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Stability Analysis on Viscous Magnetic Fluid Film Flowing Down Along a Vertical Cylinder

Published online by Cambridge University Press:  05 May 2011

P.-J. Cheng  and
K.-C. Liu
P.-J. Cheng*
Affiliation:
Department of Mechanical Engineering, Far-East University, Tainan, Taiwan 74448, R.O.C.
K.-C. Liu*
Affiliation:
Department of Mechanical Engineering, Far-East University, Tainan, Taiwan 74448, R.O.C.
*
*Corresponding author
**Associate Professor
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Abstract

The paper investigates the hydromagnetic stability theory of a thin electrically conductive fluid film flowing down along the outside surface of a vertical cylinder. The long-wave perturbation method is employed to solve for generalized kinematic equations with free film interface. The normal mode approach is used to compute the stability solution for the film flow. The modeling results display that the degree of instability in the film flow is further intensified by the lateral curvature of cylinder. This is somewhat different from that of the planar flow. It is also observed that by increasing the effect of the magnetic field and increasing the radius of the cylinder the film flow can become relatively more stable as traveling down along the vertical cylinder.

Keywords

Thin filmHydromagnetic stability analysisLong-wave perturbation
Type
Articles
Information
Journal of Mechanics , Volume 23 , Issue 2 , June 2007 , pp. 127 - 134
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2007

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References

1.Yih, C. S., “Stability of Parallel Laminar Flow with a Free Surface,” Proceedings of the second U.S. National Congress of Applied Mechanics, pp. 623–628 (1954).Google Scholar
2.Landau, L. D., “On the Problem of Turbulence,” C.R. Acad. Sci. U.R.S.S.,44,pp. 311–314(1944).Google Scholar
3.Stuart, J. T., “On the Role of Reynolds Stresses in Stability Theory,” J. Aero. Sci., 23, pp. 86–88 (1956).Google Scholar
4.Benjamin, T. B., “Wave Formation in Laminar Flow Down an Inclined Plane,” J. Fluid Mech., 2, pp. 554–574 (1957).CrossRefGoogle Scholar
5.Yih, C. S., “Stability of Liquid Flow Down an Inclined Plane,” Phys. Fluids, 6, pp. 321–334 (1963).CrossRefGoogle Scholar
6.Benney, D. J., “Long Waves on Liquid Film,” J. Math. Phys., 45, pp. 150–155 (1966).CrossRefGoogle Scholar
7.Lin, S. P., “Finite Amplitude Side-Band Stability of a Viscous Film,” J. Fluid Mech., 63, pp. 417–429 (1974).CrossRefGoogle Scholar
8.Nakaya, C., “Equilibrium State of Periodic Waves on the Fluid Film Down a Vertical Wall,” J. Phys. Soc. Japan, 36, pp. 921–926(1974).CrossRefGoogle Scholar
9.Krishna, M. V. G. and Lin, S. P., “Nonlinear Stability of a Viscous Film with Respect to Three-Dimensional Side-Band Disturbance,” The Physics of Fluids, 20, pp. 1039–1044 (1977).CrossRefGoogle Scholar
10.Pumir, A., Manneville, P. and Pomeau, Y., “On Solitary Waves Running Down on Inclined Plane,” J. Fluid Mech. 135, pp. 27–50(1983).CrossRefGoogle Scholar
11.Miladinova, S., Lebon, G. and Toshev, E., “Thin-Film Flow of a Power-Law Liquid Falling Down an Inclined Plate,” J. Non-Newtonian Fluid Mech., 122, pp. 69–78 (2004).CrossRefGoogle Scholar
12.Gorla, R. S. R., “Rupture of the Thin Power-Law Liquid Film on a Cylinder,” Transactions of the ASME: J. of Appl. Mech., 68, pp. 294–297 (2001).CrossRefGoogle Scholar
13.Wu, L. Y. and Tsai, Y. F., “Variational Stability Analysis of Cohesive Slope by Applying Boundary Integral Equation Method,” Journal of Mechanics, 21, pp. 187–198 (2005).CrossRefGoogle Scholar
14.Cheng, P. J. and Lai, H. Y., “Nonlinear Stability Analysis of Thin Film Flow from a Liquid Jet Impinging on a Circular Concentric Disk,” Journal of Mechanics, 22, pp. 115–124(2006).CrossRefGoogle Scholar
15.Lin, S. P. and Liu, W. C., “Instability of film coating of wires and tubes,” AICHEJ., 21, pp. 775–782 (1975).CrossRefGoogle Scholar
16.Krantz, W. B. and Zollars, R. L., “The Linear Hydrody-Namic Stability of Film Flow Down a Vertical Cylinder,” AICHEJ., 22, pp. 930–934 (1976).CrossRefGoogle Scholar
17.Rosenau, P. and Oron, A., “Evolution and Breaking of Liquid Film Flowing on a Vertical Cylinder,” Phys. Fluids A, 1,pp. 1763–1766(1989).CrossRefGoogle Scholar
18.Davalos-Orozco, L. A. and Ruiz-Chavarria, G., “Hydrodynamic Instability of a Liquid Layer Flowing Down a Rotating Cylinder,” Phys. Fluids A, 5, pp. 2390–2404 (1993).CrossRefGoogle Scholar
19.Hung, C. I., Chen, C. K. and Tsai, J. S., “Weakly Nonlinear Stability Analysis of Condensate Film Flow Down a Vertical Cylinder,” Int. J. Heat Mass Transfer, 39, pp. 2821–2829 (1996).CrossRefGoogle Scholar
20.Cheng, P. J., Chen, C. K. and Lai, H. Y., “Nonlinear Stability Analysis of the Thin Micropolar Liquid Film Flowing Down on a Vertical Cylinder,” Transactions of the ASME: J. of Fluids Engineering, 123, pp. 411–421 (2001).Google Scholar
21.Tsai, J. S., Hung, C. I. and Chen, C. K., “Nonlinear Hydromagnetic Stability Analysis of Condensation Film Flow Down a Vertical Plate,” Acta Mechanica, 118, pp. 197–212(1996).CrossRefGoogle Scholar
22.Hsieh, D. Y., “Stability of Conducting Fluid Flowing Down an Inclined Plane in a Magnetic Field,” Phys. Fluids, 8, pp. 1785–1791(1965).CrossRefGoogle Scholar
23.Renardy, Y. and Sun, S. M., “Stability of a Layer of Viscous Magnetic Fluid Flow Down an Inclined Plane,” Phys. Fluids, 6, pp. 3235–3246 (1994).CrossRefGoogle Scholar
24.Shen, M. C., Sun, S. M. and Meyer, R. E., “Surface Waves on Viscous Magnetic Fluid Flow Down an Inclined Plane,” Phys. Fluids A, 3, pp. 439–445 (1991).CrossRefGoogle Scholar
25.Kakac, S., Shah, R. K. and Aung, W., “Handbook of Single-Phase Heat Transfer,” John Wiley & Sons (1987).Google Scholar
26.Edwards, D. A., Brenner, H. and Wasan, D. T., “Interfacial Transport Processes and Rheology,” Butterworth-Heinemann, a Division of Reed Publishing (U.S.A.) Inc (1991).Google Scholar