An interior layer in the thermal power-law blown film model

Film blowing is a highly complex industrial process used to manufacture thin sheets of polymer. Models that describe this process are highly nonlinear and numerical instabilities often occur when solving the highly nonlinear differential equations. This paper investigates the structure of typical solutions that arise when the polymer is assumed to be described by a power-law fluid operating under nonisothermal conditions. We consider both a shear-thinning and shear-thickening polymer and use a balance of orders argument to identify the structure of a region of rapid expansion in the radial profile of the film. A mixture of heuristic and singular perturbation techniques is applied to obtain a closed form approximate expression for the radial profile of the film which displays the interior layer phenomenon. We demonstrate how approximate solutions to the highly nonlinear two-point boundary value problem describing this process may be constructed using this expression as an initial estimate in an iterative scheme. Numerical solutions for the radial temperature, velocity and thickness profiles of the film are subsequently obtained by iteration.