] Shi W Y, Ermakov M K, Imaishi N 2006 J. Cryst. Growth 294 474
[14] Zheng L C, Sheng X Y, Zhang X X 2006 Acta Phys. Sin. 55 5298 (in Chinese) [郑连存, 盛晓艳, 张欣欣 2006 物理学报 55 5298]
[15] Zheng L C, Feng Z F, Zhang X X 2007 Acta Phys. Sin. 56 1549 (in Chinese) [郑连存, 冯志丰, 张欣欣 2007 物理学报 56 1549]
[16] Zhang Y, Zheng L C, Zhang X X 2009 Acta Phys. Sin. 58 5506 (in Chinese) [张艳, 郑连存, 张欣欣 2009 物理学报 58 5506]
[17] Cormack D E, Leal L G 1974 J. Fluid Mech. 65 209
[18] Merker G P, Leal L G 1980 Int. J. Heat Mass Transfer 23 677
[19] Leppinen D M 2002 Int. J. Heat Mass Transfer 45 2967
[20] Li Y R, Zhao X X, Wu S Y, Peng L 2008 Phys. Fluids 20 082107
[21] Li Y R, Ouyang Y Q, Wang S C, Wu S Y 2010 J. Eng. Thermophys. 31 1921 (in Chinese) [李友荣, 欧阳玉清, 王双成, 吴双应 2010 工程热物理学报 31 1921]
[22] Li Y R, Wang S C, Wu S Y, Peng L 2010 Microgravity Sci. Technol. 22 193
[23] Sen A K, Davis S H 1982 J. Fluid Mech. 12 163
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[1] Schwabe D, Scharmann A, Preisser F, Oeder R 1978 J. Cryst. Growth 43 305
[2] Cröll A, Mitric A, Aniol O, Schtt S, Simon P 2009 Cryst. Res. Technol. 44 1101
[3] Wang J S, Yan J J, Hu S H, Liu J P 2009 Int. J. Heat Mass Transfer 52 1533
[4] Bergman T L 1986 Phys. Fluids 29 2103
[5] Bergeon A, Henry D, Benhadid L H, Tuckerman L S 1998 J. Fluid Mech. 375 143
[6] Arafune K, Hirata A 1998 Numerical Heat Transfer A 44 421
[7] Arafune K, Yamamoto K, Hirata A 2001 Int. J. Heat Mass Transfer 44 2405
[8] Chen C F, Chan C L 2010 Int. J. Heat Mass Transfer 53 1563
[9] Li Y S, Chen Z W, Zhan J M 2010 Int. J. Heat Mass Transfer 53 5223
[10] Chen Z W, Li Y S, Zhan J M 2010 Phys. Fluids 22 0341006
[11] Zhan J M, Chen Z W, Li Y S, Nie Y H 2010 Phys. Rev. E 82 066305
[12] Li Y R, Wu C M, Wu S Y, Peng L 2009 Phys. Fluids 21 084102
[13] Shi W Y, Ermakov M K, Imaishi N 2006 J. Cryst. Growth 294 474
[14] Zheng L C, Sheng X Y, Zhang X X 2006 Acta Phys. Sin. 55 5298 (in Chinese) [郑连存, 盛晓艳, 张欣欣 2006 物理学报 55 5298]
[15] Zheng L C, Feng Z F, Zhang X X 2007 Acta Phys. Sin. 56 1549 (in Chinese) [郑连存, 冯志丰, 张欣欣 2007 物理学报 56 1549]
[16] Zhang Y, Zheng L C, Zhang X X 2009 Acta Phys. Sin. 58 5506 (in Chinese) [张艳, 郑连存, 张欣欣 2009 物理学报 58 5506]
[17] Cormack D E, Leal L G 1974 J. Fluid Mech. 65 209
[18] Merker G P, Leal L G 1980 Int. J. Heat Mass Transfer 23 677
[19] Leppinen D M 2002 Int. J. Heat Mass Transfer 45 2967
[20] Li Y R, Zhao X X, Wu S Y, Peng L 2008 Phys. Fluids 20 082107
[21] Li Y R, Ouyang Y Q, Wang S C, Wu S Y 2010 J. Eng. Thermophys. 31 1921 (in Chinese) [李友荣, 欧阳玉清, 王双成, 吴双应 2010 工程热物理学报 31 1921]
[22] Li Y R, Wang S C, Wu S Y, Peng L 2010 Microgravity Sci. Technol. 22 193
[23] Sen A K, Davis S H 1982 J. Fluid Mech. 12 163
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