On the Nonunique Solutions of Laminar Flow through a Porous Tube or Channel

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

“…In particular, the case 0 < e <C 1, which corresponds to large suction, (i.e., R > 1) leads to three such problems, one of which is the subject of this paper. This problem and related problems have been studied by Berman [3], Proudman [12], Yuan and Finkelstein [21], Terrill [16], Terrill and Thomas [17], Robinson [13], Skalak and Wang [15], and Zaturska et al [22]. The importance of exponentially small terms in some of the analyses was commented on by Van Dyke [18].…”

On the Existence of Solutions of an Equation Arising in the Theory of Laminar Flow in a Uniformly Porous Channel with Injection

“…Asymptotic results have of necessity been purely formal, since the existence of a solution has not been proved nor the necessary estimates obtained. Skalak and Wang (1978) (3) _x + h _y 0.…”

Nonlinear Flow Between Permeable Disks Using Computer‐Extended Series Method

“…Elkouh [12,13] studied this problem for velocity, skin friction, and pressure coefficient and presented a second-order analytical perturbation solution valid for small values of Reynolds number (R). Rudraiah [1,2] and Rudraiah and Chandrashekar [3][4][5][6] obtained an analytical solution for the nonlinear laminar flow between permeable disks with/without external constraints of rotation and/or magnetic field for small/large values of perturbation parameter R. Terrill [14,15], Robinson [16], and Skalak and Wang [17] studied the same problem numerically as well as by an asymptotic analysis valid for large Reynolds number. These asymptotic methods have the limitation of convergence of the solution as well as the accuracy of the results.…”