(510f) Using Templates for Demonstrating Good Programming Practices

       Computer based numerical problem solving
(CBNPS) is one of the most widespread application of the computers in chemical
engineering education and practice (Shacham et al. 2009). Mathematical software
packages such as Excel®, MAPLE?, MATHCAD®, MATLAB®, Mathematica®, and POLYMATH? are currently used routinely for numerical
problem solving in engineering education. In order to familiarize engineering
educators with the most widely used packages Cutlip et al. 1999 assembled a set
of ten benchmark problems that are  characteristic of various core courses in the
chemical engineering curriculum. The solutions of this problem set, using the
various packages were presented in the ASEE Summer School of for Chemical
Engineering Faculty which was held in Snowbird, UT in August of 1997. Shacham
and Cutlip, 1999 carried out a comparison of the various software packages
using the benchmark problems. The comparison was based on numerical
performance, user friendliness and the guidance provided by the program for
preparation and documentation of the model and the results, and alteration of
the model for parametric studies. Based on the result of this and additional
studies (Cutlip et al. 2009), it has been concluded that packages that do not
require programming (such as Polymath) can be preferable with respect to user
friendliness and the guidance provided by the program for preparation and
documentation of the model and the results, however they are usually limited to
solution of Single Model-Single Algorithm (SMSA) problems. The use of packages that require programming (such
as MATLAB) is essential for solving more complex problems with some combination
of Multiple Models and Multiple Algorithms (MMMA).

       In order to provide the required guidance
for preparation and documentation of the model and the results when using
packages that require programming, we prepared
templates that guide the user in these aspects. The templates are implemented
using MATLAB. So far templates have been prepared for solving systems of
nonlinear algebraic equations, systems of ordinary differential equations (ODE),
and polynomial, multiple linear and nonlinear regression. The template requires
input of the model, variable names, values and units in a standard  format and display a standard format results
report.

       The principles that followed while
displaying the results are: 1. Display each result the first time it becomes
available in order to help debugging the problem., 2. Display full information
(variable name, value and units) for all the variables, 3. Display also
information that is not immediately needed, but may be required in the future, and 4. Try to
minimize repeated display of the same information.

       For demonstration of the typical contents
of the standard report that follows these principles, let us consider a problem
of ?Simultaneous Multicomponent Diffusion of Gases? (problem 10.8 in Cutlip and
Shacham, 2008). This problem includes three ODEs for computation of the
concentration of various components: C_A, C_B
and C_C, three explicit equations for calculating mole
fractions of the components x_A, x_B and x_C,
six constants representing the molar fluxes, N_A, N_B
and N_C, and the molecular diffusivities,  D_AB, D_BC
and D_AC, of the various components.

       . The constant and initial variable
values (including variable names and units) are displayed in Table 1. This
information is displayed before the solution of the problem starts in order to
help with the debugging of the problem.          In Table
2, part of the tabular results, obtained after
the integration has been completed, are shown. In the ?Results Summary Table?
the names, units, minimal, maximal and final values of the state, and explicit
variables are displayed. The ?Complete Tabular Results? section contains separate
tables of the concentrations and the explicit variable values vs. the
independent variable according to the number of reporting points requested by
the user (only part of this table is displayed).  Observe that the column heading contain
variable names and units. A plot of the dependent variables (C_A,
C_B and C_C in this case) vs. the independent
variable (z) is also presented (Figure 1).

       We believe that the templates we have
developed enable better training of the engineers in the aspects of programming
that are the most important for them, namely, the preparation and debugging of
the model of the problem in hand and presentation of precise,  accurate and complete information regarding
the computational results.

       The complete set of templates and the associated
explanations and examples are available at ftp://ftp.bgu.ac.il/shacham/templates.
Our intention is to develop MATLAB templates for advanced numerical problem
solving, including solution of ODE boundary value problems, differential-algebraic
system of Equations (DAE), partial differential equations (PDE), parameter estimation
in dynamic systems and linear and nonlinear programming

       In the extended abstract and the
presentation the complete set of templates that we have developed will be
described in more detail and their use in ChE education
will be discussed.

References

1.    
Cutlip, M., J.J. Hwalek,
H.E. Nuttall, M. Shacham, J. Brule, J. Widman, T. Han, B. Finlayson, E.M.
Rosen, and R. Taylor, ?A Collection of 10 Numerical Problems in Chemical
Engineering Solved by Various Mathematical Software Packages,? Computer
Applications in Engineering Education, 6, 169 (1998)

2.    
Cutlip, M. B. and Shacham, M.  Problem Solving In Chemical and
Biochemical Engineering with Polymath, Excel and MATLAB. Prentice-Hall,
Upper Saddle River, New-Jersey, 2008.

3.    
Cutlip, M. B.,  Brauner, N. and M. Shacham, " Biokinetic Modeling of Imperfect Mixing in a Chemostat ? an Example of Multiscale
Modeling", Chemical Engineering Education , Vol. 43. No. 3, 243-248
(2009)

4.    
Shacham, M. and M. B. Cutlip,
?Selecting the Appropriate Numerical Software for a Chemical Engineering
Course?, Computers chem. Engng., 23(suppl.),
S645-S649(1999)

5.    
Shacham, M., Cutlip, M. B. and N.
Brauner, "From Numerical Problem Solving to Model Based Experimentation ? Incorporationg Computer Based Tools of Various Scales into
the ChE Curriculum", Chemical Engineering
Education, Vol. 43. No. 4, 315- 321 (2009)

Table
1.  Display of the initial values for the
example problem

Figure
1.  Plot of the dependent variables vs.
the independent variable  for the example
problem

Table
2.  Display of the solution for the
example problem