The Airy wall jet with transpiration and stretching surface

Abstract

The combined effects of wall stretching and transpiration on an Airy wall jet is considered. An exact solution dependent on two parameters is found. One parameter fw measures the transpiration through the surface and the other parameter λ measures the extensional motion of the surface. Suction occurs for fw>0 and blowing occurs for fw<0. The surface stretches when λ>0 and shrinks when λ<0. When fw=λ=0 the original result of Weidman et al. (1997) is recovered; when λ=0 the results of Magyari et al. (2003) are recovered; when fw=0 the results of Kubitschek and Weidman (2017) are recovered. Solution of an implicit equation provides the boundary in fw-λ space for the existence of solutions. The region of existence of solutions increases with increasing suction.