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Nonisothermal Film Blowing: Mathematical Insights

Abstract -- In this paper, we talk about the importance of having a proper mathematical description when dealing with problems that originate in Engineering. We describe part of our work regarding the nonisothermal situation of film blowing with the intents of making engineers get an interest in proper mathematical modelling. We talk about how the history of the problem was until 2002, when we started working with it, and what sort of wealth we added to its analysis that made it look more mathematical. We also talk about minor aspects of the mathematical description that can be changed a little to improve the results of the analysis of the problem.


Index & Keywords --


nonisothermal, film, blowing, polymer, melt, bubble, plastic, park, han, tam

 


References --


[1]     Pinheiro, M. R. (2005). Nonisothermal Newtonian Film Blowing. Mathematical Modelling and Analysis. Vol. 10, issue 3, pp. 305 -- 308.

[2]     Han, C. D. and Park, J. Y. (1975). Studies on Blown Film Extrusion II. Analysis of the Deformation and Heat Transfer Processes.  Journal of Applied Polymer Science. Vol. 19, pp. 3277 – 3290.

[3]     Tam, D. C. H. (2003). Mathematical Analysis of the Blown Newtonian Film. RMIT, Department of Mathematics and Statistics.

[4]     Alaie, S. M. and Papanastasiou, T. C. (1993). Modeling of non-isothermal film blowing with integral constitutive equations.Hanser Publishers.

[5]     Kanai, T. and White, J. L. (1984). Dynamics and stability of the tubular film extrusion of various polyethylenes. Polym. Eng. Sci. Vol. 24, pp. 1185 – 1201.

[6]     Yamane, H. and White, J. L. (1987). Int. Polym. Process. Vol. 2, issue 107.

[7]     Pearson, J. R. and Petrie, C. J. S. (1970). The flow of a tubular film. Part 2: Interpretation of the model and discussion of solutions. J. Fluid Mech. Vol. 42, issue 60.

[8]     Pearson, J. R. and Petrie, C. J. S. (1970). The flow of a tubular film. Part 1: Formal mathematical representation. J. Fluid Mech. Vol. 40, issue 1.

[9]     Han, C. D. and Park, J. Y. (1975). Studies on Blown Film Extrusion I. Experimental determination of Elongational Viscosity. Journal of Applied Polymer Science. Vol. 19, pp. 3257 -- 3276.

[10] Muke, S., Connell, H. and Bhattacharya, S. N. (2003). Numerical modeling and experimental verification of blown film processing. Journal of Non-Newtonian Fluid Mechanics.

[11] Sheppherd, J. J., Connell, H. J. and Tam, D. C. H. (2005). An Interior Layer in a Film-Blowing Problem. Preprint, RMIT.

[12] Pearson, J. R.(1985). Mechanics of Polymer Processing. Elsevier Applied Science, USA.

 

 

 

 

 

 

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About the Author

Dr. M. R. Pinheiro

Dr. MARCIA PINHEIRO

RGMIA

PO Box 12396 A’Beckett St, Melbourne, VIC, AU, 8006

AUSTRALIA

drmarciapinheiro@gmail.com


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