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.<\/p>\r\n","references":"[1] Matovich, M. A., Pearson, J. R. A. Spinning a Molten Threadline:\r\nSteady-State Isothermal Viscous Flows, I&EC Fundamentals, vol. 8, No.\r\n3, August 1969.\r\n[2] Boratav, O. (Industrial Mentor). IMA Minneapolis. Mathematical\r\nModeling in Industry XII Workshop Report 2008.\r\n[3] Amosov, A., Boratav, O. & Zheng, Z. Draw Resonance in Viscous\r\nSheets. Bulletin of APS. DFD Vol. 54, No. 19 2009.\r\n[4] Boratav, O. & Zheng. Z. Influence of Inertia, Gravity and Thermal\r\nConditions on the Draw Resonance. Bulletin of APS. DFD Vol. 55, No.\r\n19 2010.\r\n[5] Boratav, O., Zheng, Z. & Zhou, C.Draw Resonance in Non-Isothermal\r\nNon-Newtonian Viscous Sheets. Bulletin of APS. DFD Vol. 56, No. 18\r\n2011. Also: Influence of Heat Transfer on Stability of Newtonian and\r\nNon-Newtonian Extending Films. Bulletin of APS. DFD Vol. 57, No. 18\r\n2012\r\n[6] Pearson, J. R. A., Matovich, M. A. Spinning a Molten Threadline:\r\nStability, I&EC Fundamentals, vol. 8, No. 4, November 1969.\r\n[7] Yeow, Y. L. On the Stability of Extending Films: A Model for the Film\r\nCasting Process, J. Fluid Mech., vol. 66, Part 21, pp. 613-622, 1974.\r\n[8] German, R., Khayat, R., and Cui, J. K. Influence of Inertia and Gravity\r\non the Stability of Filament Jet Flow, Phys. Fluids, 18, 064108, 2006.\r\n[9] Howell, P. D. Models for Thin Viscous Sheets, Euro Jnl of Applied\r\nMathematics,Vol. 7, pp. 321-343, 1996.\r\n[10] Suman, B. and Kumar, S. Draw Ratio Enhancement in Non-Isothermal\r\nMelt Spinning, AIChe Journal, 55: 581-593, 2008.\r\n[11] Zhou, C. & Kumar, S. Thermal instabilities in melt spinning of\r\nviscoelastic fibers. J. Non-Newtonian Fluid Mech. 165, 879-891, 2010.\r\n[12] Bird, R.B., Armstrong, R.C., Hassager, O., Dynamics of polymeric\r\nliquid, Fluid Mechanics, Vol. 1. Wiley, New York. 1987.\r\n[13] Fisher, R.J., Denn, M.M., A theory of isothermal melt spinning and\r\ndraw resonance. AIChE J., 22, 236-246, 1976.\r\n[14] Boratav, O. N., Zheng, Z., Zhou, C., \"Stability of non-Newtonian, nonisothermal\r\nExtended Films\", 289-292, in book \"Advances in Fluid\r\nMechanics and Heat \\& Mass Transfer\" editors: Petr Mastny and\r\nValeriyPerminov, WSEAS Press. ISSN: 2227-4596, ISBN: 978-1-\r\n61804-114-2 (2012).","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 78, 2013"}