Unsteady three-dimensional boundary layer flow due to a stretching surface in a micropolar fluid
In this paper, the unsteady three-dimensional boundary layer flow due to a stretching surface in a viscous and incompressible micropolar fluid is considered. The partial differential equations governing the unsteady laminar boundary layer flow are solved numerically using an implicit finite-difference scheme. The numerical solutions are obtained which are uniformly valid for all dimensionless time from initial unsteady-state flow to final steady-state flow in the whole spatial region. The equations for the initial unsteady-state flow are also solved analytically. It is found that there is a smooth transition from the small-time solution to the large-time solution. The features of the flow for different values of the governing parameters are analyzed and discussed. The solutions of interest for the skin friction coefficient with various values of the stretching parameter c and material parameter K are presented. Copyright (C) 2011 John Wiley & Sons, Ltd.
boundary layer stretching surface micropolar fluid numerical solution unsteady three-dimensional flow