NON-LINEAR DARCY LAW IN A RANDOM POROUS MEDIUM

1999 ◽  
pp. 107-132
Author(s):  
A.Yu. BELIAEV
Keyword(s):  
Porous Medium ◽  
Darcy Law ◽  
Non Linear ◽  
Random Porous Medium

Homogenization of a non-stationary non-Newtonian flow in a porous medium containing a thin fissure

2018 ◽  
Vol 30 (2) ◽  
pp. 248-277
Author(s):  
MARÍA ANGUIANO
Keyword(s):  
Porous Medium ◽  
Fluid Flow ◽  
Critical Case ◽  
Stokes System ◽  
Characteristic Size ◽  
Time Dependent ◽  
Darcy Law ◽  
Flow Index ◽  
Newtonian Flow ◽  
Non Linear

We consider a non-stationary incompressible non-Newtonian Stokes system in a porous medium with characteristic size of the pores ϵ and containing a thin fissure of width ηϵ. The viscosity is supposed to obey the power law with flow index$\frac{5}{3}\leq q\leq 2$. The limit when size of the pores tends to zero gives the homogenized behaviour of the flow. We obtain three different models depending on the magnitude ηϵwith respect to ϵ: if ηϵ≪$\varepsilon^{q\over 2q-1}$the homogenized fluid flow is governed by a time-dependent non-linear Darcy law, while if ηϵ≫$\varepsilon^{q\over 2q-1}$is governed by a time-dependent non-linear Reynolds problem. In the critical case, ηϵ≈$\varepsilon^{q\over 2q-1}$, the flow is described by a time-dependent non-linear Darcy law coupled with a time-dependent non-linear Reynolds problem.

Stochastic homogenization and macroscopic modelling of composites and flow through porous media

2002 ◽  
pp. 337-378 ◽  
Author(s):  
Jozef Telega ◽  
Wlodzimierz Bielski
Keyword(s):  
Porous Medium ◽  
Random Distribution ◽  
Flow Through Porous Media ◽  
Macroscopic Models ◽  
Linear Elastic ◽  
Multi Scale ◽  
Convergence Method ◽  
Flow Through ◽  
The Mean ◽  
Random Porous Medium

The aim of this contribution is mainly twofold. First, the stochastic two-scale convergence in the mean developed by Bourgeat et al. [13] is used to derive the macroscopic models of: (i) diffusion in random porous medium, (ii) nonstationary flow of Stokesian fluid through random linear elastic porous medium. Second, the multi-scale convergence method developed by Allaire and Briane [7] for the case of several microperiodic scales is extended to random distribution of heterogeneities characterized by separated scales (stochastic reiterated homogenization). .

Heat and mass transfer effects on MHD non-Newtonian fluids flow through an inclined thermally-stratified porous medium

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Gladys Tharapatla ◽  
Pamula Rajakumari ◽  
Ramana G.V. Reddy
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Velocity Profile ◽  
Heat And Mass Transfer ◽  
Newtonian Fluids ◽  
Transfer Effects ◽  
Content Type ◽  
Non Linear ◽  
Homotopy Analysis ◽  
Flow Through

Purpose This paper aims to analyze heat and mass transfer of magnetohydrodynamic (MHD) non-Newtonian fluids flow past an inclined thermally stratified porous plate using a numerical approach. Design/methodology/approach The flow equations are set up with the non-linear free convective term, thermal radiation, nanofluids and Soret–Dufour effects. Thus, the non-linear partial differential equations of the flow analysis were simplified by using similarity transformation to obtain non-linear coupled equations. The set of simplified equations are solved by using the spectral homotopy analysis method (SHAM) and the spectral relaxation method (SRM). SHAM uses the approach of Chebyshev pseudospectral alongside the homotopy analysis. The SRM uses the concept of Gauss-Seidel techniques to the linear system of equations. Findings Findings revealed that a large value of the non-linear convective parameters for both temperature and concentration increases the velocity profile. A large value of the Williamson term is detected to elevate the velocity plot, whereas the Casson parameter degenerates the velocity profile. The thermal radiation was found to elevate both velocity and temperature as its value increases. The imposed magnetic field was found to slow down the fluid velocity by originating the Lorentz force. Originality/value The novelty of this paper is to explore the heat and mass transfer effects on MHD non-Newtonian fluids flow through an inclined thermally-stratified porous medium. The model is formulated in an inclined plate and embedded in a thermally-stratified porous medium which to the best of the knowledge has not been explored before in literature. Two elegance spectral numerical techniques have been used in solving the modeled equations. Both SRM and SHAM were found to be accurate.

scholarly journals Numerical simulation of the motion of a micropolar Casson fluid through a porous medium over a stretching surface

2020 ◽  
Vol 24 (2 Part B) ◽  
pp. 1285-1297 ◽  
Author(s):  
Nabil El-Dabe ◽  
Galal Moatimid ◽  
Abd-Elhafez Elshekhipy ◽  
Naglaa Aballah
Keyword(s):  
Porous Medium ◽  
Casson Fluid ◽  
Similarity Solutions ◽  
Physical Parameters ◽  
Stretching Surface ◽  
Transform Method ◽  
Differential Transform ◽  
Non Linear ◽  
Linear Differential ◽  
External Uniform Magnetic Field

The present study examines the motion of a micropolar non-Newtonian Casson fluid through a porous medium over a stretching surface. The system is pervaded by an external uniform magnetic field. The heat transfer and heat generation are taken into consideration. The problem is modulated mathematically by a system of non-linear PDE which describe the equations of continuity, momentum, and energy. Suitable similarity solutions are utilized to transform the system of equation ordinary non-linear differential equations. In accordance with the appropriate boundary conditions, are numerically solved by means of the finite difference technique. Also, the system is solved by using multistep differential transform method. The effects of the various physical parameters, of the problem at hand, are illustrated through a set of diagrams.

scholarly journals Numerical study of heat transfer of a micropolar fluid through a porous medium with radiation

2018 ◽  
Vol 22 (1 Part B) ◽  
pp. 557-565 ◽  
Author(s):  
Fakhrodin Mohammadi ◽  
Mohammad Rashidi
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Collocation Method ◽  
Micropolar Fluid ◽  
Legendre Polynomials ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Shifted Legendre Polynomials ◽  
Non Linear

An efficient Spectral Collocation method based on the shifted Legendre polynomials was applied to get solution of heat transfer of a micropolar fluid through a porous medium with radiation. A similarity transformation is applied to convert the governing equations to a system of non-linear ordinary differential equations. Then, the shifted Legendre polynomials and their operational matrix of derivative are used for producing an approximate solution for this system of non-linear differential equations. The main advantage of the proposed method is that the need for guessing and correcting the initial values during the solution procedure is eliminated and a stable solution with good accuracy can be obtained by using the given boundary conditions in the problem. A very good agreement is observed between the obtained results by the proposed Spectral Collocation method and those of previously published ones.

Entropy Generation on Maxwell Fluid Flow Past an Inclined Stretching Plate with Slip and Convective Surface Conditon: Darcy-Forchheimer Model

2019 ◽  
Vol 26 ◽  
pp. 62-83
Author(s):  
Tunde Abdulkadir Yusuf ◽  
Jacob Abiodun Gbadeyan
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Entropy Generation ◽  
Mhd Flow ◽  
Maxwell Fluid ◽  
Entropy Generation Rate ◽  
Physical Parameters ◽  
Convective Boundary ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

In this study the effect of entropy generation on two dimensional magnetohydrodynamic (MHD) flow of a Maxwell fluid over an inclined stretching sheet embedded in a non-Darcian porous medium with velocity slip and convective boundary condition is investigated. Darcy-Forchheimer based model was employed to describe the flow in the porous medium. The non-linear thermal radiation is also taken into account. Similarity transformation is used to convert the non-linear partial differential equations to a system of non-linear ordinary differential equations. The resulting transformed equations are then solved using the Homotopy analysis method (HAM). Influence of various physical parameters on the dimensionless velocity profile, temperature profile and entropy generation are shown graphically and discussed in detail while the effects of these physical parameters on velocity gradient and temperature gradient are aided with the help of Table. Furthermore, comparison of some limiting cases of this model was made with existing results. The results obtained are found to be in good agreement with previously published results. Moreover, increase in local inertial coefficient parameter is found to decrease the entropy generation rate.

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