Analysis of Variants Within the Porous Media Transport Models

Abstract

An investigation of variants within the porous media transport models is presented in this work. Four major categories in modeling the transport processes through porous media, namely constant porosity, variable porosity, thermal dispersion, and local thermal nonequilibrium, are analyzed in detail. The main objective of the current study is to compare these variances in models for each of the four categories and establish conditions leading to convergence or divergence among different models. To analyze the effects of variants within these transport models, a systematic reduction and sensitivity investigation for each of these four aspects is presented. The effects of the Darcy number, inertia parameter, Reynolds number, porosity, particle diameter, and the fluid-to-solid conductivity ratio on the variances within each of the four areas are analyzed. It is shown that for some cases the variances within different models have a negligible effect on the results while for some cases the variations can become significant. In general, the variances have a more pronounced effect on the velocity field and a substantially smaller effect on the temperature field and Nusselt number distribution. [S0022-1481(00)02602-5]

First and second law analyses of nanofluid forced convection in a partially-filled porous channel – The effects of local thermal non-equilibrium and internal heat sources

“…Two well established interface models (Model 1A and model 2A of Alazmi and Vafai [45], or Models A and B…”

“…Similar to the analysis in Ref. [40] 5 different porous-fluid interface models [44,45] are employed to define the thermal boundary conditions. The 6 current study builds upon the work of Karimi et al [40] and extends that to nanofluids.…”

Flow over a Darcy Porous Layer of Variable Permeability

“…In the above investigations, permeability has, in general, been considered constant (although in some of the models reported in Alazmi and Vafai [5], permeability was defined in terms of the medium porosity or given as a function of porosity). In reality, however, it can be argued that naturally occurring porous layers (such as soil sediments) possess a layered structure with variable permeability.…”

“…This has received the most attention in order to determine the most appropriate model to use in the porous layer (that is, a Darcy or a non-Darcy model) and the most appropriate matching condition at the interface between the fluid layer and the porous medium. A survey of the various models employed in the porous layer, and the matching conditions at the interface, have been provided in an elegant article by Alazmi and Vafai [5]. Models of Darcy, Brinkman, and Forchheimer have been used, without consensus, by various authors to govern the flow in the porous layer, and matching conditions have ranged from Beavers and Joseph's slip hypothesis [6] to the jump stress condition of Ochoa and Whitaker [7], and continuity of velocity and shear stress at the interface (as suggested by Neale and Nader [8]).…”

“…This problem involves coupled parallel flow through a free-space channel underlain by a porous layer of either finite or infinite depth. Flow through free-space is governed by Navier-Stokes equations and in the porous sediment by an appropriate model [5]. The use of Darcy's law in the porous sediment has been predominant.…”