Multiple Solutions for Laminar Flow through a Channel with Different Permeability

Speaker: 桂长峰 教授 澳门大学

Inviter: 秦国林

Title: Multiple Solutions for Laminar Flow through a Channel with Different Permeability 

Language: Chinese

Time & Venue: 2025.12.25 14:00-15:00  南楼204

Abstract: The existence and multiplicity of similarity solutions for the steady, incompressible and fully developed laminar flow in a uniformly porous channel with two permeable walls that the upper wall is with injection and the lower with suction is investigated. It is shown that there are three solutions labeled as type I, type II and type III for the channel flow which agree well with the numerical results obtained by the collocation method. The numerical results suggest that a single solution is found for the Reynolds number $0<R<14.10$ and two additional solutions appear for $R>14.10$. The corresponding asymptotic solution for each of the multiple solutions is constructed by the method of boundary layer correction or matched asymptotic expansion for the most difficult high Reynolds number case. Asymptotic solutions are all verified by their corresponding numerical solutions.

We also give a classification of the bounded and unbounded solutions of a related third-order nonlinear ordinary differential equation. Through careful analysis, we characterize all possible solution types under various conditions on initial data, providing an explicit description of their graphical behaviors.

This is a joint work with H. X. Guo, P. Lin and M. F. Zhao.