Asymptotic solutions on multiple solutions arising from laminar flow in a uniformly porous channel with expanding or contracting walls

Abstract

Abstract This paper is concerned with asymptotic solutions of a nonlinear boundary value problem which arises from laminar flow in a uniformly porous channel with expanding or contracting walls. For values of the wall suction Reynolds number, multiple solutions are observed. A method involving the inclusion of exponentially small terms in a perturbation series is mainly considered to obtain two of the solutions analytically. In addition, numerical solutions presented for each case agree well with asymptotic solutions, which illustrates that the asymptotic solutions constructed in this paper are more reliable.

Keywords

• Laminar flow
• Expanding and contracting walls
• Singular perturbation method
• Exponentially small terms