Study of Two-Dimensional, all – Time Dispersion of a Solute in a Fluid – Saturated Porous Medium

2017 ◽  
Vol 13 (3) ◽  
pp. 67-85
Author(s):  
Pranesh S
Keyword(s):  
Porous Medium ◽  
Dispersion Coefficient ◽  
Dispersion Model ◽  
Saturated Porous Medium ◽  
Mathematical Formulation ◽  
Unidirectional Flow ◽  
Time Dispersion ◽  
Flow Through ◽  
Mean Concentration ◽  
Generalized Dispersion Model

The paper presents the mathematical formulation which describes the dispersion of solute in a laminar flow in a sparsely packed porous medium. The effect of interphase mass transfer on dispersion in a unidirectional flow through a horizontally extent of infinite porous channel is examined using the generalized dispersion model of Sankarasubramanian and Gill. The model brings into focus three important coefficients namely the exchange coefficient, the convection coefficient and the dispersion coefficient. The time-dependent dispersion coefficient and mean concentration distribution are computed and results are represented graphically. The problem finds many applications in waste water management, in chromatography and in biomechanical problems.

scholarly journals Unsteady Convective Diffusion with Interphase Mass Transfer in Casson Liquid

2017 ◽  
Vol 62 (2) ◽  
pp. 215 ◽  
Author(s):  
Ashis Kumar Roy ◽  
Apu Kumar Saha ◽  
Sudip Debnath
Keyword(s):  
Yield Stress ◽  
Constant Pressure ◽  
Dispersion Coefficient ◽  
Convective Diffusion ◽  
Dispersion Model ◽  
Transport Coefficients ◽  
Exchange Coefficient ◽  
Dependent Behavior ◽  
Flow Through ◽  
Generalized Dispersion Model

This study aims to examine the  dispersion of a passive contaminant of solute released  in Casson liquid flow through a tube. The wall of the tube is taken to be chemically active where the flow is driven by the constant pressure gradient. To evaluate the transport coefficients, Aris-Barton’s Moment technique is considered, a finite difference implicit scheme is adopted to handle the differential equation arises in moment methodology. Also to confirm the results obtained by Aris-Barton’s method,  the generalized dispersion model has been applied. Unlike the previous studies on dispersion in Casson liquid, the time-dependent behavior of the transport coefficients has been established. Some significant observations have been founded, e.g. exchange coefficient is independent of yield stress while the convection coefficient and dispersion coefficient are inversely proportional to yield stress. Results reveal that transport coefficients are enormously affected by wall absorption.

Thermal Ignition in a Reactive Viscous Flow Through a Channel Filled With a Porous Medium

2006 ◽  
Vol 128 (6) ◽  
pp. 601-604 ◽  
Author(s):  
O. D. Makinde
Keyword(s):  
Porous Medium ◽  
Nonlinear Boundary ◽  
Saturated Porous Medium ◽  
Perturbation Technique ◽  
Exothermic Reaction ◽  
Thermal Ignition ◽  
Arrhenius Kinetics ◽  
Thermal Criticality ◽  
Flow Through ◽  
Steady State Solutions

This paper examines the steady-state solutions of a strongly exothermic reaction of a viscous combustible material in a channel filled with a saturated porous medium under Arrhenius kinetics, neglecting reactant consumption. The Brinkman model is employed and analytical solutions are constructed for the governing nonlinear boundary-value problem using a perturbation technique together with a special type of Hermite-Padé approximants and important properties of the temperature field including bifurcations and thermal criticality are discussed.

scholarly journals Numerical study of heat transfer in a porous medium of steel balls

2019 ◽  
Vol 23 (1) ◽  
pp. 271-279
Author(s):  
Mehmet Pamuk
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Numerical Study ◽  
Fluid Phase ◽  
Commercial Software ◽  
Number Range ◽  
Unidirectional Flow ◽  
Flow Through ◽  
Steel Balls

In this study, heat transfer in unidirectional flow through a porous medium with the fluid phase being water is analyzed using the commercial software Comsol?. The aim of the study is to validate the suitability of this package for similar problems regarding heat transfer calculations in unidirectional flow through porous media. The porous medium used in the study is comprised of steed balls of 3 mm in diameter filled in a pipe of 51.4 mm inner diameter. The superficial velocity range is 3-10 mm/s which correspond to a Reynolds number range of 150-500 for an empty pipe. Heat is applied peripherally on the outer surface of the pipe at a rate of 7.5 kW/m2 using electrical ribbon heaters. The numerical results obtained using the commercial software Comsol? are compared with those obtained in the experiments once conducted by the author of this article. Results have shown that Comsol? can generate reliable results in heat transfer problems through porous media, provided all parameters are selected correctly, thus making it unnecessary to prepare expensive experimental set-ups and spending extensive time to conduct experiments.

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.

Dispersion of oil spilled under solid ice cover

2014 ◽  
Vol 11 (5) ◽  
pp. 495-506
Author(s):  
Nirmala Ratchagar ◽  
S. Hemalatha
Keyword(s):  
Particle Concentration ◽  
Dispersion Model ◽  
Perturbation Technique ◽  
Ice Cover ◽  
Axial Distance ◽  
Dimensionless Time ◽  
Pure Solvent ◽  
The Mean ◽  
Mean Concentration ◽  
Generalized Dispersion Model

The model, presented here, is developed to study the axial dispersion and distribution of oil particle concentration in the presence of coriolis force of oil spilled under solid ice cover. The movement of oil slick is obtained by employing perturbation technique and the dispersion of oil is studied using generalized dispersion model proposed by Gill (1967). The mean concentration is computed by introducing a slug of finite length separated from pure solvent using suitable impermeable barriers by varying the dimensionless time, axial distance and length of solute slug. The results obtained are discussed in detail with the help of graphs and tables.

Effect of couple stress and magnetic field on the unsteady convective diffusion in blood flow

2014 ◽  
Vol 11 (4) ◽  
pp. 403-412 ◽  
Author(s):  
Nirmala Ratchagar ◽  
R. Kumar
Keyword(s):  
Magnetic Field ◽  
Couple Stress ◽  
Dispersion Coefficient ◽  
Convective Diffusion ◽  
Dispersion Model ◽  
Artificial Organs ◽  
Axial Distance ◽  
The Mean ◽  
The Magnetic Field ◽  
Mean Concentration

The effect of magnetic field on unsteady convective diffusion in a couple stress fluid (blood) is studied using a time dependent dispersion model. This model is used to calculate the mean concentration distribution of a solute, bounded by the porous layer and is expressed as a function of dimensionless axial distance and time. The magnetic field, arising as a body couple in the governing equations is shown to increase the axis dispersion coefficient. This is useful to the control of haemolysis caused by artificial organs implanted or extracorporeal. Dispersion coefficient and mean concentration are computed for different values of Hartmann number (M), Couple Stress Parameter (a) and Porous Parameter (σ).

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