scholarly journals An exact solution for a diffusive flow in a porous medium

1969 ◽  
Vol 36 (1) ◽  
pp. 17-19 ◽  
Author(s):  
E. J. List
Keyword(s):  
Exact Solution ◽  
Porous Medium ◽  
Homogeneous Fluid ◽  
Diffusive Flow

It is shown that Yih's exact solution for the non-diffusive flow of a non-homogeneous fluid into a sink in a confined porous medium is equivalent to a class of diffusive flows with isopycnic lateral boundaries.

scholarly journals Effect of chemical reaction and radiation on double diffusive flow of a viscous, dissipative fluid through porous medium in a rectangular cavity with heat sources

2013 ◽  
Vol 18 (4) ◽  
pp. 1115-1150
Author(s):  
T.L. Raju ◽  
P. Muralidhar
Keyword(s):  
Porous Medium ◽  
Stream Function ◽  
Rectangular Cavity ◽  
Heat Sources ◽  
Element Analysis ◽  
Coupled Equations ◽  
Stiffness Matrices ◽  
Diffusive Flow ◽  
Transfer Flow ◽  
And Diffusion

Abstract In this paper, an attempt is made to discuss the combined influence of radiation and dissipation on the convective heat and mass transfer flow of a viscous fluid through a porous medium in a rectangular cavity using the Darcy model. Making use of the incompressibility, the governing non-linear coupled equations for the momentum, energy and diffusion are derived in terms of the non-dimensional stream function, temperature and concentration. The Galerkin finite element analysis with linear triangular elements is used to obtain the global stiffness matrices for the values of stream function, temperature and concentration. These coupled matrices are solved using an iterative procedure and expressions for the stream function, temperature and concentration are obtained as linear combinations of the shape functions. The behavior of temperature, concentration, the Nusselt number and Sherwood number is discussed computationally for different values of the governing parameters, such as the Rayleigh Number (Ra), heat source parameter (α), Eckert number (Ec), Schmidt Number (Sc), Soret parameter (S0), buoyancy ratio (N).

Exact solution of the Linear Parabolic Approximation for flow-depth based diffusive flow routing

2018 ◽  
Vol 563 ◽  
pp. 620-632 ◽  
Author(s):  
Luigi Cimorelli ◽  
Luca Cozzolino ◽  
Andrea D'Aniello ◽  
Domenico Pianese
Keyword(s):  
Exact Solution ◽  
Flow Depth ◽  
Parabolic Approximation ◽  
Flow Routing ◽  
Diffusive Flow

scholarly journals New exact solution for Rayleigh–Stokes problem of Maxwell fluid in a porous medium and rotating frame

2011 ◽  
Vol 1 (1) ◽  
pp. 9-12 ◽  
Author(s):  
Faisal Salah ◽  
Zainal Abdul Aziz ◽  
Dennis Ling Chuan Ching
Keyword(s):  
Exact Solution ◽  
Porous Medium ◽  
Stokes Problem ◽  
Maxwell Fluid ◽  
Rotating Frame

scholarly journals DETERMINING THE LENGMUR COEFFICIENT OF THE FILTRATION PROBLEM

2020 ◽  
Vol 16 (4) ◽  
pp. 50-56
Author(s):  
Liudmila Kuzmina ◽  
Yuri Osipov
Keyword(s):  
Exact Solution ◽  
Porous Medium ◽  
Least Squares Method ◽  
Size Exclusion ◽  
Underground Structures ◽  
Particle Capture ◽  
Filtration Problem ◽  
Problem Finding ◽  
Langmuir Coefficient ◽  
Exclusion Mechanism

Filtration of suspension in a porous medium is actual in the construction of tunnels and underground structures. A model of deep bed filtration with size-exclusion mechanism of particle capture is considered. The inverse filtration problem - finding the Langmuir coefficient from a given concentration of suspended particles at the porous medium outlet is solved using the asymptotic solution near the concentrations front. The Langmuir coefficient constants are obtained by the least squares method from the condition of best approximation of the asymptotics to exact solution. It is shown that the calculated parameters are close to the coefficients of the model, and the asymptotics well approximates the exact solution

scholarly journals Effects of the Hydro Anisotropy and the Magnetic Field on the Dynamic Thermo-Bi-Diffusive Flow in a Horizontal Cavity Confining a Porous Medium Saturated by a Binary Fluid

2021 ◽  
pp. 1-13
Author(s):  
Faras Issiako ◽  
Christian Akowanou ◽  
Macaire Agbomahena
Keyword(s):  
Magnetic Field ◽  
Mass Transfer ◽  
Porous Medium ◽  
Heat And Mass Transfer ◽  
Transverse Magnetic Field ◽  
Mass Transfer Rate ◽  
Transverse Magnetic ◽  
Binary Fluid ◽  
Diffusive Flow ◽  
Horizontal Cavity

We analyze analytically the effects of anisotropy in permeability and that of a transverse magnetic field on thermal convection in a porous medium saturated with a binary fluid and confined in a horizontal cavity. The porous medium, of great extension, is subjected to various conditions at the thermal and solutal boundaries. The axes of the permeability tensor are oriented obliquely with respect to the gravitational field. Based on a scale analysis, the velocity, temperature, and heat and mass transfer rate fields were determined. These results were validated by the study of borderline cases which are: pure porous media and pure fluid media discussed in the literature. It emerges from this study that the anisotropy parameters influence the convective flow. The application of a transverse magnetic field significantly reduces the speed of the flow and thereby affects the temperature field and the rate of heat and mass transfer.

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