Abstract
AbstractThe 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.
Funder
University of New South Wales
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Geometry and Topology,Modeling and Simulation
Reference27 articles.
1. Almuthaybiri, S.S., Tisdell, C.C.: Sharper existence and uniqueness results for solutions to fourth-order boundary value problems and elastic beam analysis. Open Math. 18(1), 1006–1024 (2020). https://doi.org/10.1515/math-2020-0056
2. Asghar, S., Mushtaq, M., Hayat, T.: Flow in a slowly deforming channel with weak permeability: an analytical approach. Nonlinear Anal. Real World Appl. 11(1), 555–561 (2010). https://doi.org/10.1016/j.nonrwa.2009.01.049
3. Berman, A.S.: Laminar flow in channels with porous walls. J. Appl. Phys. 24(9), 1232–1235 (1953). https://doi.org/10.1063/1.1721476
4. Eckert, E. R.G., Donoughe, P.L.: Moore, Betty Jo. Velocity and friction characteristics of laminar viscous boundary-layer and channel flow over surfaces with injection or suction. Technical Note 4102. Washington: National Advisory Committee for Aeronautics, (1957). http://hdl.handle.net/2060/19930084837
5. Guo, H., Gui, C., Lin, P., Zhao, M.: Multiple solutions and their asymptotics for laminar flows through a porous channel with different permeabilities. IMA J. Appl. Math. 85, 280–308 (2020). https://doi.org/10.1093/imamat/hxaa006
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献