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The existence and multiplicity of similarity solutions for the steady,incompressible and fully developed laminar flows in a uniformly porous channelwith two permeable walls are investigated. We shall focus on the so-calledasymmetric case where the upper wall is with an amount of flow injection andthe lower wall with a different amount of suction. We show that there existthree solutions designated as type $I$, type $II$ and type $III$ for theasymmetric case. The numerical results suggest that a unique solution existsfor the Reynolds number $0\leq R<14.10$ and two additional solutions appear for$R>14.10$. The corresponding asymptotic solution for each of the multiplesolutions is constructed by the method of boundary layer correction or matchedasymptotic expansion for the most difficult high Reynolds number case.Asymptotic solutions are all verified by their corresponding numericalsolutions.

Multiple solutions and their asymptotics for laminar flows through a porous channel with different permeabilities