Eigenvalues of higher order Sturm-Liouville boundary value problems with derivatives in nonlinear terms

We shall consider the Sturm-Liouville boundary value problem y(m)(t)+λF(t,y(t),y′(t),…,y(q)(t))=0, t∈(0,1), y(k)(0)=0, 0≤k≤m−3, ζy(m−2)(0)−θy(m−1)(0)=0, ρy(m−2)(1)+δy(m−1)(1)=0 where m≥3, 1≤q≤m−2, and λ>0. It is noted that the boundary value problem considered has a derivative-dependent nonlinear term, which makes the investigation much more challenging. In this paper we shall develop a new technique to characterize the eigenvalues λ so that the boundary value problem has a positive solution. Explicit eigenvalue intervals are also established. Some examples are included to dwell upon the usefulness of the results obtained.Published versio

Standard numerical schemes for coupled parallel flow over porous layers

In this work, we develop finite difference schemes of various orders of accuracy that are suitable for the simulation of flow through and over porous layers. The flow through the porous layer is assumed to be governed by a Brinkman-type equation, and that through free-space by the Navier-Stokes equations. Matching conditions at the interface between layers are invoked to derive numerical expressions for the velocity and shear stress. Results are compared with the exact solution of flow through a channel bounded by a porous layer. © 2007 Elsevier Inc. All rights reserved

Analytical approach to the Darcy–Lapwood–Brinkman equation

Three exact solutions are obtained for flow through porous media, as governed by the Darcy–Lapwood–Brinkman model, for a given vorticity distribution. The resulting flow fields are identified as reversing flows; stagnation point flows; and flows over a porous flat plate with blowing or suction. Dependence of the flow Reynolds number on the permeability of the flow through the porous medium is illustrated

Analysis of particulate behavior in porous media

In this work, we analyze the behavior of the particle phase in the flow of a particle-laden mixture through a porous medium. An attempt is made to model the diffusion and dispersion processes, and to quantify the deviation terms that arise when intrinsic volume averaging is used to derive the flow equation