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A plume model is used to describe the variation of the salt concentration at the discharge of a river into a saline water. The integral model of the plume behavior consists of a set of ordinary differential equations derived from conservation of mass, momentum and salt concentration. The temperatures of the plume and ambient saline water are considered equal. The concentration of the salt in the river water is null. The saline water is assumed motionless. After release from the river, the concentration of the salt in the plume increases by mixing with the ambient saline water. The rate of mixing depends upon the local plume and ambient fluid properties such as velocity and salt concentration. [ABSTRACT FROM AUTHOR]

The mass transfer from two spheres in tandem to an incompressible fluid flow accompanied by chemical reactions (first-order and second-order irreversible) into the fluid was analysed numerically. Creeping flow was assumed. The spheres have the same diameter, initial concentrations and physical properties. The concentration of the transferring species inside the spheres is considered: (1) constant and (2) spatially uniform and varying in time. The mathematical model equations were solved numerically in bi-spherical coordinates system. The computations focused on the conditions when the interaction between spheres does not influence the mass transfer rate. [ABSTRACT FROM AUTHOR]

The unsteady mass transfer of the packaging constituents to a food has been analysed. The diffusion coefficient inside the packaging was considered concentration - variable while the food was considered concentration spatially gradientless. A well-known technique (Kirchhoff transformation) was used to solve the non-linear mass balance equation. The influence of the non-linear diffusion on the mass transfer mechanism and rate was analysed for different values of the partition coefficient and dilution coefficient. [ABSTRACT FROM AUTHOR]

The splitting method used in a previous study for the numerical solution of mass transfer equations in ternary systems is generalized to mixtures withn-components. The diffusion coefficients are considered constant. Theoretical results about the stability of the method are presented, as well as numerical simulations for mixtures withn = 4, 5, and 6. The numerical experiments confirmed the theoretical results and show good numerical performances. Moreover, multicomponent diffusion effects without an imposed concentration gradient are investigated for mixtures withn = 4, 5, and 6 components. [ABSTRACT FROM PUBLISHER]

Composite films of sodium carboxymethyl cellulose and bacterial cellulose (NaCMC–BC) cross-linked with citric acid (CA) were prepared by solution casting method. Ibuprofen sodium salt (IbuNa) has been used to study the mechanism of drug release from composite films. Surface morphology was investigated by scanning electron microscopy (SEM) and proved that the BC content influences the aspect of the films. Fourier transformed infrared spectroscopy (FTIR) revealed specific peaks in IR spectra of composite films which sustain that NaCMC was cross-linked with CA. Starting from swelling observations, the release kinetic of IbuNa was described using a model which neglects the volume expansion due to polymer swelling and which considers non-linear diffusion coefficients for drug and solvent. The IbuNa release is also influenced by BC content, the drug release rate was decreasing with the increase of BC content. [ABSTRACT FROM AUTHOR]

The unsteady, conjugate, forced convection heat transfer from a fluid sphere to a surrounding fluid flow in the presence of viscous dissipation has been analysed. The fluid flow inside and outside the sphere was considered laminar, axisymmetric, steady and incompressible. The heat balance equations were solved numerically in spherical coordinates system by a splitting finite difference method. The influence of the Reynolds, Brinkman and Peclet numbers on the heat transfer mechanism and rate was analysed for different values of the physical properties ratios (thermal conductivity ratio, heat capacity ratio, viscosity ratio and density ratio). [ABSTRACT FROM AUTHOR]

For the flow past an impervious cylinder embedded in a fluid saturated porous medium only the linear (Darcy and Darcy - Brinkman) models were used. In this work, the flow past an impermeable cylinder embedded in a fluid saturated porous medium was studied numerically considering a nonlinear model valid (the Brinkman – Forchheimer – Darcy or Brinkman – Hazen – Dupuit – Darcy model). The flow is viscous, laminar, steady and incompressible. The porous medium is isotropic, rigid and homogeneous. The stream function - vorticity equations were solved numerically in cylindrical coordinates system. The influence of the cylinder Reynolds number, Darcy number and Forchheimer term on the velocities field and surface pressure was investigated for two boundary conditions on the surface of the cylinder: slip and no - slip. [ABSTRACT FROM AUTHOR]

The flow past an impermeable sphere embedded in a fluid saturated porous medium was studied numerically considering valid the Brinkman-Forchheimer-Darcy (or Brinkman-Hazen-Dupuit-Darcy) model. The flow is viscous, laminar, axisymmetric, steady and incompressible. The porous medium is isotropic, rigid and homogeneous. The stream function-vorticity equations were solved numerically in spherical coordinates system by a multigrid method. The influence of the Darcy number and Forchheimer term on the velocities field was investigated for two boundary conditions on the surface of the sphere: slip and no - slip. [ABSTRACT FROM AUTHOR]

In a series of two papers, we analyze the numerical performances of the preconditioned conjugate gradient algorithms (BICGSTAB and GMRES) and multigrid method in solving two-dimensional multicomponent mass transfer equations. The present test problems are steady-state, linear and nonlinear diffusion-reaction equations. The nonlinear algorithm used in connection with the preconditioned conjugate gradient methods is the modified Picard iteration. Theoretical results about the preconditioning are presented. The multigrid algorithm used is the Full Approximation Storage algorithm. The finite difference method was used to discretize the mathematical model equations. The numerical results obtained show good numerical performances. [ABSTRACT FROM PUBLISHER]

This work continues our previous analysis concerning the performances of the nonlinear multigrid (the Full Approximation Storage algorithm) method and modified Picard preconditioned conjugate gradient methods for the numerical solution of the two-dimensional, steady-state, multicomponent mass transfer equations. The present test problems are steady-state, linear and nonlinear, convection-diffusion-reaction equations. The upwind finite difference method was used to discretize the mathematical model equations. The numerical results obtained show good numerical performances. [ABSTRACT FROM PUBLISHER]

The unsteady, conjugate, forced convection heat transfer from a porous sphere embedded in another porous medium has been analysed. Both porous media are fluid saturated. Local thermal equilibrium between the two phases is assumed. The fluid flow inside and outside the sphere was considered axisymmetric, steady and incompressible (Darcy and Brinkman flows). The heat balance equations were solved numerically in spherical coordinates system by an implicit alternating direction finite difference method. The influence of the porous media permeability and sphere Peclet numbers on the heat transfer mechanism and rate was analysed for different values of the physical properties ratios (thermal conductivity ratio and heat capacity ratio). [ABSTRACT FROM AUTHOR]

The paper examined the steady-state multiplicity of the porous, non-isothermal, finite hollow cylindrical catalyst pellet in the absence of external transport resistances. A numerical multigrid continuation technique with the preconditioned conjugate gradient squared as coarse grid solver was used. The continuation parameter is the reaction parameter (Thiele modulus). The effect of the other governing parameters (especially the geometric ratios) was analyzed. The numerical results obtained show that the finite hollow cylindrical catalyst pellet exhibits similar multiplicity patterns to the finite solid cylindrical catalyst pellet. [ABSTRACT FROM AUTHOR]

Abstract: The transient mass transfer from a binary gas bubble to an incompressible liquid accompanied by a chemical reaction into the liquid phase is analysed numerically. Only one of the bubble components transfers into the liquid phase where a first-order, irreversible chemical reaction occurs. The concentration of the transferring species inside the bubble is considered spatially uniform but not constant in time. Creeping flow was assumed. The mathematical model equations were solved numerically in spherical coordinates system. The computations focused on the influence of the Damkohler number and Henry number on the mass transfer rate for Pe =10, 100, 1000 and Da/Pe =0.1, 1, 10. [Copyright &y& Elsevier]

Abstract: Numerical methods are used to investigate the transient mass transfer from a binary gas bubble to an incompressible liquid. The bubble has two components: A – soluble and B – insoluble in the surrounding fluid. The concentration of A inside the bubble is considered spatially uniform but not constant in time. The maximum value of the initial volumetric fraction of A is 0.3. The mathematical model equations were solved numerically in spherical coordinates system. Creeping flow, moderate Re number flow, 10⩽ Re ⩽100, and potential flow around the bubble were assumed. The computations focused on the influence of the initial fraction of A and Henry number on the mass transfer rate for Pe ⩽104. [ABSTRACT FROM AUTHOR]

Abstract: Numerical methods are used to investigate the transient heat transfer from an oblate/prolate spheroid to a steady stream of viscous, incompressible fluid. The temperature of the spheroid is considered spatially uniform but not constant in time. The momentum and heat balance equations were solved numerically in oblate/prolate spheroidal coordinates system. The solutions span the parameter ranges 10⩽ Re ⩽100 (for the oblate spheroid), 10⩽ Re ⩽200 (for the prolate spheroid), Pr =1, 10 and axis ratio ε, 0.1⩽ ε ⩽0.9. The computations were focused on the influence of the axis ratio and volume heat capacity ratio on the heat transfer rate. [Copyright &y& Elsevier]

Abstract: Numerical methods are used to investigate the transient, forced convection heat/mass transfer inside circulating spheres at low to moderate Reynolds numbers. The heat/mass balance equations were solved numerically in spherical coordinates system by a finite difference method. The values considered for the sphere interior Reynolds number are Re int ⩽ 1000. The computations were focused on the influence of the sphere Peclet number, Pe, and Re int on heat/mass transfer rate for Pe/(1+ μ)⩽104. [Copyright &y& Elsevier]

Abstract: The unsteady, conjugate, forced convection heat/mass transfer from ensembles of mono-size Newtonian fluid spheres to Newtonian fluids has been studied at moderate Peclet and Reynolds numbers. The cell model has been used to account for the spheres hydrodynamic interactions. The momentum and heat/mass balance equations were solved numerically in spherical coordinates system by a finite difference method. The values considered for the sphere exterior Reynolds number are . The influence of the voidage and physical properties ratios on the heat/mass transfer rate was analysed for sphere Peclet numbers, Pe 1(2) ⩽104, and three fluid – fluid systems: gas–liquid, liquid–liquid and liquid–gas. [Copyright &y& Elsevier]

Abstract: Unsteady mass transfer between two rigid spheres in tandem and a surrounding fluid flow with reversible second-order chemical reaction on the surface of the spheres has been analysed. The spheres have the same diameter and initial concentration. The dispersed phase reactant and product are insoluble in the continuous phase. The continuous phase reactant and product are insoluble in the dispersed phase. Axisymmetric, slow, viscous flow (Stokes flow) around the spheres was considered. The mass balance equations were solved numerically in spherical/bispherical coordinates systems by a finite difference nonlinear multigrid method. For moderate Pe number, Pe = 100, modified Hatta modulus, Ha 2 = 10, 100, 1000, and different values of the diffusion coefficients, the computations focused on the influence of the spheres spacing on the mass transfer rates. [Copyright &y& Elsevier]

Abstract: Numerical methods are used to investigate the transient, conjugate, forced convection heat/mass transfer in multiparticle systems at low to moderate Reynolds numbers. The interparticle interactions have been accounted for by using the simple cell models. The momentum and heat/mass balance equations were solved numerically in spherical coordinates system by a finite difference method. The values considered for the sphere Reynolds number are Re <100. The computations were focused on the influence of the voidage and physical properties ratios on the heat/mass transfer rate for sphere Peclet number, 10⩽ Pe ⩽1000. [Copyright &y& Elsevier]

Abstract: Numerical methods are used to investigate the transient heat transfer from an elliptic cylinder to a steady stream of viscous, incompressible fluid. The temperature of the cylinder is considered spatially uniform but not constant in time. The momentum and heat balance equations were solved numerically in elliptic coordinate system. The solutions span the parameter ranges 5⩽ Re ⩽40, 1⩽ Pr ⩽100 and axis ratio ε, 0.1⩽ ε ⩽0.75. The computations were focused on the influence of the axis ratio and volume heat capacity ratio on the heat transfer rate. [Copyright &y& Elsevier]

Abstract: This paper presents a computational study of the forced convection heat/mass transfer from two spheres placed in a uniform viscous flow parallel to their line of centers. The temperature/concentration inside the spheres are assumed spatially uniform but not constant in time. Axisymmetric, slow, viscous flow (Stokes flow) around the spheres was considered. The appropriate energy/chemical species balance equations were solved numerically in bispherical coordinates. The finite difference method was used to discretize the mathematical model equations. Various spheres spacing, sizes and physical properties were considered at moderate Pe numbers. [Copyright &y& Elsevier]

Abstract: This work presents a computational study of the forced convection heat transfer around two circular cylinders in tandem. Axisymmetric, steady, laminar flow around the cylinders was assumed. The temperature inside the cylinders is considered spatially uniform but not constant in time. Numerical solutions have been obtained in bipolar cylindrical coordinates. The finite difference method was used to discretize the equations of the mathematical model. The influence of the model parameters on the heat transfer rate was analysed for the upstream cylinder Reynolds number, Re, varying from 1 to 30 and fluid phase Prandtl number equal to 0.1, 1, 10 and 100. [Copyright &y& Elsevier]

Abstract: This work presents a computational study of the steady, axisymmetric, viscous flow around two circular cylinders in tandem. The vorticity–stream function formulation of the Navier–Stokes equations was chosen. Numerical solutions have been obtained in bipolar cylindrical coordinates. A compact, high-order, finite difference method was used to discretize the model equations. Iterative algorithms were tested to solve the discrete equations. Different cylinders spacing and sizes were considered for the upstream cylinder Reynolds number up to 30. Vorticity and pressure distributions on the cylinders surfaces and drag coefficients are presented and compared with those calculated for an isolated cylinder. [Copyright &y& Elsevier]

Abstract: The paper examined the steady-state multiplicity behaviour of the porous, non-isothermal, finite cylindrical catalyst pellet in the absence of external transport resistances. A numerical multigrid continuation technique with the preconditioned conjugate gradient squared as coarse grid solver was used. The numerical methods proved to be efficient and reliable so that computations with fine grids (up to 129×129 grid points on the unit square) are easily performed. The key parameter of the investigation is the reaction parameter. The effect of the other governing parameters (especially the aspect ratio) was also analysed. An infinite number of steady states, with a scenario different from that usually used to explain this situation, were obtained at small values of the aspect ratio (the height of the cylinder is greater than the diameter of the cylinder). [Copyright &y& Elsevier]

Abstract: Conjugate mass transfer between a sphere and a surrounding fluid flow with consecutive second-order chemical reaction (van de Vusse chemical reaction) inside the sphere has been analysed. The dispersed phase components are insoluble in the continuous phase and their complete depletion is allowed. Two sphere models were considered: the rigid sphere and the fluid sphere with internal circulation. For each sphere model, two hydrodynamic regimes were taken into consideration, creeping flow and moderate sphere Reynolds numbers. Slow, intermediate and fast chemical reactions were analysed at moderate Peclet numbers (Pe). The mass balance equations were solved numerically in spherical coordinates by a finite difference nonlinear multigrid method. The computations focused on the influence of diffusivity ratio and Henry number of the transferring species on the dimensionless sphere average concentrations (especially the intermediate component). [Copyright &y& Elsevier]

Abstract: The transient mass transfer from a sphere with rigid surface into a surrounding fluid flow has been analysed for a ternary system. The concentrations inside the sphere are considered uniform. Steady, creeping flow is assumed around the sphere. The mass balance equations were solved numerically in spherical coordinates by a finite difference splitting method. The computations focused on the influence of the cross diffusion coefficients on the mass transfer rate at moderate Peclet numbers and different values of the Henry numbers and self-diffusivity rates. The occurrence on the sphere''s surface of osmotic diffusion, diffusion barrier and reverse diffusion phenomena was also studied. [Copyright &y& Elsevier]