Analysis of the Laminar Newtonian Fluid Flow Through a Thin Fracture Modelled as a Fluid-Saturated Sparsely Packed Porous Medium

2017 ◽  
Vol 72 (3) ◽  
pp. 253-259 ◽  
Author(s):  
Igor Pažanin ◽  
Pradeep G. Siddheshwar
Keyword(s):  
Porous Medium ◽  
Fluid Flow ◽  
Order Approximation ◽  
Saturated Porous Medium ◽  
Darcy Law ◽  
Brinkman Model ◽  
Order Of Accuracy ◽  
Flow Through ◽  
Fluid Saturated Porous Medium ◽  
Flow Inertia

AbstractIn this article we investigate the fluid flow through a thin fracture modelled as a fluid-saturated porous medium. We assume that the fracture has constrictions and that the flow is governed by the prescribed pressure drop between the edges of the fracture. The problem is described by the Darcy-Lapwood-Brinkman model acknowledging the Brinkman extension of the Darcy law as well as the flow inertia. Using asymptotic analysis with respect to the thickness of the fracture, we derive the explicit higher-order approximation for the velocity distribution. We make an error analysis to comment on the order of accuracy of the method used and also to provide rigorous justification for the model.

Numerical Investigation of Heat Transfer in Forced Convection in a Helical Pipe Filled With a Porous Medium

2005 ◽  
Author(s):  
Liping Cheng ◽  
Andrey V. Kuznetsov
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Saturated Porous Medium ◽  
Axial Flow ◽  
Darcy Number ◽  
Momentum Equation ◽  
Darcy Law ◽  
Helical Pipe ◽  
Fluid Saturated Porous Medium ◽  
Flow Inertia

This paper investigates numerically heat transfer in a helical pipe filled with a fluid saturated porous medium. The analysis is based on the full momentum equation for porous media that accounts for the Brinkman and Forchheimer extensions of the Darcy law as well as for the flow inertia. Numerical computations are performed in an orthogonal helical coordinate system. The effects of the Darcy number, the Forchheimer coefficient as well as the Dean and Germano numbers on the axial flow velocity, secondary flow, temperature distribution, and the Nusselt number are analyzed.

Numerical Investigation of Laminar Flow in a Helical Pipe Filled With a Fluid Saturated Porous Medium: The Sensitivity of Secondary Flow to Parameter Variations

2004 ◽  
Author(s):  
Liping Cheng ◽  
Andrey V. Kuznetsov
Keyword(s):  
Porous Medium ◽  
Laminar Flow ◽  
Secondary Flow ◽  
Saturated Porous Medium ◽  
Axial Flow ◽  
Flow In Porous Media ◽  
Darcy Law ◽  
Helical Pipe ◽  
Fluid Saturated Porous Medium ◽  
Flow Inertia

Laminar flow in a helical pipe filled with a fluid saturated porous medium is investigated numerically. The analysis is based on a full momentum equation for the flow in porous media that accounts for the Brinkman and Forchheimer extensions of the Darcy law as well as for the flow inertia. Accounting for the flow inertia is shown to be important for predicting secondary flow in a helical pipe. The effects of the Darcy number, the Forchheimer coefficient as well as the curvature and torsion of the helical pipe on the axial flow velocity and secondary flow are investigated numerically.

Similar Solutions of Brinkman Equations for a Two-Dimensional Plane Jet in a Porous Medium

1983 ◽  
Vol 105 (4) ◽  
pp. 474-478 ◽  
Author(s):  
R. Friedrich ◽  
N. Rudraiah
Keyword(s):  
Porous Medium ◽  
Saturated Porous Medium ◽  
Transverse Velocity ◽  
Infinite Length ◽  
Brinkman Model ◽  
Brinkman Equations ◽  
Fluid Saturated Porous Medium ◽  
The Difference ◽  
Similar Solutions ◽  
Plane Jet

The similar solution of the Brinkman equations for flow of a plane jet issuing into a fluid saturated porous medium is studied. The velocity field is determined in the plane of physical as well as transformed coordinates. It is shown that the jet in a porous medium is of finite length in contrast to the infinite length in the case of pure viscous flow. The difference in the volume rate of discharge and the width of the jet between the Brinkman model and the pure viscous case is brought out clearly and it is shown that the Darcy resistance tends to make the jet broader. Near the origin, the streamlines show an entrainment of fluid from infinity which results in negative transverse velocity.

Numerical Solution of Conjugate Free Convection From a Vertical Fin Embedded in a Non-Darcy Porous Medium

2017 ◽  
Vol 73 (1) ◽  
pp. 35-42
Author(s):  
Vikash Kumar ◽  
Abha Rani ◽  
Ajay Kumar Singh
Keyword(s):  
Porous Medium ◽  
Nusselt Number ◽  
Finite Difference ◽  
Free Convection ◽  
Saturated Porous Medium ◽  
Brinkman Model ◽  
Implicit Finite Difference Scheme ◽  
Implicit Finite Difference ◽  
Fluid Saturated Porous Medium ◽  
Convection Parameter

AbstractThe problem of conjugate free convection from a vertical fin embedded in a fluid-saturated porous medium is investigated. The governing nonlinear equations are solved iteratively by a highly implicit finite difference scheme. In this paper, the results based on four models, viz the Darcy model, the Brinkman model, the non-Darcian model with nonlinear inertia and viscous terms, and also the non-Darcian model with viscous, nonlinear inertia and velocity square terms, are compared. It is seen that fin cooling is more effective at higher Grashof or Darcy numbers due to stronger convection effects. The local Nusselt number is observed to increase with the Grashof or Darcy numbers and decrease slightly with the conduction–convection parameter. The limitation of the Darcy’s law is observed at higher values of permeability when the non-Darcian models are more relevant.

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