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The gas-phase mass transfer coefficient is one of the significant parameter for the determination of mass transfer in absorption columns. A novel correlation was obtained for the calculation of the gas phase mass transfer coefficient in the current research study based on the theoretical investigation and experimental data. Buckingham pi-theorem was utilized to develop an overall dimensionless correlation. The correlation was derived based on the experimental data conducted at the operating conditions’ range of temperature 40–100 °C, CO2 partial pressure of 18-66 kPa, and piperazine (PZ) concentration of 2-8 M. The correlation was validated using the experimental data with an acceptable error of 7.47%. The results showed that the gas-phase mass transfer coefficient was increased by enhancing the amount of holdup and Schmidt number (Sc) at different temperatures and PZ concentrations. Furthermore, by comparing the Sc number with holdup, it was observed that a higher temperature resulted in a higher hold-up amount in the gas-phase of the absorption column.

Binary distillation in continuous contact equipment is an important section in the oil refinery. In order to provide information about the temperature of the phases as well as the compositions, the heat and mass transfer that are nonlinear should be solved simultaneously. In this research, the heat and mass transfer of the binary distillation in a vertical wetted wall column is solved using the Adomian Decomposition Method (ADM). To this aim, the three nonlinear equations of momentum, energy and mass transfer are solved simultaneously. The recursive relations and the Adomian polynomials are programmed in the Maple environment computer package with the accuracy digits set to 14 for the numerical calculation. Results of the ADM analysis are in agreement with the experiment data. The Effects of the Prandtl and Schmidt numbers on the temperature and the concentration distribution profiles are presented and discussed. The distribution of temperature was revealed shown to increase with an the increase of in the Prandtl number of the vapor, and distribution of while the concentration was demonstrated to decrease with the an increase in Schmidt number.

This work aims to experimentally study the bubble size distribution and the oxygen transfer on the electroflotation process. The distribution of bubbles was measured using a high-speed camera. The measurements were conducted in a three-phase electroflotaion column (water- gas-olive stone) equipped with insoluble electrodes, stainless steel as cathode and titanium, covered with ruthenium oxide, as anode. The volumetric mass transfer coefficient kla was determined for some operating parameters such as current density, solid concentrations and sizes. In order to calculate the global coefficient of mass transfer kl, the specific interfacial area, a, was determined. It was chiefly found that bubble size distribution depends on current density and solid concentration, and the wide range of bubble sizes was found to be affected by the phenomenon of break up and coalescence. kla tended to decrease with the increase of solid concentrations. kl exhibited the same behavior as the volumetric mass transfer coefficient. The experimental results were also fitted with the theoretical models, relating ‘kla’, ‘kl’ and ‘a’ with Reynolds number, Schmidt number and operating conditions.

The effects of thermal radiation, magnetic field and chemical reaction on momentum, heat and mass transfer of mixed convection flow of a non-Newtonian power-law fluid across a horizontal cylinder are presented. Governing equations have been reduced to a set of dimensionless equations using appropriate transformations. The resulting equations are solved employing an implicit finite difference method up to the point of boundary layer separation. For the non-Newtonian fluids, the Nusselt number and the Sherwood number demonstrate completely different characteristics from the Newtonian fluids near the front stagnation point. The magnetic field parameter produces lower skin friction, heat transfer, and mass transfer, whereas these are increased for the thermo-solutal parameter and the mixed convection parameter. The skin friction and the Nusselt number are found to decrease and the Sherwood number increases with an increase of the Schmidt number and the chemical reaction parameter. Moreover, the conduction-radiation parameter generates higher skin friction and mass transfer and lower heat transfer rate.

The Walters-B liquid model is employed to simulate medical creams and other rheological liquids encountered in biotechnology and chemical engineering. This rheological model introduces supplementary terms into the momentum conservation equation. The combined effects of thermal radiation and heat sink/source on transient free convective, laminar flow and mass transfer in a viscoelastic fluid past a vertical plate are presented by taking thermophoresis effect into account. The transformed conservation equations are solved using a stable, robust finite difference method. A parametric study illustrating the influence of viscoelasticity parameter (Γ), thermophoretic parameter (τ), thermal radiation parameter (F), heat sink/source (ϕ), Prandtl number (Pr), Schmidt number (Sc), thermal Grashof number (Gr), solutal Grashof number (Gm), temperature and concentration profiles as well as local skin-friction, Nusselt and Sherwood number is conducted. The results of this parametric study are shown graphically and inform of table. The study has applications in polymer materials processing.

The mass transfer to turbulent flow through back-to-back pipe bends arranged in a 180° configuration with different lengths of pipe between the bends was measured using a dissolving gypsum test section in water. The measurements were performed for bends with a radius of curvature of 1.5 times the pipe diameter (D) at a Reynolds numbers of 70,000 and Schmidt number of 1280. The maximum mass transfer in the bends decreased from approximately 1.8 times the mass transfer in the upstream pipe when there was no separation distance between the bends to 1.7 times when there was a 1D or 5D length of pipe between the bends. The location of the maximum mass transfer was on the inner sidewall downstream of the second bend when there was no separation distance between the bends. This location changed to the inner wall at the beginning of the second bend when there was a 1D long pipe between the bends, and to the inner sidewall at the end of the first bend when there was a 5D long pipe between the bends.

Knowledge of the fluid flow and mass transfer over circular strands is fundamental to the cell culture of tissue scaffolds in bio-reactors. This paper presents a study on the simulation of fluid flow and mass transfer over the circular strands of a tissue scaffold by using the multiple relaxation time lattice Boltzmann method for the low Reynolds number regime, with Re D = 0.01 and 0.1, respectively. The mass transfer problem approximates the transport of a scalar nutrient from the bulk fluid to the strand surface, such as is encountered in the flow through tissue scaffolds placed in bio-reactors. The circular geometry of the scaffold strand is treated and implemented by means of the interpolated bounce-back boundary condition formulation. Our simulation illustrates that the flow accelerates around the strand, resulting in the maximum shear stress at the shoulder of the strand and that diffusion mass transfer plays the dominant role in the scalar transport. The local Sherwood number varies significantly over the surface of the strand, with a peak value located on the upstream surface. Increasing the Schmidt number of the scalar and decreasing the blockage ratio results in higher mass transfer rates on the surface of the stand. Overall, the simulation results provide one with the insight into the fluid flow and mass transfer over the circular strands of a tissue scaffold in a bio-reactor, which would be impractical to obtain by experiments.

We report on RANS simulations of high Schmidt number turbulent mass transfer due to a first-order reaction on the surface of a d-type rough wall. We find that for low reaction coefficients, the additional surface area of the rough wall causes an increased mass transfer in comparison with a smooth wall. However, when the reaction coefficient is high, the mass transfer becomes lower than for a smooth wall. A detailed analysis shows that the mass transport in the cavity is dominated by diffusion which becomes the limiting factor at high reaction coefficients. A conceptual model, which is in good agreement with the simulations, highlights that the influence of geometry roughness is not confined to the roughness Reynolds number for molecular-diffusion-dominated cavities. Refereed/Peer-reviewed

Turbulent mixed-convection mass transfer in vertical cylinders was measured using a sulfuric acid–copper sulfate electroplating technique. The Grashof numbers ranged from 5.3 × 109 to 6.9 × 1010, the Reynolds numbers ranged from 4,000 to 14,000, and the Schmidt numbers were approximately 2,000. The test results under buoyancy-aided and buoyancy-opposed flow conditions successfully reproduced typical turbulent mixed-convection heat-transfer behavior and agreed well with existing studies performed by Ko et al. and Parlatan et al. Previous studies have used the cylinder diameter as the characteristic length for the buoyancy coefficient; however, this study focused on the influence of the cylinder height on the mixed-convection mass-transfer rates because the height determines the buoyancy. The tests performed for various heights with a fixed diameter or for various diameters with a fixed height demonstrated the influence of the height-to-diameter ratio on the mass-transfer rate, revealing that the height of the cylinder should be considered as a length scale. A new empirical correlation was derived for turbulent mixed-convection mass transfer that includes the influence of the height-to-diameter ratios.

Paradichlorobenzene cylinders were cast, then suspended vertically and allowed to sublimate in air. Data on mass versus time were measured, and a sublimation rate was calculated. Three cylinders of different diameters were used: 1 inch (2.54 cm), 1.5 inch (3.81 cm), and 2 inch (5.08 cm). The length of all three cylinders was 10 in. (25.4 cm). Calculations indicate that the Schmidt number was constant. The Sherwood number ranged from 23 to 26, and Rayleigh numbers varied from 11 × 103 to 88 × 103. The objective of this study was to develop a correlation for determining the mass transfer coefficient of vertically suspended paradichlorobenzene cylinders in a natural convection environment. An equation relating Sherwood and Rayleigh numbers was derived.

Turbulent heat and mass transfer of a rotating disk for Prandtl and Schmidt numbers much larger than unity was modeled using an integral method validated against empirical equations of different authors for Sherwood numbers. As shown, decrease in relative thickness of thermal/diffusion boundary layers with increasing local radii entails additional increase of the exponent at the Reynolds number in expressions for Nusselt and Sherwood numbers in comparison with air flows.

The problem of laminar natural convection flow from a permeable semi-infinite accelerating vertical surface that is coated with a reacting chemical species is studied. The plate velocity and the species concentration vary as power laws. The fundamental parameters of the problem are the Schmidt number, the surface permeability and the reaction rate. The governing equations were transformed to a non-similar form and then solved analytically and numerically using the Keller box method. A parametric study illustrating the effects of the flow parameters on the velocity and the concentration fields was conducted and the physical aspects of the problem discussed. The study found, inter alia, that the fluid motion is decelerated by increases in the permeability of the accelerating surface and that the rate of mass transfer increases with Schmidt numbers but reduces with increasing reaction rates and the porosity of the accelerating surface.

The concentration distribution in the wake of a soluble sphere immersed in a granular bed of inert particles, through which fluid flows with "uniform velocity", has been obtained numerically, for solute transport by both advection and diffusion/dispersion. Fluid flow in the granular bed around the sphere was assumed to follow Darcy's law and, at each point, dispersion of solute was considered in both the cross-stream and streamwise directions. The elliptic PDE equation, resulting from a differential material balance on the solute, was solved numerically over a wide range of values of the relevant parameters (Peclet number and Schmidt number). The solution gives the concentration contour plots and, for each concentration level, the width and downstream length of the corresponding contour surface were determined. General expressions are presented to predict contaminant "plume" size downstream of the polluting source.

The present work describes the mass transfer process between a moving fluid and a slightly soluble cylinder, with the axis perpendicular to flow direction, buried in a packed bed of small inert particles, with uniform voidage. Fluid flow in the packed bed around the cylinder was assumed to follow Darcy’s law and, at each point, dispersion of solute was assumed to be determined by radial and axial dispersion coefficients, in the cross-stream and streamwise directions, respectively. Numerical solutions of the differential equation describing solute mass conservation were undertaken to obtain the concentration field near the soluble surface and the mass transfer flux was integrated to give the Sherwood number as a function of the relevant parameters. Mathematical expressions are proposed that describes accurately the dependence found numerically between the value of the Sherwood number and the values of Peclet number, Schmidt number and the ratio between the diameter of cylinder and the diameter of inerts.

The phenomenon of dispersion (transverse and longitudinal) in packed beds is summarized and reviewed for a great deal of information from the literature. Dispersion plays an important part, for example, in contaminant transport in ground water flows, in miscible displacement of oil and gas and in reactant and product transport in packed bed reactors. There are several variables that must be considered, in the analysis of dispersion in packed beds, like the length of the packed column, viscosity and density of the fluid, ratio of column diameter to particle diameter, ratio of column length to particle diameter, particle size distribution, particle shape, effect of fluid velocity and effect of temperature (or Schmidt number). Empirical correlations are presented for the prediction of the dispersion coefficients (D T and D L) over the entire range of practical values of Sc and Pem, and works on transverse and longitudinal dispersion of non-Newtonian fluids in packed beds are also considered.

An electrochemical technique is used to study local mass transfer coefficients on surfaces of inclined enclosures over the range 1.1×104 < RaH < 1.4×1010 for a nominal Schmidt number of 2280. Scaling with gcosθ instead of g in the Rayleigh number correlates the data well at low angles of inclination; however, as either the aspect ratio or the angle of inclination increase, the longitudinal density stratification causes the data to deviate from a power law scaling.

A general analysis has been developed to study the combined effect of the free convective heat and mass transfer on the steady three-dimensional laminar boundary layer flow over a stretching surface. The flow is subject to a transverse magnetic field normal to the plate. The governing three-dimensional partial differential equations for the present case are transformed into ordinary differential equation using three-dimensional similarity variables. The resulting equations, are solved numerically by applying a fifth order Runge-Kutta-Fehlberg scheme with the shooting technique. The effects of the Magnetic field Parameter M, buoyancy parameter N, Prandtl number Pr and Schmidt number Sc are examined on the velocity, temperature and concentration distributions. Numerical data for the skin-friction coefficients, Nusselt and Sherwood numbers have been tabulated for various parametric conditions. The results are compared with known from the literature.

We present a comparative numerical study about the overall mixing process in a coaxial jet mixer. The two-stream mixing problem was investigated in non-reacting single phase gas and liquid mixtures using Large-Eddy Simulations with wall functions and subgrid scale models from eddy viscosity concepts. The influence of different parameters like Reynolds number, Schmidt number, Prandtl number, density ratio and flow rate ratio on the overall mixing process was investigated. Additionally two methods of control of mixing are shown to have a significant effect on the overall mixing in a coaxial jet mixer.

The present paper deals with the study of momentum, heat and mass transfer characteristics in a viso-elastic fluid flow over a porous sheet, where the flow is generated due to linear stretching of the sheet and influenced by a uniform magnetic field applied vertically and a continuous injection of the fluid through porous boundary. In the flow region, heat balance is maintained with a temperature dependent heat source/sink, viscous dissipation, dissipation due to elastic deformation and stress work produced as the result of magnetic field on the non-Newtonian fluid. In mass transfer analysis we have taken into account the loss of mass of the chemically reactive diffusive species by means of first order chemical conversion rate. Using suitable similarity transformations on the highly non-linear partial differential equations we derive several closed form analytical solutions for non-dimensional temperature, concentration, heat flux, mass flux profiles in the form of confluent hyper geometric (Kummer's) functions and some other elementary functions as its special form, for two different cases of the boundary conditions, namely, (i) wall with prescribed second order power law temperature (PST) and prescribed second order power law concentration (ii) wall with prescribed second order power law heat flux (PHF) and prescribed second order power law mass flux. The effect of the non-dimensional magnetic parameter on momentum, heat and mass transfer characteristics for non-isothermal boundary condition and different physical situations of the fluid, having various degrees of visco-elasticity, Prandtl number, heat source/sink strength and Schmidt number, are discussed in detail. Some of the several important findings reported in this paper are: (i) The combined effect of magnetic field, visco-elasticity and impermeability of the wall is to increase skin-friction largely at the wall; (ii) maximum enhancement of wall-temperature profile due to the application of transverse magnetic field occurs when the boundary heating is maintained with prescribed heat flux, boundary wall is porous and Prandtl number of the fluid is low; (iii) the effect of transverse uniform magnetic field is to increase concentration in the flow region, however, enhancement of concentration is higher when the stretching wall is porous and subjected to injection and (iv) the reduction of concentration due to chemical conversion is of significant order near the wall in PHF case when the wall is maintained with prescribed power low mass flux, in comparison with the PST case when the wall is maintained with prescribed power law surface concentration.

We study the onset of time dependent Marangoni-Benard convection in binary mixtures subject to Soret effect by numerical computation of linear instability thresholds in infinite fluid layers and two-dimensional boxes. The calculations are done for positive Marangoni numbers (Ma > 0) and negative Marangoni Soret parameters S M = –(D S γ c )/(Dγ T ) where D S and D are the Soret and mass diffusion coefficients, respectively, and γ T , γ c are the first derivatives of the surface tension with respect to temperature and concentration. Our purpose is to understand why for particular choices of Prandtl and Schmidt numbers, the increase of the stabilizing solutal contribution leads to a decrease of the critical temperature difference, a phenomenon already reported by Chen & Chen [5] and Skarda et al. [12] For various choices of Prandtl and Schmidt numbers we analyze the evolution of the critical Marangoni number Ma c , critical wavenumber k c and angular frequency ω c with S M and compute the corresponding eigenvectors. We next propose a physical mechanism which explains how the stabilizing solutal contribution acts as a catalyst for overstability. Finally, we extend our results to two dimensional boxes of small aspect ratio.

The problem of steady, laminar, simultaneous heat and mass transfer by natural convection flow over a vertical permeable plate embedded in a uniform porous medium in the presence of inertia and thermal dispersion effects is investigated for the case of linear variations of both the wall temperature and concentration with the distance along the plate. Appropriate transformations are employed to transform the governing differential equations to a non-similar form. The transformed equations are solved numerically by an efficient implicit, iterative, finite-difference scheme. The obtained results are checked against previously published work on special cases of the problem and are found to be in good agreement. A parametric study illustrating the influence of the porous medium effects, heat generation or absorption, wall suction or injection, concentration to thermal buoyancy ratio, thermal dispersion parameter, and the Schmidt number on the fluid velocity, temperature and concentration as well as the skin-friction coefficient and the Nusselt and Sherwood numbers is conducted. The results of this parametric study are shown graphically and the physical aspects of the problem are highlighted and discussed.

In this paper we present a mathematical analysis of heat and mass transfer phenomena in a visco–elastic fluid flow over an accelerating stretching sheet in the presence of heat source/sink, viscous dissipation and suction/blowing. Similarity transformations are used to convert highly non-linear partial differential equations into ordinary differential equations. Several closed form analytical solutions for non-dimensional temperature, concentration, heat flux, mass flux profiles are obtained in the form of confluent hypergeometric (Kummer's) functions for two different cases of the boundary conditions, namely, (i) wall with prescribed second order power law temperature and second order power law concentration (PST), and (ii) wall with prescribed second order power law heat flux and second order power law mass flux (PHF). The effect of various physical parameters like visco–elasticity, Eckert number, Prandtl number, heat source/sink, Schmidt number and suction/blowing parameter on temperature and concentration profiles are analysed. The effects of all these parameters on wall temperature gradient and wall concentration gradient are also discussed.

The mixed convection flow over a continuous moving vertical slender cylinder under the combined buoyancy effect of thermal and mass diffusion has been studied. Both uniform wall temperature (concentration) and uniform heat (mass) flux cases are included in the analysis. The problem is formulated in such a manner that when the ratio λ(= u w/(u w + u ∞), where u w and u ∞ are the wall and free stream velocities, is zero, the problem reduces to the flow over a stationary cylinder, and when λ = 1 it reduces to the flow over a moving cylinder in an ambient fluid. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. We have also obtained the solution using a perturbation technique with Shanks transformation. This transformation has been used to increase the range of the validity of the solution. For some particular cases closed form solutions are obtained. The surface skin friction, heat transfer and mass transfer increase with the buoyancy forces. The buoyancy forces cause considerable overshoot in the velocity profiles. The Prandtl number and the Schmidt number strongly affect the surface heat transfer and the mass transfer, respectively. The surface skin friction decreases as the relative velocity between the surface and free stream decreases.

The unsteady natural convection boundary layer flow over a semi-infinite vertical cylinder is considered with combined buoyancy force effects, for the situation in which the surface temperature T′w(x) and C′w(x) are subjected to the power-law surface heat and mass flux as K(T′/r) = −axn and D(C′/r) = −bxm. The governing equations are solved by an implicit finite difference scheme of Crank-Nicolson method. Numerical results are obtained for different values of Prandtl number, Schmidt number ‘n’ and ‘m’. The velocity, temperature and concentration profiles, local and average skin-friction, Nusselt and Sherwood numbers are shown graphically. The local Nusselt and Sherwood number of the present study are compared with the available result and a good agreement is found to exist.

Finite difference solution of the transient free-convection flow of an incompressible viscous fluid past an impulsively started semi-infinite vertical plate with heat and mass transfer is presented here. The steady state velocity, temperature and concentration profiles are shown graphically. Velocity profiles are compared with exact solution. It has been observed that there is a rise in the velocity due to the presence of a mass diffusion. An increase in Schmidt number, leads to a fall in the velocity. Stability and the convergence of the finite difference scheme are established.

A numerical solution for the transient natural convection flow over a vertical cylinder under the combined buoyancy effect of heat and mass transfer is presented. The velocity, temperature and concentration profiles, local and average skin-friction, Nusselt number and Sherwood number are shown graphically. It is observed that time taken to reach steady state increases with Schmidt number and decreases as combined buoyancy ratio parameter N increases. Stability and convergence of the finite difference scheme are established.

An exact solution to the problem of flow past an impulsively started infinite vertical plate in the presence of a foreign mass and constant mass flux at the plate is presented by the Laplace-transform technique. The velocity, the temperature and the concentration profiles are shown on graphs. The skin-friction and the Sherwood number are also shown on graphs. The effects of different parameters likeG (the Grashof number),Gc (the modified Grashof number),Pr (the Prandtl number) andSc (the Schmidt number) are discussed.

An exact solution to the flow of a viscous incompressible fluid past an infinite vertical oscillating plate, in the presence of a foreign mass has been derived by the Laplace-transform technique when the plate temperature is linearly varying as time. The velocity profiles are shown on graphs and the numerical values of the skin-friction are listed in a table. It is observed that the skin-friction increases with increasingSc, ωt orGr but decreases with increasingGm ort, whereSc (the Schmidt number), ω (frequency),t (time),Gr (the Grashof number) andGm is (the modified Grashof number) andt.

The effect of chemical reaction on free convective flow and mass transfer of a viscous, incompressible and electrically conducting fluid over a stretching surface is investigated in the presence of a constant transverse magnetic field. The non-linear boundary layer equations with the boundary conditions are transferred by a similarity transformation into a system of non-linear ordinary differential equations with the appropriate boundary conditions. Furthermore, the similarity equations are solved numerically by using a fourth order Runge-Kutta scheme with the shooting method. Numerical results of the skin friction coefficient, the local Nusselt number Nu, the local Sherwood number Sh, as will as the velocity, temperature and concentration profiles are presented for gases with a Prandtl number of 0.71 for various values of chemical reaction parameter, order of reaction, magnetic parameter and Schmidt number.