SOLVE program

Newell, A., Shaw, J. C., and Simon, H. A., Report on a general problem solving program. Proc. ICIP, 256 (1960). 

This, then, became the task of a small core of UCLA faculty to create an actual academic program which, by contrast with chance or the slowly accumulating scars of experience, would efficiently prepare people for the transition from the idealized, contemplative world of the university to the harsh and often political realities of environmental problem-solving. Program ideas were tested and the concept took on a recognizable structure. A program existed, even if in embryo form and only as a "bootstrap" operation, largely fueled by the after-hours effort of a number of the principals. 

The polynomial root-solving program POLRT was used in the examples below. It is from the IBM Scientific Subroutines. A listing of the source program is given in Table 10.1. POLRT is vyy fast, even on a personal computer. 

Calculate the equilibrium composition (component mole fractions) of the reactor contents. [Suggestion Express ATi and Ki in terms of the extents of the two reactions, ii and (See Section 4.6d.) Then use an equation-solving program or a trial-and-error procedure, such as the Newton-Raphson method (Appendix A.2), to solve for 1 and fe, and use the results to determine the equilibrium mole fractions.]... 

This equation can be solved using an equation-solving program or a spreadsheet. The solution is... 

If the third-order polynomial heat capacity formulas in Table B.2 are used to determine i( ad) for each product species. Equation 9.6-4 becomes a fourth-order polynomial equation. Solving this equation for Tad is easily accomplished with a spreadsheet or equation-solving program. The next example illustrates the procedure. 

For a single complex nonlinear equation of the form /(,t) = 0, use a spreadsheet or an equation-solving program. If you use a spreadsheet, put an estimated value of x in one cell and the formula for f(x) in a second cell, then use the goalseek tool to set the value in the second cell equal to zero by varying the value in the first cell. The final value in the first cell is the desired solution. 

For linear equations with > 3 or nonlinear equations with n a 2. use an equation-solving program. 

We thus have eight equations in eight unknowns. The equations may easily be entered into an equation-solving program and solved to obtain = 48.1, ni = 2.65, = 35.3, 4 = 14.0. /15 =... 

Examining the 10 equations, we see that two are nonlinear (Equations 7 and 8) and the remainder are linear. The full set of 10 simultaneous equations could be entered into an equation-solving program, or the following procedure involving no more than two simultaneous equations could... 

At this point we have 17 equations in 17 unknowns mo, mi, mo.me.mi, mg, m,t to mn, Ta, ft, ft, and the four mass fractions defined by Equations 7 through 10. The system of equations can be solved by an equation-solving program such as E-Z Solve. 

The flowchart for the absorber involves seven unknown variables (mo and rha- having been determined in Problem 12.5). Write the seven equations you would use to calculate those variables, notii that the amounts of chlorine and water in the head space are constant and so do not enter into steady-state material balances. Then solve the equations. Note Trial-and-error will be required as part of the solution. An equation-solving program or spreadsheet is a convenient tool for performing the required calculations.)... 

Computer programming is not covered explicitly, but problems that lend themselves to computer-aided solution are given after each chapter. An exceptionally robust and user-friendly equation-solving program (E-Z Solve) included on the Interactive Chemical Process Principles CD makes it possible for students to analyze relatively large processes without having to spend excessive time on algebraic and numerical calculations. 

D. R. Woods, Unit 1, Developing Awareness, the McMaster Problem Solving Program, Mc-Master University, Hamilton, Ont., Canada, 1985. 

Note that many of the problems in this chapter can be solved relatively easily with two programs. The first is CHEMEQ which makes the calculation of the chemical equilibrium constant at any temperature very easy. The second is an equation solving program, such as Mathcad, for solving the nonlinear algebraic equation(s) which result. It is advisable that students know how to use both. [I have used Mathcad for many of the problem solutions reported here.]... 

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