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Hydromagnetic Stability Analysis of a Film Coating Flow Down a Rotating Vertical Cylinder

Published online by Cambridge University Press:  31 March 2011

P.-J. Cheng ,
K.-C. Liu  and
D. T. W. Lin
P.-J. Cheng*
Affiliation:
Department of Mechanical Engineering, Far-East University, Tainan City, Taiwan 74448, R.O.C.
K.-C. Liu
Affiliation:
Department of Mechanical Engineering, Far-East University, Tainan City, Taiwan 74448, R.O.C.
D. T. W. Lin
Affiliation:
Institute of Mechatronic System Engineering, National University of Tainan, Tainan City, Taiwan 70005, R.O.C.
*
* Professor, corresponding author
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Abstract

The influence of both the Rossby number and the Hartmann number on the hydromagnetic stability of a thin liquid film flowing down along the surface of a vertical cylinder is investigated. The long-wave perturbation method is employed to solve for generalized nonlinear kinematic equations with a free film interface. The normal mode approach is used to compute the stability solution for the film flow. The modeling results indicate that the stability of the liquid film is enhanced by increasing the strength of the magnetic field or reducing the speed at which the cylinder rotates. By contrast, the flow becomes relatively more unstable as the cylinder radius is increased at larger values of the Rossby number. Notably, this finding is the opposite of that observed for film flows along a stationary vertical cylinder.

Keywords

Hydromagnetic stability analysisHartmann numberRossby number
Type
Articles
Information
Journal of Mechanics , Volume 27 , Issue 1 , March 2011 , pp. 27 - 36
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2011

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References

REFERENCES

1.Kapitza, P. L., “Wave Flow of Thin Viscous Liquid Films,” Zhurnal Eksperimentalnoii Teoreticheskoi Fiziki, 18, pp. 3–28 (1948).Google Scholar
2.Yih, C. S., “Stability of Parallel Laminar Flow with a Free Surface,” Proceedings of the Second U.S. National Congress of Applied Mechanics, ASME, pp. 623–628 (1954).Google Scholar
3.Benjamin, T. B., “Wave Formation in Laminar Flow Down an Inclined Plane,” Journal of Fluid Mechanics, 2, pp. 554–574 (1967).CrossRefGoogle Scholar
4.Yih, C. S., “Stability of Liquid Flow Down an Inclined Plane,” Physics of Fluids, 6, pp. 321–334 (1963).CrossRefGoogle Scholar
5.Lin, S. P., “Finite Amplitude Side-Band Stability of a Viscous Film,” Journal of Fluid Mechanics, 63, pp. 417–429 (1974).CrossRefGoogle Scholar
6.Nakaya, C., “Equilibrium State of Periodic Waves on the Fluid Film Down a Vertical Wall,” Journal of the Physical Society of Japan, 36, pp. 921–926 (1974).CrossRefGoogle Scholar
7.Krishna, M. V. G. and Lin, S. P., “Nonlinear Stability of a Viscous Film with Respect to Three-Dimensional Side-Band Disturbance,” Physics of Fluids, 20, pp. 1039–1044 (1977).CrossRefGoogle Scholar
8.Pumir, A., Manneville, P., Pomeau, Y., “On Solitary Waves Running Down on Inclined Plane,” Journal of Fluid Mechanics, 135, pp. 27–50 (1983)CrossRefGoogle Scholar
9.Lin, S. P. and Liu, W. C., “Instability of Film Coating of Wires and Tubes,” AIChE Journal, 21, pp. 775–782 (1975).CrossRefGoogle Scholar
10.Krantz, W. B. and Zollars, R. L., “The Linear Hydrodynamic Stability of Film Flow Down a Vertical Cylinder,” AIChE Journal, 22, pp. 930–934 (1976).CrossRefGoogle Scholar
11.Rosenau, P. and Oron, A., “Evolution and Breaking of Liquid Film Flowing on a Vertical Cylinder,” Physics of Fluids A, 1, pp. 1763–1766 (1989).CrossRefGoogle Scholar
12.Cheng, P. I., Chen, C. K. and Lai, H. Y., “Nonlinear Stability Analysis of the Thin Micropolar Liquid Film Flowing Down on a Vertical Cylinder,” Journal of Fluids Engineering, ASME Transaction Journals, American Society of Mechanical Engineers, 123, pp. 411–421 (2001).CrossRefGoogle Scholar
13.Cheng, M. and Chang, H. C., “Stability of Axisymmet-ric Waves on Liquid Films Flowing Down a Vertical Column to Azimuthal and Streamwise Disturbances,” Chemical Engineering Communications, 118, pp. 327–340 (1992).CrossRefGoogle Scholar
14.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
15.Hsieh, D. Y., “Stability of Conducting Fluid Flowing Down an Inclined Plane in a Magnetic Field,” Physics of Fluids, 8, pp. 1785–1791 (1965).CrossRefGoogle Scholar
16.Renardy, Y. and Sun, S. M., “Stability of a Layer of Viscous Magnetic Fluid Flow Down an Inclined Plane,” Physics of Fluids A, 6, pp. 3235–3246 (1994).CrossRefGoogle Scholar
17.Shen, M. C., Sun, S. M. and Meyer, R. E., “Surface Waves on Viscous Magnetic Fluid Flow Down an Inclined Plane,” Physics of Fluids A, 3, pp. 439–445 (1991).CrossRefGoogle Scholar
18.Eldabe, N. T. M., El-Sabbagh, M. F. and El-Sayed, M. A. S., “Hydromagnetic Stability of Plane Poiseuille and Couette Flow of Viscoelastic Fluid,” Fluid Dynamics Research, 38, pp. 699–715 (2006).CrossRefGoogle Scholar
19.Cheng, P. J., “Hydromagnetic Stability of a Thin Electrically Conducting Fluid Film Flowing Down the Outside Surface of a Long Vertically Aligned Column,” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 223, pp. 415–426 (2009).Google Scholar
20.Chen, C. I., Chen, C. K. and Yang, Y. T., “Nonlinear-Stability Analysis of a Thin Newtonian Film Flowing Down an Infinite Vertical Rotating Cylinder,” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 219, pp. 911–923 (2005).Google Scholar
21.Chen, C. I., Chen, C. K. and Yang, Y. T., “Weakly Nonlinear Stability Analysis of Thin Viscoelastic Film Flowing Down on the Outer Surface of a Rotating Vertical Cylinder,” International Journal for Engineering Science, 41, pp. 1313–1336 (2003).CrossRefGoogle Scholar
22.Moffatt, H. K., “Behaviour of a Viscous Film on the Outer Surface of a Rotating Cylinder,” Journal de Mécanique, 16, pp. 651–673 (1977).Google Scholar
23.Davalos-Orozco, L. A. and Ruiz-Chavarria, G., “Hy-drodynamic Instability of a Liquid Layer Flowing Down a Rotating Cylinder,” Physics of Fluids A, 5, pp. 2390–2404 (1993).CrossRefGoogle Scholar
24.Kakac, S., Shah, R. K. and Aung, W., Handbook of Single-Phase Heat Transfer, John Wiley and Sons (1987).Google Scholar
25.Edwards, D. A., Brenner, H. and Wasan, D. T., Interfacial Transport Processes and Rheology, Butterworth-Heinemann, a Division of Reed Publishing (USA) Inc. (1991).Google Scholar