The boundary-layer flow induced by a flat plate emerging normally to a wall

Abstract

This paper investigates the unsteady boundary-layer flow induced when an infinitely thin plate issues at constant velocity from a slit on a flat wall into a stagnant atmosphere. It is shown that the use of the increasing plate length and characteristic boundary-layer thickness as scales for the longitudinal and transverse coordinates enables a self-similar parameter-free solution for the velocity field, which is obtained by numerical integration of the resulting elliptic problem. The analysis also considers the thermal boundary layer corresponding to a constant temperature plate, which is computed for different values of the Prandtl number. The study provides quantitative information of interest, including the distributions of boundary-layer thickness, skin friction and Nusselt number along the plate and the normal velocity outside the boundary layer. The solution is seen to evolve from Blasius solution, which applies near the leading edge of the plate, to Sakiadis solution, which applies at the rear end near the wall, with Rayleigh solution providing an approximate description in the intermediate transition region, where longitudinal gradients and transverse convection are relatively small.