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Hydromagnetic instability of a power-law liquid film flowing down a vertical cylinder using numerical approximation approach techniques. (English) Zbl 1205.76295
Summary: The long-wave perturbation method is employed to investigate the hydromagnetic stability of a thin electrically-conductive power-law liquid film flowing down the external surface of a vertical cylinder in a magnetic field. The validity of the numerical results is improved through the introduction of the flow index and the magnetic force into the governing equation. In contrast to most previous studies presented in the literature, the solution scheme employed in this study is based on a numerical approximation approach rather than an analytical method. The normal mode approach is used to analyze the stability of the film flow. The modeling results reveal that the stability of the film flow system is weakened as the radius of the cylinder is reduced. However, the flow stability can be enhanced by increasing the intensity of the magnetic field and the flow index, respectively. In general, the optimum conditions can be found through the use of a system to alter stability of the film flow by controlling the applied magnetic field.
76W05Magnetohydrodynamics and electrohydrodynamics
76A05Non-Newtonian fluids
Full Text: DOI
[1] Lin, S. P.; Liu, W. C.: Instability of film coating of wires and tubes, Aiche J. 21, 775-782 (1975)
[2] Krantz, W. B.; Zollars, R. L.: The linear hydrodynamic stability of film flow down a vertical cylinder, Aiche J. 22, 930-934 (1976)
[3] Rosenau, P.; Oron, A.: Evolution and breaking of liquid film flowing on a vertical cylinder, Phys. fluids A 1, 1763-1766 (1989)
[4] Davalos-Orozco, L. A.; Ruiz-Chavarria, G.: Hydrodynamic instability of a liquid layer flowing down a rotating cylinder, Phys. fluids A 5, 2390-2404 (1993) · Zbl 0796.76034 · doi:10.1063/1.858753
[5] Hung, C. I.; Chen, C. K.; Tsai, J. S.: Weakly nonlinear stability analysis of condensate film flow down a vertical cylinder, Int. J. Heat mass transfer 39, 2821-2829 (1996) · Zbl 0964.76507 · doi:10.1016/0017-9310(95)00355-X
[6] Kudrolli, A.; Pier, B.; Gollub, J. P.: Superlattice patterns in surface waves, Phys. D 123, 99-111 (1998) · Zbl 0953.76521 · doi:10.1016/S0167-2789(98)00115-8
[7] Alekseenko, S. V.; Markovich, D. M.: Jet flow in a bank of cylinders, Prev. heat mass transfer 21, 302 (1995)
[8] Chang, C. L.: Nonlinear stability analysis of thin micropolar film flows traveling down on a vertical moving plate, J. phys. D: appl. Phys. 39, 984-992 (2006)
[9] Cheng, P. J.; Chen, C. K.; Lai, H. Y.: Nonlinear stability analysis of the thin micropolar liquid film flowing down on a vertical cylinder, Trans. ASME: J. Fluids eng. 123, 411-421 (2001)
[10] Gupta, A. S.: Stability of a viscoelastic liquid film flowing down an inclined plane, J. fluid mech. 28, 17-28 (1967) · Zbl 0145.46303 · doi:10.1017/S0022112067001879
[11] Chen, C. I.; Chen, C. K.; Yang, Y. T.: Nonlinear stability analysis of thin viscoelastic film flowing down on the inner surface of a rotating vertical cylinder, Nonlinear dyn. 42, 1-23 (2005) · Zbl 1142.76382 · doi:10.1007/s11071-005-0044-z
[12] Bird, R. B.; Armstrong, R. C.; Hassager, O.: Dynamics of polymeric liquids -- fluid mechanics, (1977)
[13] Ng, C. O.; Mei, C. C.: Roll waves on a shallow layer of mud modelled as a power-law fluid, J. fluid mech. 263, 151-183 (1994) · Zbl 0841.76011 · doi:10.1017/S0022112094004064
[14] Hwang, C. C.; Chen, J. L.; Wang, J. S.; Lin, J. S.: Linear stability of power law liquid film flows down an inclined plane, J. phys. D: appl. Phys. 27, 2297-2301 (1994)
[15] Miladinova, S.; Lebon, G.; Toshev, E.: Thin-film flow of a power-law liquid falling down an inclined plate, J. non-Newtonian fluid mech. 122, 69-78 (2004) · Zbl 1143.76341 · doi:10.1016/j.jnnfm.2004.01.021
[16] Gorla, R. S. R.: Rupture of the thin power-law liquid film on a cylinder, Trans. ASME: J. Appl. mech. 68, 294-297 (2001) · Zbl 1110.74460 · doi:10.1115/1.1355033
[17] Perazzo, C. A.; Gratton, J.: Steady and traveling flows of a power-law liquid over an incline, J. non-Newtonian fluid mech. 118, 57-64 (2004) · Zbl 1078.76010 · doi:10.1016/j.jnnfm.2004.02.003
[18] Tsai, J. S.; Hung, C. I.; Chen, C. K.: Nonlinear hydromagnetic stability analysis of condensation film flow down a vertical plate, Acta mech. 118, 197-212 (1996) · Zbl 0872.76038 · doi:10.1007/BF01410517
[19] Hsieh, D. Y.: Stability of conducting fluid flowing down an inclined plane in a magnetic field, Phys. fluids 8, 1785-1791 (1965)
[20] Renardy, Y.; Sun, S. M.: Stability of a layer of viscous magnetic fluid flow down an inclined plane, Phys. fluids 6, 3235-3246 (1994) · Zbl 0832.76026 · doi:10.1063/1.868056
[21] Shen, M. C.; Sun, S. M.; Meyer, R. E.: Surface waves on viscous magnetic fluid flow down an inclined plane, Phys. fluids A 3, 439-445 (1991) · Zbl 0733.76089 · doi:10.1063/1.858100
[22] Eldabe, N. T. M.; El-Sabbagh, M. F.; El-Sayed, M. A. -S.: Hydromagnetic stability of plane Poiseuille and Couette flow of viscoelastic fluid, Fluid dyn. Res. 38, 699-715 (2006) · Zbl 1135.76025 · doi:10.1016/j.fluiddyn.2006.05.002
[23] Kakac, S.; Shah, R. K.; Aung, W.: Handbook of single-phase heat transfer, (1987)
[24] Cheng, P. J.; Lin, D. T. W.: Surface waves on viscoelastic magnetic fluid film flow down a vertical column, Int. J. Eng. sci. 45, 905-922 (2007) · Zbl 1213.76066 · doi:10.1016/j.ijengsci.2007.07.001
[25] Edwards, D. A.; Brenner, H.; Wasan, D. T.: Interfacial transport processes and rheology, (1991)
[26] Goren, S.: The instability of an annular thread of fluid, J. fluid mech. 12, 309-319 (1962) · Zbl 0105.39602 · doi:10.1017/S002211206200021X
[27] Solorio, F. J.; Sen, M.: Linear stability of a cylindrical falling film, J. fluid mech. 183, 365-377 (1987)