On the Chebyshev collocation spectral approach to stability of fluid flow in a porous medium

Abstract

SUMMARYIn this paper, the temporal development of small disturbances in a pressure-driven fluid flow through a channel filled with a saturated porous medium is investigated. The Brinkman flow model is employed in order to obtain the basic flow velocity distribution. Under normal mode assumption, the linearized governing equations for disturbances yield a fourth-order eigenvalue problem, which reduces to the wellknown Orr-Sommerfeld equation in some limiting cases solved numerically by a spectral collocation technique with expansions in Chebyshev polynomials. The critical Reynolds number Re c , the critical wave number c , and the critical wave speed c c are obtained for a wide range of the porous medium shape factor parameter S. It is found that a decrease in porous medium permeability has a stabilizing effect on the fluid flow.

Effect of Horizontal Alternating Current Electric Field on the Stability of Natural Convection in a Dielectric Fluid Saturated Vertical Porous Layer

“…All these contri butions, for instance, Makinde [1], Hill and Straughan [2], and Straughan and Harfash [3] are, however, limited to the case of a horizontal layer of porous medium. Nonetheless, the stability of natural convection in a vertical fluid saturated porous layer is im portant in analysis of natural convection flow arising from a heated impermeable surface, embedded in fluid saturated porous media, and has been used to model the heating of groundwater in an aqui fer by a dike, which is idealized as a vertical impermeable surface.…”

Stability of fluid flow in a Brinkman porous medium—A numerical study

“…In the present study, the results are presented by taking = 80 N in Eq.(22). To compare our results with those of Makinde [6] , the results obtained for different values of porous parameter for a fixed value of…”

“…The influence of slip boundary conditions on the modal and nonmodal stability of pressure-driven channel flows was studied by Lauga and Cossu [5] . By employing the Brinkman model with fluid viscosity same as effective viscosity, Makinde [6] investigated the temporal development of small disturbances in a pressure-driven fluid flow through a channel filled with a saturated porous medium. The critical stability parameters were obtained for a wide range of porous medium shape factor parameter.…”

On the Successive Linearisation Approach to the Flow of Reactive Third-Grade Liquid in a Channel with Isothermal Walls

“…where are unknown functions and are successive approximations whose solutions are obtained recursively from solving the linear part of the equation that results from substituting (12) in the governing equations (2) using 0 ( ) as an initial approximation. The linearisation technique is based on the assumption that becomes increasingly smaller as becomes larger, that is,…”

“…In most cases, the nonlinear nature of the model equations precludes its exact solution. In recent time, several approximation techniques have been developed to tackle this problem [10][11][12][13], for example, the Adomian decomposition method, the variation iteration method, the improved finite differences method, the spectral method, and so forth. The ideas of developing new hybrids of numerical-analytical scheme to tackle nonlinear differential equations have experienced a revival.…”