One-dimensional mass flow

Transient mass diffusion in bodies of simple geometry with one-dimensional mass flow... 

Shear flow of one-dimensional mass flow (ideal image)... 

The quasi-one-dimensional model of flow in a heated micro-channel makes it possible to describe the fundamental features of two-phase capillary flow due to the heating and evaporation of the liquid. The approach developed allows one to estimate the effects of capillary, inertia, frictional and gravity forces on the shape of the interface surface, as well as the on velocity and temperature distributions. The results of the numerical solution of the system of one-dimensional mass, momentum, and energy conservation equations, and a detailed analysis of the hydrodynamic and thermal characteristic of the flow in heated capillary with evaporative interface surface have been carried out. 

Estimates (9.12) and (9.14) effectively reduce the problem of flow in a heated micro-channel to solving a system of one-dimensional mass, momentum and energy balance equations. They have the following form ... 

The subject of the present chapter is the analysis of possible states of capillary flow with distinct evaporative meniscus. The system of quasi-one-dimensional mass, momentum and energy equations are applied to classify the operating parameters corresponding to various types of flow. The domains of steady and unsteady states are also outlined. 

The distribution of the solute between the mobile and the stationary phases is continuous. A differential equation that describes the travel of a zone along the column is composed. Then the band profile is calculated by the integration of the differential mass balance equation under proper initial and boundary conditions. Throughout this chapter, we assume that both the chemistry and the packing density of the stationary phase are radially homogeneous. Thus, the mobile and stationary phase concentrations as well as the flow velocities are radially uniform, and a one-dimensional mass balance equation can be considered. 

The one-dimensional mass transport equation for plug flow with dispersion, and a... 

One of the simplest models used to describe the performance of tubular reactors is the well-known isothermal one-dimensional plug flow tubular reactor (PFTR) model. The mass balance of this model for steady-state conditions, the simultaneous occurrence of M reactions and a constant volumetric flow rate V is ... 

One-dimensional reactive flow. As a preliminary trial problem in our computations of reactive flow, we have studied a simple situation in which a fluid obeying first-order chemical kinetics moves at constant velocity and temperature in the positive x direction. Here only the mass-transport equation is operative, and it takes the simple form ... 

The general mass balance equation for one-dimensional solute flow can be written as follows ... 

We observe that the mass flow rate increases steadily as we lower P2, until P2/Pi equals 0.5283, and then further lowering of P2 does not increase the mass flow rate. If we refer to App. A.5, we see that if the assumptions of isentropic, one-dimensional, steady flow apply, then this pressure ratio corresponds exactly to the sonic velocity (M = l) at the throat of the nozzle. Lowering the downstream pressure more does not increase the mass flow rate, because the flow that the value of... 

TABLE 4-6 One-Dimensional Mass and Thermal Energy Balances for Plug-Flow Thbular Reactors with Cocurrent Cooling in a Concentric Double-Pipe Configuration"... 

SIMPLIFICATION OF THE GENERALIZED MASS TRANSFER EQUATION FOR A ONE-DIMENSIONAL PLUG FLOW MODEL... 

The effectiveness factor E is evaluated for the appropriate kinetic rate law and catalyst geometry at the corresponding value of the intrapellet Damkohler number of reactant A. When the resistance to mass transfer within the boundary layer external to the catalytic pellet is very small relative to intrapellet resistances, the dimensionless molar density of component i near the external surface of the catalyst (4, surface) IS Very similar to the dimensionless molar density of component i in the bulk gas stream that moves through the reactor ( I, ). Under these conditions, the kinetic rate law is evaluated at bulk gas-phase molar densities, 4, . This is convenient because the convective mass transfer term on the left side of the plug-flow differential design equation d p /di ) is based on the bulk gas-phase molar density of reactant A. The one-dimensional mass transfer equation which includes the effectiveness factor. 

If reactant A participates in one second-order irreversible chemical reaction and its stoichiometric coefficient is —1 in that reaction, then the one-dimensional plug-flow mass balance in dimensionless form, given by (22-11), is described by... 

The numerical solution of second-order nonlinear ODEs with split boundary conditions requires trial and error integration of two coupled first-order ODEs. If one defines d p./di = Axial Grad, then the one-dimensional plug-flow mass balance with axial dispersion,... 

TABLE 22-1 Numerical Solution of the One-Dimensional Plug Flow Mass Transfer Equation with Convection, Interpeilet Axial Dispersion, and Second-Order Irreversible Chemical Kinetics"... 

It is only necessary to consider diffusional fiux across the lateral surface because axial diffusion is insignificant at high mass transfer Peclet numbers. The generalized quasi-macroscopic mass balance for one-dimensional fluid flow through a straight channel with arbitrary cross section and nonzero mass flux at the lateral boundaries is... 

Mass transfer rates attainable In menbrane separation devices, such as gas permeators or dlalyzers, can be limited by solute transport through the menbrane. The addition Into the menbrane of a mobile carrier species, which reacts rapidly and reversibly with the solute of Interest, can Increase the membrane s solute permeability and selectivity by carrier-facilitated transport. Mass separation is analyzed for the case of fully developed, one-dimensional, laminar flow of a Newtonian fluid in a parallel-plate separation device with reactive menbranes. The effect of the diffusion and reaction parameters on the separation is investigated. The advantage of using a carrier-facilitated membrane process is shown to depend on the wall Sherwood number, tfrien the wall Sherwood nunber Is below ten, the presence of a carrier-facilitated membrane system is desirable to Improve solute separation. 

In this paper, we analyze mass transfer in a parallel-plate mass exchanger with reactive membranes. We consider the case of fully developed, one-dimensional laminar flow between two membranes. Equilibrium carrier-facilitated transport of the solute takes place in the membrane phase. The effect of the diffusion and reaction parameters of the carrier-facilitated system on solute separation is Investigated. 

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