Laminar flow in channels with porous walls: advancing the existence, uniqueness and approximation of solutions via fixed point approaches

Abstract

The purpose of this work is to develop a more complete theory regarding solutions to the problem of laminar flow in channels with porous walls. We establish new knowledge regarding the qualitative and quantitative properties of solutions to a fourth order boundary value problem under consideration. In contrast to the previous literature, our strategy involves establishing new a priori bounds on solutions and draws on contractive mapping principles. This enables a deeper understanding of the problem by strategically addressing the questions of existence, uniqueness and approximation of solutions under one integrated framework, rather than applying somewhat disjointed approaches. Through this strategy, we advance current knowledge by extending the range of values of the Reynolds number under which the problem will admit a unique solution; and we furnish a sequence of functions whose limit converges to this solution, enabling an iterative approximation to any theoretical degree of accuracy.