Abstract
High Weissenberg boundary layer flow of viscoelastic fluids on a stretching surface has been studied. The flow is considered to be steady, low inertial, and two-dimensional. Upon proper scaling and by means of an exact similarity transformation, the nonlinear momentum and constitutive equations of each layer transform into the respective system of highly nonlinear and coupled ordinary differential equations. Numerical solutions to the resulting boundary value problem are obtained using an efficient shooting technique in conjunction with a variable stepping method for different values of pressure gradients. It is observed that, unlike the Newtonian flows, in order to maintain a potential flow, normal stresses must inevitably develop. The velocity field and stresses distributions over plate are presented for difference values of pressure gradient and Weissenberg numbers.
Highlights
The flow of a liquid within a thin film over stretching plate is often encountered in most manufacturing processes
The boundary layer formed by the flow of viscoelastic fluid over stretching sheet is presented
The flow is at high Weissenberg number and low Reynolds number
Summary
The flow of a liquid within a thin film over stretching plate is often encountered in most manufacturing processes. Examples include extrusion of plastic sheets, fabrication of adhesive tapes, and application of coating layers onto rigid substrates. Coating processes demand a smooth glossy surface to meet the requirements for best appearance and optimum service properties such as low friction, transparency, and strength. Like polymers, show strong viscoelastic effects at small deformations, and their measurement is very useful as a physical probe of the microstructure. More applications specific to the viscoelastic model include the modeling of plastics such as PET resins, which are used in, for example, film casting [2]. It has been used to simulate the flow of polymer which is used for the process of wire-coating [3]
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