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.

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 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.

Impedance loading an acoustic source in a borehole located in a fluid‐saturated porous medium

2021 ◽  
Author(s):  
Irina Markova ◽  
Mikhail Markov ◽  
Jetzabeth Ramírez Sabag ◽  
Gerardo Ronquillo Jarillo
Keyword(s):  
Porous Medium ◽  
Saturated Porous Medium ◽  
Acoustic Source ◽  
Fluid Saturated Porous Medium
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