Power-law fluids over a viscous sheet with mass suction/blowing: Multiple solutions

Abstract

Multiple states emerge in the fluid flow with certain or sudden external interference. In this paper, multiple solutions of the velocity and temperature distributions of power-law fluids are found when the fluid is flowing through a viscous sheet with suction or blowing. By coupling the sheet dynamics with the surrounding fluid equations by the stress balance, the investigation results shed some light on many engineering applications of flow on various soft surfaces, for example, the synthetic plastics. The present research considers the nonuniformity of the mass suction or blowing effects, which is connected with both the stretching velocity and the thickness of the sheet. A similar transformation is adopted to transform the boundary layer equations into a series of ordinary differential equations, and multiple solutions are obtained. The existence of similar solutions has some limitations. The multiple solutions of the friction coefficient and the generalized Nusselt number affected by the power-law index n and the suction/blowing rate fw are shown, and we also discuss the influence of the generalized Prandtl number Npr and the Eckert number Ec on the velocity and temperature distributions.