Unsteady Convective Diffusion with Interphase Mass Transfer in Casson Liquid (original) (raw)
Related papers
Effect of Boundary Absorption in Dispersion in Casson Fluid Flow in a Tube
Annals of Biomedical Engineering, 2004
The combined effect of yield stress and irreversible boundary reaction on dispersion process in a Casson fluid flowing in a conduit (pipe/channel) is studied using the generalized dispersion model proposed by Sankarasubramanian and Gill (Sankarasubramanian, R., and W. N. Gill. Proc. R. Soc. London, Ser. A 333:115–132, 1973). The study describes the development of dispersive transport following the injection of a tracer in terms of the three effective transport coefficients, viz., exchange, convection, and dispersion coefficients. The exchange coefficient does not depend on yield stress but the convection and dispersion coefficients depend on yield stress or equivalently plug flow region. For large times, when the plug flow radius is one-tenth of pipe radius, the convective coefficient is reduced by 0.41 times of the corresponding value for a Newtonian fluid at equivalent wall absorption parameter; in channel case the reduction is by 39%. It is seen that the asymptotic dispersion coefficient decreases with increase in wall absorption parameter and yield stress of the fluid. When the plug radius in pipe (channel) is 0.1, depending upon the values of wall absorption parameter, say (0.01–100) the reduction factor in dispersion coefficient is in the range (0.1–0.3) in comparison to the values of the Newtonian case. The results reduce to those of Sankarasubramanian and Gill (Sankarasubramanian, R., and W. N. Gill. Proc. R. Soc. London, Ser. A 333:115–132, 1973) when there is no yield stress for the pipe flow analysis and to those of Dash et al. (Dash, R. K., G. Jayaraman, and K. N. Mehta. Ann. Biomed. Eng. 28:373–385, 2000) when there is no interphase mass transfer. The study can be used as a starting first approximation solution for studying the dispersion in the cardiovascular system.
Hydrodynamic Dispersion of Solute under Homogeneous and Heterogeneous Reactions
International Journal of Heat and Technology, 2019
The present investigation deals with Taylor dispersion of reactive species in Casson liquid in an oscillatory flow because of the pulsatile pressure gradient. The solute is considered to be chemically active at the boundary and also participate a first order reaction within the bulk flow. To evaluate transport coefficients, Aris-Barton moment technique is considered. The solute transport process is discoursed in detailed with respect to yield stress, chemical reaction parameter, Womersly number etc. The study reveals that both wall absorption and bulk flow reaction have a significant response on dispersion phenomena. Both the chemical reactions agree to diminish the negative exchange coefficient and the apparent dispersion coefficient, however, increases the negative convection coefficient. The negative exchange coefficient is independent of yield stress but a significant variation is observed due to yield stress in the cases of negative convection coefficient and the apparent dispersion coefficient. The axial distribution of mean concentration is approximated by using the Hermite polynomial representation of central moments as a function of reaction rate parameters, wall absorbing parameter, yield stress etc. The present article may be useful for the studies related to physiological blood flow analysis.
Dispersion of a solute in a Herschel–Bulkley fluid flowing in a conduit
Journal of …, 2012
The dispersion of a solute in a Herschel-Bulkley fluid is studied by using the generalized dispersion model in both pipe and channel. With this method the entire dispersion process is described as a simple diffusion process with the effective diffusion coefficient as a function of time. The results for Newtonian fluid, power law fluid and Bingham fluid are obtained as special cases by giving appropriate values to the power law index and yield stress. The effects of power law index, yield stress on the dispersion coefficient and mean concentration have been discussed computationally and graphically. The effect of power law index and yield stress is found to reduce the dispersion coefficient. It is observed that the critical time for dispersion coefficient to reach the steady state is varying with the yield stress and power law index. It is noticed that time to assume the critical value in Newtonian case is 0.5 and in the channel case the corresponding value of time is 0.55 which are in agreement with the existed results. It is also observed that in the non-Newtonian fluids this time is less than that of Newtonian fluid case and in Bingham fluid the critical value of time in pipe flow analysis (channel flow analysis) is attained at 0.45 (0.52) while in power law fluid it is at 0.43(0.48) and in the case of Herschel-Bulkley fluid it is 0.41 (0.45).
Journal of Hydrodynamics, 2013
In this paper we investigate the two-dimensional flow of a non-Newtonian fluid over an unsteady stretching permeable surface. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. First-order constructive/destructive chemical reaction is considered. With the help of a shooting method, numerical solutions for a class of nonlinear coupled differential equations subject to appropriate boundary conditions are obtained. For the steady flow, the exact solution is obtained. The flow features and the mass transfer characteristics for different values of the governing parameters are analyzed and discussed in detail.
Numerical Solution to Mass Transfer on Mhd Flow of Casson Fluid With Suction and Chemical Reaction
international journal of chemical sciences, 2016
In the present work, the effect of mass transfer of a MHD Casson fluid over a porous stretching sheet is discussed in presence of chemical reaction is investigated using keller box method. The resulting nonlinear flow is solved to get a series solution. The variations in velocity and concentration fields are presented for various flow parameters. We further analyzed that the concentration profile decreases rapidly compared with the velocity of the fluid with increase in suction parameter.
Acta Mechanica, 2009
The combined effect of annular gap, yield stress and irreversible boundary reaction on the dispersion process in a Casson fluid flow is studied using generalized dispersion model. The study describes the development of dispersive transport following the injection of a tracer in terms of the three effective transport coefficients viz. absorption, convection and dispersion coefficients. The combined effect of annular gap, yield stress and wall absorption parameter on the above three effective transport coefficients is discussed. It is observed that the absorption coefficient is independent of the yield stress of the fluid and depends on the annular gap and wall absorption parameter. It is also observed that the asymptotic convection, dispersion coefficients are dependent on the yield stress of the fluid, annular gap and wall absorption parameter. The effect of the flow parameters on the mean concentration is studied. Application of this model for understanding the dispersion of solute in blood in a catheterized artery is discussed.
Convection-diffusion in unsteady non-Newtonian fluid flow in an annulus with wall absorption
Korea-Australia Rheology Journal, 2018
The present study investigates the combined effects of non-Newtonian rheology and unsteady nature of the fluid on dispersion of a soluble substance between two coaxial cylinders having wall permeability at the outer wall with the flowing fluid is modelled as Casson fluid. Generalized dispersion method in combination with a finite difference scheme is used to study the dispersion phenomenon. Using the generalized dispersion model, the entire process of dispersion is expressed in terms of three transport coefficients viz., absorption, convection, and dispersion (effective diffusion) coefficients. These transport coefficients are evaluated numerically using Crank-Nicolson finite difference method. The mean concentration is expressed in terms of these transport coefficients. Effects of annular gap, yield stress, Womersley frequency parameter, amplitude of the pressure pulsation, and the absorption parameter on the transport coefficients and mean concentration are studied. Flow unsteadiness is observed influencing the dispersion coefficient both quantitatively and qualitatively. It is observed that, as Womersley number increases the fluctuation of the dispersion coefficient increases and the magnitude of dispersion coefficient decreases for small values of time (< 0.5) and increases for later values of time.
Frontiers in Heat and Mass Transfer
The primary objective of this paper is to examine the impact of variable viscosity and thermal conductivity on peristaltic transport of Casson liquid in a convectively heated inclined porous tube. The viscosity differs over the radial axis, and temperature dependent thermal conductivity is taken into account. The perturbation technique is utilized to solve the governing nonlinear equations under the assumption of long wavelength and small Reynolds number. The analytical solutions are obtained for velocity, streamlines, pressure rise, frictional force, and temperature when subjected to slip and convective boundary conditions. The impacts of related parameters on physiological quantities of interest are discussed and analyzed through graphs. It is seen that the variable viscosity has a noteworthy part in upgrading the velocity profiles. The investigation additionally demonstrates that the size of trapped bolus diminishes with an expansion in the velocity slip parameter.
Gas diffusion into viscous and non-Newtonian liquids
Chemical Engineering Science, 1992
A quiescent technique has been developed to determine the diffusion coefficients of carbon dioxide in water and viscous and non-Newtonian liquids. The rate of gas absorption was measured accurately as the pressure change of a fixed volume of gas by a micromanometer. Gas penetration analysis suggests that a plot of gas absorption rate against the square root of contact time should be linear. The plot revealed a distinct initial phase of molecular diffusion lasting for about 100 seconds when water was instantaneously exposed to carbon dioxide. This was followed by non-linear behaviour in which natural convection is driven by density gradients. The diffusion coefficient of carbon dioxide in water was found to agree well with the values reported in the literature. Mass transfer coefficients, k , were detennincd for the interface in the convective regime. Diffusion without natural convection of C?Oz into viscous and pseudoplastic aqueous solutions appeared to be prolonged and proceeded at a slower rate. The onset of convection was suppressed considerably depending on the (apparent) viscosity of the solutions. A critical Rayleigh number was computed to characterise the onset of linear instability leading to natural convection. The critical times for stable diffusion were predicted from this critical Rayleigh number. Agreement with observed values is fair. KEYWORDS Diffision coefficients; non-Newtonian liquids; linear instability; critical Rayleigh number. critical times. INTRODUCIION In this paper we first describe experiments to measure the diffusion coefficients of COz into water and aqueous solutions of car-boxy methyl cellulose (CMC). In the experiments we observed a time of stable molecular diffusion which was followed by natural convection. The second part of the paper deals with the latter phenomenon. Diffusion coefficients (0) am fundamental constants in gas-liquid mass transfer and am used in associated correlations to calculate mass transfer coefficients. In most cases, the transfer coefficients are found to be proportional to D to the power q, where q is between 0.2 to 1.
Acta Mechanica, 2006
The dispersion of a solute in the flow of a Casson fluid in an annulus is studied. The generalized dispersion model is employed to study the dispersion process. The effective diffusion coefficient, which describes the whole dispersion process in terms of a simple diffusion process, is obtained as a function of time, in addition to its dependence on the yield stress of the fluid and on the annular gap between the two cylinders. It is observed that the dispersion coefficient changes very rapidly for small values of time and becomes essentially constant as time takes large values. In non–Newtonian fluids the steady state is reached at earlier instants of time when compared to the Newtonian case and the time taken to reach the steady state is seen to depend on the values of the yield stress. It is observed that a decrease in the annular gap inhibits the dispersion process for all times both in Newtonian as well as in non–Newtonian fluids. When the yield stress is 0.05, depending upon the size of the annular gap (0.9–0.7) the reduction factor in the dispersion coefficient varies in the range 0.58–0.08. The application of this study for understanding the dispersion of an indicator in a catheterized artery is discussed.