M.H. Hamdan

Fully developed flow through a porous channel bounded by flat plates

Plane, parallel and fully-developed flow through straight porous channels is considered in an attempt to study the effects of the porous matrix and the microscopic inertia on the velocity profiles, for different flow-driving mechanisms. By comparison, flows through free-space in the same configuration, as governed by the Navier-Stokes equations and subject to Poiseuille and Couette type entry profiles have become bench-mark problems in the study of flow equations that can be solved analytically by the method of reduction to ordinary differential equations. In this work, we therefore consider three types of Poiseuille-Couette combinations, together with the main models governing flow through porous media, and offer a comparison with the corresponding flow through free-space.

Single-phase flow through porous channels a review of flow models and channel entry conditions

Abstract The leading models of single-phase fluid flow through porous media are reviewed and the boundary conditions associated with these models are discussed. Entry conditions to a porous channel that are compatible with the different flow models when the flow is fully developed are derived. Comparison of these entry profiles is made for different flow parameters with the corresponding entry condition when the flow is governed by the Navier–Stokes equations.

Coupled parallel flow through composite porous layers

In this work, we consider fluid flow through composite porous layers. The flow through the layers is either governed by the same flow model with different permeabilities, or by different models. In both cases, a matching condition at the interface between the layers is employed in the numerical solution of the flow problem. Finite difference expressions are derived for the interfacial velocity, and take into account the local truncation error, which is expressed as a function of the flow parameters and the step size employed.

An alternative approach to exact solutions of a special class of Navier-Stokes flows

An exact solution to the two-dimensional, viscous fluid flow, as governed by the Navier-Stokes equations, is obtained for Riabouchinsky-type flows. A modified solution methodology is developed in this work to better handle the type of flow considered, and is promising in overcoming some of the disadvantages of the traditional approach.

Analytical approach to the Darcy–Lapwood–Brinkman equation

Abstract 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.

On the Darcy-Lapwood-Brinkman-Saffman dusty fluid flow models through porous media part I: models development

Abstract Mathematical models based on the differential equations approach are developed to describe the motion of an incompressible dusty fluid in porous media. The macroscopic governing equations are derived through the volume-averaging technique and take into account the cases of one-way and two-way interaction between the phases present. The models, based on Saffmans dusty gas model, are then subclassified to account for the different types of flow through porous media.

On the Ni(x) integral function and its application to the Airy’s non-homogeneous equation

In this article, we discuss a recently introduced function, Ni(x), to which we will refer as the Nield–Kuznetsov function. This function is attractive in the solution of inhomogeneous Airy’s equation. We derive and document some elementary properties of this function and outline its application to Airy’s equation subject to initial conditions. We introduce another function, Ki(x), that arises in connection with Ni(x) when solving Airy’s equation with a variable forcing function. In Appendix A, we derive a number of properties of both Ni(x) and Ki(x), their integral representation, ascending and asymptotic series representations. We develop iterative formulae for computing all derivatives of these functions, and formulae for computing the values of the derivatives at x = 0. An interesting finding is the type of differential equations Ni(x) satisfies. In particular, it poses itself as a solution to Langer’s comparison equation.

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.

Fluid-particle model of flow through porous media: The case of uniform particle distribution and parallel velocity fields

Under the assumption of a uniform distribution of dust particles, we develop a mathematical model to describe the flow of a dusty fluid through isotropic consolidated and granular porous materials. Intrinsic volume averaging is employed to develop continuity and momentum equations when the fluid- and dust-phase velocities are everywhere parallel.

Infiltration of oil into porous sediments

The continuum flow of a dilute system through a porous sediment is considered. The fluid system is composed of a carrier fluid-phase and an oil-phase. Model equations governing the time-dependent flow of the incompressible two-phase fluid are developed based on volume averaging.