Influence of Heat Transfer on Stability of Newtonian and Non-Newtonian Extending Films
The stability of Newtonian and Non-Newtonian extending films under local or global heating or cooling conditions are considered. The thickness-averaged mass, momentum and energy equations with convective and radiative heat transfer are derived, both for Newtonian and non-Newtonian fluids (Maxwell, PTT and Giesekus models considered). The stability of the system is explored using either eigenvalue analysis or transient simulations. The results showed that the influence of heating and cooling on stability strongly depends on the magnitude of the Peclet number. Examples of stabilization or destabilization of heating or cooling are shown for Pe<< 1, and Pe = O(1) cases, for Newtonian and non-Newtonian flows.
[1] Matovich, M. A., Pearson, J. R. A. Spinning a Molten Threadline:
Steady-State Isothermal Viscous Flows, I&EC Fundamentals, vol. 8, No.
3, August 1969.
[2] Boratav, O. (Industrial Mentor). IMA Minneapolis. Mathematical
Modeling in Industry XII Workshop Report 2008.
[3] Amosov, A., Boratav, O. & Zheng, Z. Draw Resonance in Viscous
Sheets. Bulletin of APS. DFD Vol. 54, No. 19 2009.
[4] Boratav, O. & Zheng. Z. Influence of Inertia, Gravity and Thermal
Conditions on the Draw Resonance. Bulletin of APS. DFD Vol. 55, No.
19 2010.
[5] Boratav, O., Zheng, Z. & Zhou, C.Draw Resonance in Non-Isothermal
Non-Newtonian Viscous Sheets. Bulletin of APS. DFD Vol. 56, No. 18
2011. Also: Influence of Heat Transfer on Stability of Newtonian and
Non-Newtonian Extending Films. Bulletin of APS. DFD Vol. 57, No. 18
2012
[6] Pearson, J. R. A., Matovich, M. A. Spinning a Molten Threadline:
Stability, I&EC Fundamentals, vol. 8, No. 4, November 1969.
[7] Yeow, Y. L. On the Stability of Extending Films: A Model for the Film
Casting Process, J. Fluid Mech., vol. 66, Part 21, pp. 613-622, 1974.
[8] German, R., Khayat, R., and Cui, J. K. Influence of Inertia and Gravity
on the Stability of Filament Jet Flow, Phys. Fluids, 18, 064108, 2006.
[9] Howell, P. D. Models for Thin Viscous Sheets, Euro Jnl of Applied
Mathematics,Vol. 7, pp. 321-343, 1996.
[10] Suman, B. and Kumar, S. Draw Ratio Enhancement in Non-Isothermal
Melt Spinning, AIChe Journal, 55: 581-593, 2008.
[11] Zhou, C. & Kumar, S. Thermal instabilities in melt spinning of
viscoelastic fibers. J. Non-Newtonian Fluid Mech. 165, 879-891, 2010.
[12] Bird, R.B., Armstrong, R.C., Hassager, O., Dynamics of polymeric
liquid, Fluid Mechanics, Vol. 1. Wiley, New York. 1987.
[13] Fisher, R.J., Denn, M.M., A theory of isothermal melt spinning and
draw resonance. AIChE J., 22, 236-246, 1976.
[14] Boratav, O. N., Zheng, Z., Zhou, C., "Stability of non-Newtonian, nonisothermal
Extended Films", 289-292, in book "Advances in Fluid
Mechanics and Heat \& Mass Transfer" editors: Petr Mastny and
ValeriyPerminov, WSEAS Press. ISSN: 2227-4596, ISBN: 978-1-
61804-114-2 (2012).
[1] Matovich, M. A., Pearson, J. R. A. Spinning a Molten Threadline:
Steady-State Isothermal Viscous Flows, I&EC Fundamentals, vol. 8, No.
3, August 1969.
[2] Boratav, O. (Industrial Mentor). IMA Minneapolis. Mathematical
Modeling in Industry XII Workshop Report 2008.
[3] Amosov, A., Boratav, O. & Zheng, Z. Draw Resonance in Viscous
Sheets. Bulletin of APS. DFD Vol. 54, No. 19 2009.
[4] Boratav, O. & Zheng. Z. Influence of Inertia, Gravity and Thermal
Conditions on the Draw Resonance. Bulletin of APS. DFD Vol. 55, No.
19 2010.
[5] Boratav, O., Zheng, Z. & Zhou, C.Draw Resonance in Non-Isothermal
Non-Newtonian Viscous Sheets. Bulletin of APS. DFD Vol. 56, No. 18
2011. Also: Influence of Heat Transfer on Stability of Newtonian and
Non-Newtonian Extending Films. Bulletin of APS. DFD Vol. 57, No. 18
2012
[6] Pearson, J. R. A., Matovich, M. A. Spinning a Molten Threadline:
Stability, I&EC Fundamentals, vol. 8, No. 4, November 1969.
[7] Yeow, Y. L. On the Stability of Extending Films: A Model for the Film
Casting Process, J. Fluid Mech., vol. 66, Part 21, pp. 613-622, 1974.
[8] German, R., Khayat, R., and Cui, J. K. Influence of Inertia and Gravity
on the Stability of Filament Jet Flow, Phys. Fluids, 18, 064108, 2006.
[9] Howell, P. D. Models for Thin Viscous Sheets, Euro Jnl of Applied
Mathematics,Vol. 7, pp. 321-343, 1996.
[10] Suman, B. and Kumar, S. Draw Ratio Enhancement in Non-Isothermal
Melt Spinning, AIChe Journal, 55: 581-593, 2008.
[11] Zhou, C. & Kumar, S. Thermal instabilities in melt spinning of
viscoelastic fibers. J. Non-Newtonian Fluid Mech. 165, 879-891, 2010.
[12] Bird, R.B., Armstrong, R.C., Hassager, O., Dynamics of polymeric
liquid, Fluid Mechanics, Vol. 1. Wiley, New York. 1987.
[13] Fisher, R.J., Denn, M.M., A theory of isothermal melt spinning and
draw resonance. AIChE J., 22, 236-246, 1976.
[14] Boratav, O. N., Zheng, Z., Zhou, C., "Stability of non-Newtonian, nonisothermal
Extended Films", 289-292, in book "Advances in Fluid
Mechanics and Heat \& Mass Transfer" editors: Petr Mastny and
ValeriyPerminov, WSEAS Press. ISSN: 2227-4596, ISBN: 978-1-
61804-114-2 (2012).
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:52720", author = "Olus N. Boratav and Zheming Zheng and Chunfeng Zhou", title = "Influence of Heat Transfer on Stability of Newtonian and Non-Newtonian Extending Films", abstract = "The stability of Newtonian and Non-Newtonian extending films under local or global heating or cooling conditions are considered. The thickness-averaged mass, momentum and energy equations with convective and radiative heat transfer are derived, both for Newtonian and non-Newtonian fluids (Maxwell, PTT and Giesekus models considered). The stability of the system is explored using either eigenvalue analysis or transient simulations. The results showed that the influence of heating and cooling on stability strongly depends on the magnitude of the Peclet number. Examples of stabilization or destabilization of heating or cooling are shown for Pe", keywords = "Extended films, stability, eigen-analysis for stability, transient response, polymer instability, Non-Newtonian fluids.", volume = "7", number = "6", pages = "1041-4", }
