Asymptotic solution of a laminar flow in a porous channel with large suction: A nonlinear turning point problem

Abstract

The boundary-value problem e/G") = [/ /'" -/' /"], /(0) = /"(0) = /'(I) = 0, /(I) = 1, is a version of Berman's problem and its solutions describe a laminar flow in a channel with porous walls. When 0 < e <C 1, the problem is a singular perturbation problem and physically corresponds to large suction through the walls. This case is known to possess three solutions, types I, II, III. The asymptotic analysis of the type III solution-the only nonmonotone solution for small positive e-is the subject of the present investigation. A feature of the analysis is the introduction of a transition layer approximation whose domain of uniform validity overlaps with the outer and the boundary-layer approximations. The asymptotic approximations are consistent with two theorems proved, and the validity of the asymptotics is strongly supported by evidence from numerical experiments.