Forchheimer and Brinkman extended Darcy flow model of natural convection in a vertical cylindrical porous annulus
type: Item
instance of: scholarly article
title: Forchheimer and Brinkman extended Darcy flow model of natural convection in a vertical cylindrical porous annulus
zbMATH Open document ID: 0866.76087
DOI: 10.1007/BF01176815
author: D. R. Marpu
published in: Acta Mechanica
publication date: 1997-07-20T00:00:00Z
review text: The paper treats numerically the Forchheimer and Brinkman extended Darcy flow model for studying the natural convection heat transfer in vertical cylindrical annuli filled with fluid saturated porous media. Numerical results are obtained employing the SAR scheme proposed by the author. In order to investigate the influence of Brinkman viscous terms on heat transfer, numerical results are given neglecting Forchheimer inertial terms. The average Nusselt number at the inner wall, \(\overline{\text{Nu}}_i\), based on the annulus gap, has been calculated for different values of involved parameters. The obtained results are compared with experimental results available in the literature. It is shown that for an annulus filled with water and glass spheres of diameter \(d=22.5\text{ mm}\) having an aspect ratio of unity and a radii ratio of \(4.338\), the \(\overline{\text{Nu}}_i\) is significantly lower that the theoretically obtained value of \(\overline{\text{Nu}}_i\) by employing the Darcy flow model. This is due to the fact that Darcy's law is applicable only to low permeability porous media. The difference between experimental and theoretical values can be reduced by considering, in general, the non-Darcy extensions, since the non-Darcy extension decreases the average Nusselt number. This work is certainly an improvement over earlier work concerning the natural convection in a vertical cylindrical porous annulus. The reviewer recommends this valuable paper to all workers in convective flow in porous media.
Mathematics Subject Classification ID: 76R10
Mathematics Subject Classification ID: 76S05
Mathematics Subject Classification ID: 80A20
zbMATH DE Number: 885169
zbMATH Keywords: SAR scheme
zbMATH Keywords: Brinkman viscous terms
zbMATH Keywords: Forchheimer inertial terms
zbMATH Keywords: average Nusselt number
reviewed by: Ioan Pop
MaRDI profile type: Publication
cites work: Axisymmetric free convection at small Rayleigh number in porous cavities
cites work: A numerical study of the applicability of the Boussinesq approximation for a fluid-saturated porous medium
cites work: Natural convection in a vertical porous annulus
cites work: A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles
cites work: The departure from Darcy flow in natural convection in a vertical porous layer
cites work: A boundary-layer analysis for natural convection in vertical porous enclosures - Use of the Brinkman-extended Darcy model
cites work: Natural convection in a shallow porous cavity - The Brinkman model
full work available at URL: https://doi.org/10.1007/bf01176815
OpenAlex ID: W2328349311
description: scientific article; zbMATH DE number 885169