An iterative approach to the thermal Newtonian blown film model

Film blowing, by which thin polymer film is manufactured, is an industrial process with products used in a wide range of applications. Modelling of this process requires solving the highly nonlinear differential equations necessary to describe the complex chemical and physical interactions involved. Earlier work applied a mixture of analytic and numerical techniques to this modelling when the polymer involved was a Newtonian fluid operating under isothermal conditions. Subsequent calculations extended this analysis to the non-isothermal Newtonian film. However, the numerical procedures used were found to be computationally expensive. We apply a more robust finite element approach to these computations, that avoids the difficulties of the earlier methods, and is an improvement on these previous efforts. References Ervin V. J., Non-uniqueness of the Newtonian film blowing model, in preparation. Bennett J. C., Interior Layer Structure in the Blown Newtonian Film, Honours Thesis, School of Mathematical and Geospatial Science, RMIT, 2004. Bennett J. C. and Shepherd J. J., Analysis of the non-isothermal Newtonian model in the blown film process, ANZIAM Journal (E), 47, pp. C325--C338, 2006. http://anziamj.austms.org.au/V47EMAC2005/Bennett Luo X.-L. and Tanner R. I., A computer study of film blowing, Polymer Engineering and Science Vol. 25, No. 10, 1985, pp. 620--629. Muke S., Connell H., Sbarski I. and Bhattacharya S. N., Numerical modelling and experimental verification of blown film processing, Journal of Non-Newtonian Fluid Mechanics Vol. 116, 2003, pp. 113--138. doi:10.1016/j.jnnfm.2003.09.002 Pearson J. R. A., Mechanics of Polymer Processing, Elsevier Applied Science Publishers, 1985. Pearson J. R. A. and Petrie C. J. S., The flow of a tubular film. Part 1. Formal mathematical representation, Journal of Fluid Mechanics Vol. 40, 1970, pp. 1--19. Pearson J. R. A. and Petrie C. J. S., The flow of a tubular film. Part 2. Interpretation of the model and discussion of solutions, Journal of Fluid Mechanics Vol. 42, 1970, pp. 609--625. Shepherd J. J. and Bennett J. C., Interior layer structure in the Newtonian blown film, ANZIAM Journal 46(E), 2005, pp. C839--C853. http://anziamj.austms.org.au/V46/CTAC2004/Shep/ Shepherd J. J., Connell H. J. and Tam D. C. H., An interior layer in a film-blowing problem, Proceedings of the Fifth Biennial Engineering Mathematics and Applications Conference (EMAC2002), M. Pemberton, I. Turner, P. Jacobs (eds), The Institution of Engineers Australia, Brisbane, Queensland (2002), pp. 181--186. Tam D. C. H., Shepherd J. J. and Connell H. J., Modelling the film blowing process, Proceedings of the Fourth Biennial Engineering Mathematics and Applications Conference (EMAC2000), R L. May, G. F. Fitz-Gerald, I. H. Grundy (eds), The Institution of Engineers Australia, Melbourne (2000), pp. 271--274