The Conservation Equations for Species

The conservation equation for species K, as given by equation (17), is readily seen to be identical with the corresponding relation in the kinetic... 

The conservation equation for species i can rhea be written in a form that explicitly recognizes transport by convection at the mass average velocity and by diffusive transport relative to the average veiociiy ... 

For a stationary control volume, the conservation equation for species is dC... 

The conservation equation for channel species is [R total] = [AR open ] -T [ARciosecj] + [R... 

The formulation of combustion dynamics can be constructed using the same approach as that employed in the previous work for state-feedback control with distributed actuators [1, 4]. In brief, the medium in the chamber is treated as a two-phase mixture. The gas phase contains inert species, reactants, and combustion products. The liquid phase is comprised of fuel and/or oxidizer droplets, and its unsteady behavior can be correctly modeled as a distribution of time-varying mass, momentum, and energy perturbations to the gas-phase flowfield. If the droplets are taken to be dispersed, the conservation equations for a two-phase mixture can be written in the following form, involving the mass-averaged properties of the flow ... 

Next, we treat the case of mass conservation of a species. The difference between the conservation of total mass and the conservation of the mass of a species is that other species may react to form the species under consideration. Hence, the reactions must be included. The conservation equation for a species k can be written as... 

The DNS model can be deployed subsequently on the liquid water blocked CL structure pertaining to a saturation level for the evaluation of the hindered oxygen transport. In brief, the DNS model is a top-down numerical approach based on a fine-scale CFD framework which solves point-wise accurate conservation equations for species and charge transport in the CL with appropriate source terms due to the oxygen reduction reaction (ORR) directly on the CL microstructures.25-27 67 The conservation equations for proton, oxygen and water vapor transport, respectively, are given by 25-27 68... 

The corresponding conservation equations are less familiar, but they contain the same information as a set of independent chemical reactions. The conservation equations for a system containing Ns species are given by... 

If concentration gradients are assumed negligible except in the direction normal to the material interface,the mass conservation equation for species i in a frame 7, attached to the lamellae, that translates and rotates with the flow is ... 

The conservation equations for continuous flow of species K will be derived by using the idea of a control volume r t) enclosed by its control surface o t) and lying wholly within a region occupied by the continuum here t denotes the time. In this appendix only, the notation of Cartesian tensors will be used. Let i = 1, 2, 3) denote the Cartesian coordinates of a point in space. In Cartesian tensor notation, the divergence theorem for any scalar function belonging to the Kth continuum a (x, t), becomes... 

Irrespective of these deviations, it is also possible from this transfer number approach to obtain some idea of the species profiles in the droplet burning case. It is best to establish the conditions for the nitrogen profile for this quasi-steady fuel droplet burning case in air first. The conservation equation for the inert i (nitrogen) in droplet burning is... 

Example 2.5 Diffusion in an Infinite Domain The conservation equation for dijfusion of species i in an infinite medium can be expressed as... 

It is often suitable to write the mass conservation equations in terms of mass fractions of species rather than molar concentrations, especially for flow processes, where properties of the fluid may vary with composition and temperatures. The mass conservation equation for species k can therefore be written (in vector symbolism) ... 

The describing equation for chemical reaction mass transfer is obtained by applying the conservation law for either mass or moles on a time rate basis to the contents of a batch reactor. It is best to work with moles rather than mass since the rate of reaction is most conveniently described in terms of molar concentrations. The describing equation for species A in a batch reactor takes the form... 

In Section 4.2.4, the governing equations of fluid mechanics for a turbulent flow are derived. Similarly, the governing equations for heat transfer and mass transfer can be derived from the principles of energy and mass conservation. In fact, the species conservation equation is an extension of the overall mass conservation (or the continuity) equation. For species i, it has the following form ... 

The conservation equation for the total receptor species is given as... 

The conservation equation for channel species is Rlolal] = [AR0pen] I ARc[oseci] T [Ropen] 3 [Rciosed]-... 

Dependence of Constitutive The conservation equation for receptor species is ... 

A wide range of physical models is available in most commercial CFD software. At a minimum, the flow field will be calculated by solving the conservation equations for mass and momentum. In addition to flow, many of the problems encountered in the process industry involve heat transfer also. For such applications, the temperature field can also be calculated, which is commonly done by solving a conservation equation for enthalpy. For problems involving chemical reaction, the transport equations for the chemical species involved in the reaction(s) will be solved. The creation and destruction of the species due to the reaction are modeled by means of source terms in these equations. The reaction rates determining these source terms are calculated locally, based on the values of species concentrations and temperature at each... 

The chief assumption made in the development presented previously was that the gas enviromnent is known and essentially constant throughout the reactor. This assumption simplified the treatment considerably, since an analysis based on the solid phase alone could be used to describe the bed behavior. Many practical systems using large-particle beds fluidized with a large excess of gas conform to this situation. If vigorously fluidized beds of fine particles are involved, however, the composition of the gas seen by the solid would vary. The previous simple analysis would then be inapplicable. In these instances, the conservation equations for the gas-phase species... 

We are going to consider, for simplicity, that only the diffusion of the species takes place (immobile electrolyte), using a high chemical rate constant (path II). Thus, the conservation equations, for Cr207 and Cr3+, are for a semi-infinite diffusion process on a planar electrode ... 

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