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.

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 The Effect of Particle Drag and Wall Absorption on Mass Transfer in Concentric Annulus Flows

2011 ◽  
Vol 10 (1) ◽  
pp. 1-13
Author(s):  
B. Umadevi ◽  
Dinesh P.A. ◽  
Indira R. Rao ◽  
Vinay C.V.
Keyword(s):  
Mass Transfer ◽  
Diffusion Coefficient ◽  
Diffusion Coefficients ◽  
Dispersion Model ◽  
Transport Coefficients ◽  
Time Dependent ◽  
Exchange Coefficient ◽  
Concentric Annulus ◽  
Annular Gap ◽  
And Diffusion

The effects of the irreversible boundary reaction and the particle drag on mass transfer are studied analytically in concentric annulus flows. The solution of mathematical model, based on the generalized dispersion model brings out the mass transport following by the insertion of catheter on an artery in terms of the three effective transport coefficients, viz., the exchange, convection and diffusion coefficient. A general expression is derived which shows clearly the time dependent nature of the coefficients in the dispersive model. The complete time dependent expression for the exchange coefficient is obtained explicitly and independent of velocity distribution in the flow; however it does depend on the initial solute distribution. Because of the complexity of the problem only asymptotic large time evaluations are made for the convective and diffusion coefficients, but these are sufficient to give the physical insight into the nature of the problem of the effects of drag and absorption parameters. It is found that as absorption parameter increases exchange and convection coefficients will be enhanced, but diffusion coefficient will be reduced. After certain period of time exchange coefficient will be constant for different values annular gap. As the drag parameter increases convection and diffusion coefficients will be reduced. With the enhancement of catheter radius i.e., the annular gap will be reduced then the convection and diffusion coefficients will be decreased.

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).

Certain Problems with the Application of Stochastic Diffusion Processes for the Description of Chemical Engineering Phenomena. Stochastic Model of Non-Isothermal Flow Chemical Reactor

1996 ◽  
Vol 61 (2) ◽  
pp. 242-258 ◽  
Author(s):  
Vladimír Kudrna ◽  
Libor Vejmola ◽  
Pavel Hasal
Keyword(s):  
Stochastic Model ◽  
Chemical Engineering ◽  
Diffusion Processes ◽  
Dispersion Model ◽  
Chemical Reactor ◽  
Segregation Index ◽  
One Dimensional ◽  
A Value ◽  
Isothermal Case ◽  
Flow Through

Recently developed stochastic model of a one-dimensional flow-through chemical reactor is extended in this paper also to the non-isothermal case. The model enables the evaluation of concentration and temperature profiles along the reactor. The results are compared with the commonly used one-dimensional dispersion model with Danckwerts' boundary conditions. The stochastic model also enables to evaluate a value of the segregation index.

Gaseous dispersion in laminar flow through a circular tube

1965 ◽  
Vol 284 (1399) ◽  
pp. 540-550 ◽  
Keyword(s):  
Circular Tube ◽  
Dispersion Coefficient ◽  
Straight Tube ◽  
Laminar Regime ◽  
Thermal Conductivity Detector ◽  
Longitudinal Dispersion Coefficient ◽  
Dispersion Coefficients ◽  
Effective Dispersion ◽  
Flow Through ◽  
Gaseous Dispersion

The dispersion of a pulse of ethylene injected into nitrogen, flowing in the laminar régime through straight and curved tubes, has been investigated at pressures of 1.0 and 4.4 atm. From the study of the concentration profiles with a thermal conductivity detector (katharometer) it is found that the experimental results for gas velocities between 1.00 and 16.00 cm/s agree well with the analytical solution to this problem for a straight tube given by Sir Geoffrey Taylor and extended by Aris. In particular, at low velocities, the effective dispersion coefficients tend to the molecular diffusivities. The presence of a bend slightly reduces the effective longitudinal dispersion coefficient and the introduction of constrictions enhances it. Data are also given on a number of other gas pairs. It is concluded that measurements of dispersion provide an accurate and simple way of studying diffusion in gas mixtures.

Dispersion in steady and oscillatory flows through a tube with reversible and irreversible wall reactions

2005 ◽  
Vol 462 (2066) ◽  
pp. 481-515 ◽  
Author(s):  
Chiu-On Ng
Keyword(s):  
Dispersion Coefficient ◽  
Tube Wall ◽  
Dispersion Model ◽  
Small Diameter ◽  
Chemical Species ◽  
Taylor Dispersion ◽  
Phase Partitioning ◽  
Dispersion Mechanism ◽  
Effective Dispersion ◽  
Number Flow

An asymptotic analysis is presented for the advection–diffusion transport of a chemical species in flow through a small-diameter tube, where the flow consists of steady and oscillatory components, and the species may undergo linear reversible (phase exchange or wall retention) and irreversible (decay or absorption) reactions at the tube wall. Both developed and transient concentrations are considered in the analysis; the former is governed by the Taylor dispersion model, while the latter is required in order to formulate proper initial data for the developed mean concentration. The various components of the effective dispersion coefficient, valid when the developed state is attained, are derived as functions of the Schmidt number, flow oscillation frequency, phase partitioning and kinetics of the two reactions. Being more general than those available in the literature, this effective dispersion coefficient incorporates the combined effects of wall retention and absorption on the otherwise classical Taylor dispersion mechanism. It is found that if the phase exchange reaction kinetics is strong enough, the dispersion coefficient is probably to be increased by orders of magnitude by changing the tube wall from being non-retentive to being just weakly retentive.

The effect of body acceleration on the dispersion of solute in a non-Newtonian blood flow through an artery

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Nur Husnina Saadun ◽  
Nurul Aini Jaafar ◽  
Md Faisal Md Basir ◽  
Ali Anqi ◽  
Mohammad Reza Safaei
Keyword(s):  
Blood Flow ◽  
Boundary Conditions ◽  
Yield Stress ◽  
Solute Concentration ◽  
Casson Fluid ◽  
Blood Velocity ◽  
Content Type ◽  
Body Acceleration ◽  
Lead Angle ◽  
Flow Through

Purpose The purpose of this study is to solve convective diffusion equation analytically by considering appropriate boundary conditions and using the Taylor-Aris method to determine the solute concentration, the effective and relative axial diffusivities. Design/methodology/approach >An analysis has been conducted on how body acceleration affects the dispersion of a solute in blood flow, which is known as a Bingham fluid, within an artery. To solve the system of differential equations analytically while validating the target boundary conditions, the blood velocity is obtained. Findings The blood velocity is impacted by the presence of body acceleration, as well as the yield stress associated with Casson fluid and as such, the process of dispersing the solute is distracted. It graphically illustrates how the blood velocity and the process of solute dispersion are affected by various factors, including the amplitude and lead angle of body acceleration, the yield stress, the gradient of pressure and the Peclet number. Originality/value It is witnessed that the blood velocity, the solute concentration and also the effective and relative axial diffusivities experience a drop when either of the amplitude, lead angle or the yield stress rises.

Unsteady convective diffusion with interphase mass transfer

1973 ◽  
Vol 333 (1592) ◽  
pp. 115-132 ◽  
Keyword(s):  
Dispersion Model ◽  
Reaction Rates ◽  
The Other ◽  
Time Dependent ◽  
Transport Systems ◽  
Exchange Coefficient ◽  
Dispersion Coefficients ◽  
Interfacial Transport ◽  
Order Of Magnitude ◽  
Proper Values

The theory of miscible dispersion is extended to interphase transport systems. As a specific example miscible dispersion in laminar flow in a tube in the presence of interfacial transport due to an irreversible first-order reaction at the wall is analysed by an exact procedure. A new exact dispersion model which accounts for dispersion with interphase transport is derived from first principles. The new concept of an ‘exchange coefficient’ arises naturally. This coefficient depends strongly on the rate of interfacial transport. Such transport also affects the convection and dispersion coefficients significantly. A general expression is derived which shows clearly the time-dependent nature of the coefficients in the dispersion model. The complete time-dependent expression for the exchange coefficient is obtained explicitly and is independent of the velocity distribution in the flow; however, it does depend on the initial solute distribution. Because of the complexity of the problem only asymptotic large-time evaluations are made for the convection and dispersion coefficients, but these are sufficient to give useful physical insight into the nature of the problem. When the rate of the wall reaction approaches zero the exchange coefficient also approaches zero and the other two coefficients approach their proper values in the absence of interfacial transport. At the other extreme of rapid wall reaction rates, the convection coefficient is more than 50 % larger than its value in the absence of interfacial transport and the dispersion coefficient is an order of magnitude smaller than that for zero interphase transport.

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