Flow of Micropolar Fluid Bounded By a Stretching Sheet
by
N. Kelson
CiSSaIM, QUT
Coauthors: A. Desseaux (Institut Universitaire de Technologie, Valenciennes, France)

The two-dimensional boundary layer flow caused by a moving plate or a stretching sheet is of interest in manufacture of sheeting material through an extrusion process. Tape casting is an important forming operation commonly used to prepare multilayer capacitors and packages in the ceramic industry. In this forming process a well-mixed ceramic slurry is usually placed in a container with rectangular outlet made of parallel walls and the tape casting head is set in motion on a flat substrate.

A theoretical treatment from the viewpoint of designing the process and accounting for the realistic viscous behavior of ceramic slurries is not available in the open literature. Here we consider a micropolar fluid introduced by Eringen. The concept of such fluids is to provide a mathematical model for the behavior of fluids taking into account the initial characteristics of the substructure particles which are allowed to undergo rotation. The flow is driven by a linear stretching sheet, and we have studied the similarity solutions.

In section 1 of this paper, we give the formulation of the problem of the laminar boundary layer flow driven by a moving porous plate and show that a complete similarity solution is only possible if the boundary condition is a linear function of the distance from the leading edge measured from the position of the dye.

Considering constant fluid properties, in section 2 we present a solution using a power-series expansion of the velocity and micro-rotation functions using the vortex viscosity as a parameter.

In section 3, we compare different numerical solutions with our analytical results. While it is also possible to transform the momentum equations in a recursive system and compute the different ODE equations using the fourth order Runge-Kutta method, our numerical procedure uses a quasi-Newton development of the initial set of equations.

Date received: July 30, 1999