An iterative approach to the thermal Newtonian blown film model
Bennett, J, Shepherd, J and Blyth, W 2008, 'An iterative approach to the thermal Newtonian blown film model', The ANZIAM Journal, vol. 48, pp. C837-C851.
Film blowing is an industrial process with a wide range of domestic and commercial applications. The modelling of this process requires solving the highly nonlinear differential equations necessary to describe the complex chemical and physical interactions involved. In earlier work, we have applied perturbation techniques to this process when, in particular, the polymer is viewed as a Newtonian fluid operating under isothermal conditions. Although this is a severe simplification of more physically realistic models, it still retains many of the structural features of these models. Subsequent calculations extended the analysis to the case of the non-isothermal Newtonian model, using an iteration procedure based on the isothermal results, and
incorporating the package Maple. This was found to be computationally expensive. The purpose of the present paper is to demonstrate a more robust approach to the solution of the equations of the Newtonian thermal model, that avoids the difficulties of the earlier methods above. This applies a finite element technique to construct the film profile and temperature profile, by iterating away from the isothermal profile obtained in earlier work. This is seen to be an improvement on previous efforts.
