Software packages Polymath

Instructions on how to use the different software packages (POLYMATH, MATLAB, and ASPEN PLUS) to solve examples. 

It is evident that for case 1 we need an arithmetic solution, and a software package like Polymath can be used. The rest of the cases have analytic solutions. 

Throughout this book, we have seen that when more than one species is involved in a process or when energy balances are required, several balance equations must be derived and solved simultaneously. For steady-state systems the equations are algebraic, but when the systems are transient, simultaneous differential equations must be solved. For the simplest systems, analytical solutions may be obtained by hand, but more commonly numerical solutions are required. Software packages that solve general systems of ordinary differential equations— such as Mathematica , Maple , Matlab , TK-Solver , Polymath , and EZ-Solve —are readily obtained for most computers. Other software packages have been designed specifically to simulate transient chemical processes. Some of these dynamic process simulators run in conjunction with the steady-state flowsheet simulators mentioned in Chapter 10 (e.g.. SPEEDUP, which runs with Aspen Plus, and a dynamic component of HYSYS ) and so have access to physical property databases and thermodynamic correlations. 

POLYMATH was chosen as the software package to solve this problem. The data in Table E5-6.1 were typed into the system. The following copies of the computer screens illustrate the procedure,... 

Equations (E3-9.8) and (E3-9.9) can now be solved numerically, preferably by a software package such as POLYMATH or MATLAB. (See Chapter 4)... 

A large number of ordinary differential equation solver software packages (i.e., ODE solvers) which are extremely user friendly have become available. We shall use POLYMATH S to solve the examples in the printed text. However, the CD-ROM contains an example that uses ASPEN, as well as all the MATLAB and POLYMATH solution programs to the example programs. With POLYMATH one simply enters Equations (E4-7.3) and (E4-7.4) and the corresponding parameter value into the computer Table E4-7.1) with the initial (rather, boundary) conditions and they are solved and displayed as shown in Figure E4-7.1,... 

In complex reaction systems consisting of combinations of parallel and series reactions the availability of software packages (ODE solvers) makes it much easier to solve problems using moles Nj or molar flow rates Fj rather than conversion. For liquid systems, concentration may be the preferred variable used in, the mole balance equations. The resulting coupled differential equations can be easily solved using an ODE solver. In fact, tltis section has been developed to take advantage of the vast number of computational techniques now available on mainframe (e.g., Simulsolv) and personal computers (POLYMATH). 

P2-13 Using POLYMATH, MatLab, Mathmatica, or some other software package, first fit the -ta versus X to a polynominal (i.e., = flo... 

A software package (e.g., POLYMATH) was also used to combine Equations (E9-1.3), (E9-1.4), and (E9-1.6) to determine conversion and temperature as a function of time. Table E9-1.2 shows the program, and Figures E9-1.1 and E9-1.2 show the solution results. 

P9-2a Review the example problems in this chapter, choose one, and use a software package such as POLYMATH or MATLAB to carry out a parameter sensitivity analysis. 

A number of scliools use MATLAB as their basic software package. The disadvantage of the MATLAB ODE solver is that it is not particularly user friendly when trying to determine the variation of secondary parameter values. MATLAB will be used for the same four types of programs as POLYMATH. 

We will use the Polymath software package to express concentration as a funciic of time. Here we first choose the polynomial degree (in this ease, fourth degree) an then type in the values of at various limes t to obtain... 

An alternate computer solution would be to regress versus t with a software package such as Polymath. 

See R. M. Felder. Chem. Eng. Educ.. /d (4 k 176 (1085). The August 1985 issue of Chemicai Engineering Progress may be useful for pan Ick P9 2, Review the example problems in this chapter, choose one, and u,se a software package such as Polymath or MATLAB to carry out a parameter sensitivity analysis. 

Polymath 5.1 and a special version of FEMLAB are the software packages included with this book, along with extensive tutorials using screen shots. 

Polymath is the primary software package used in this textbook. Polymath is an easy-to-use numerical computation package that allows students and professionals to use personal computers to solve the following types of problems ... 

Instructions are included on how to use not only the software package. of Polymath. MATLAB, and FEML. B. but also on how to apply ASPEN PLUS to solve CRE problems. Tutorials with detailed screen shots are provided for Polymath and FEMLAB. 

This SCI or differcnnaJ cquadoris can be soWed mang POLYMATH or a similar software package. 

This sei of differcniial equations can be solved using POLYMATH or a simitar software package-... 

There are some software packages (i.e. ODE solvers, regression etc.) available to solve problems from reaction engineering and other areas. POLYMATH is a extremely user-friendly software package which makes modeling easy for the education of chemical engineers and chemists. POLYMATH is used to numerically solve... 

However, we will see in the next chapter there is a much, much better way to solve for the catalysis weight. W, by using numerical software packages. For example, we would couple Equation E4-4.6) with Equation (2-17) and use an ordinary differential equation (ODE) solver, such as Polymath to find the conversion X as a function of catalyst weight W... 

The differential and integral methods are used primarily in analyzing batch reactor data. Because a number of software packages (e.g.. Polymath, MATLAB) are now available to analyze data, a rather extensive discussion of nonlinear regression is included. 

Polymath was chosen as the software package to solve this problem. The data in Table ElO-3.1 were typed into the system. A screen-shot by screen-shot. set of instmetions on how to carry out the regression is given in the DVD-ROMAVeb Sutn-mary Notes for Chapter 7. After entering the data and following the step-by-step procedures, the results shown in Table El0-3.2 were obtained. 

The software packages used lo solve CRE problems in the lext and on ihe DVD-ROM are Polymath. AspenTech and COM SOL. 

Polymath is an easy-to-use numerical computation package that allows students and professional.s to use personal computers to solve realistic, computationally intensive chemical reaction engineering problems. Polymath is unique in that the problems are entered just like their mathematical equations, and there is a minimal learning curve. The Polymath software package i.s uniquely suited for chemical reaction engineering as it is able lo. solve the following iype.s of problems that arise in CRE ... 

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