Use of Software Packages to Determine the Model Parameters

Substituting in terms of a, (3, and X, we arrive at two coupled differential equations deseribing the imsteady behavior of the traeer that must be solved simultaneously. 

Analytical solutions to Equations (14-60) and (14-61) are given in the CD-ROM. However, for more complicated systems, analytical solutions may not be possible to evaluate the system parameter. 

By an appropriate semilog plot of Cn/Cpo vs. time, one can evaluate the model parameters a and (3. 

First we will use POLYMATH to fit the RTD to a polynomial. Because of the steepness of the curve, we shall use two polynomials. For t s 80 min, 

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Use of Software Packages to Determine the Model Parameters 988 Other Models of Nonideal Reactors Using CSTRs and PFRs 990... 

In the examples in Sections 7.1 and 7.2.1, explicit analytical expressions for rate laws are obtained from proposed mechanisms (except branched-chain mechanisms), with the aid of the SSH applied to reactive intermediates. In a particular case, a rate law obtained in this way can be used, if the Arrhenius parameters are known, to simulate or model the reaction in a specified reactor context. For example, it can be used to determine the concentration-(residence) time profiles for the various species in a BR or PFR, and hence the product distribution. It may be necessary to use a computer-implemented numerical procedure for integration of the resulting differential equations. The software package E-Z Solve can be used for this purpose. 

In the Lagrangian frame, droplet trajectories in the spray may be calculated using Thomas 2-D equations of motion for a sphere 5791 or the simplified forms)154 1561 The gas velocity distribution in the spray can be determined by either numerical modeling or direct experimental measurements. Using the uncoupled solution approach, many CFD software packages or Navier-Stokes solvers can be used to calculate the gas velocity distribution for various process parameters and atomizer geometries/configurations. On the other hand, somesimple expressions for the gas velocity distribution can be derived from... 

The NURBS tools (curves and surfaces) are commonly used in computer-aided design (CAD) and also foimd in various 3D modeling and animation software packages. They allow representation of geometrical shapes in a compact form. NURBS surfaces are functions of two parameters mapping to a surface in three-dimensional space. The shape of the surface is determined by control points. 

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