(668b) The Role Of Smartphones and Tablets In Numerical Problem Solving
- Conference: AIChE Annual Meeting
- Year: 2013
- Proceeding: 2013 AIChE Annual Meeting
- Group: Education Division
- Session:
- Time: Thursday, November 7, 2013 - 12:51pm-1:12pm
Numerical problem
solving has been introduced into the Chemical Engineering education and practice
in the early nineteen sixties (Shacham et al. 1996). At that time Fortran or
other source code programming languages were used to implement the numerical
solution algorithms on "mainframe" computers. Starting in the mid
nineteen eighties the emphasis shifted to the use of general purpose mathematical
software packages, such as MAPLE, MATHCAD, MATLAB, Mathematica and Polymath for
numerical problem solving using the PC. PC based mathematical software packages
are routinely used, nowadays, for numerical problem solving in engineering
education and practice (Cutlip et al., 1998, Shacham and Cutlip, 1999) as they
are easy to use and provide the most time efficient route for obtaining
accurate solutions.
The dominant
position of the PC in the computing field has been challenged lately by the
mobile devices such as smartphones and tablets. Furthermore, it is predicted
that by 2017 the dominant operating system for all computing devices will be
Google's Android (Wingfield, 2013). Relying on these trends and predictions we
decided to check the possibility of the use of Android based smartphones and
tablets for numerical problem solving in chemical engineering. For this aim, we
have developed the PolyMathLite application, a slightly simplified version of
the Polymath software package (Polymath is a trademark of Polymath Software http://www.polymath-software.com ).
PolyMathLite solves systems of linear and nonlinear (NLE) algebraic equations,
systems of ordinary differential equations (ODE) and carries out polynomial,
multiple linear and nonlinear regression of data.
PolyMathLite was
evaluated on both Android smartphones and tablets using the set of test
problems listed in Table 1. Ten out of the eighteen problems are described in detail
by Cutlip et al. (1998). These ten problems were solved by a group of educators
on PC using the mathematical software packages Maple, Mathematica, MATLAB,
MathCAD, Polymath and Excel. A comparison of the performance of the various
packages in solving the set of 10 problems was reported by Shacham and Cutlip
(1999). Six additional problems are described in the textbook of Cutlip and Shacham
(2008). Sample problem 17 is from an NLE test problem library (Shacham et al., 2002)
while problem 14 is described in the reference: Shacham et al., 2009.
The test problems
used represent a great variety with respect to the complexity of the
mathematical model, the level of difficulty of the numerical solution and the
associated ChE course. The various problems are applicable to required courses,
such as: introduction to Ch. E., thermodynamics, fluid dynamics, heat transfer,
mass transfer, separation processes, reaction engineering, process dynamics and
control; and to the elective courses: mathematical methods, biotechnology and
optimization. The simplest problems consist of a single NLE (Problems 2 and 4),
while the most complex consist of 12 NLEs (Problem 18) and 9 ODEs. Some of the
problems pose special challenges to the solution algorithms. In Prob. 11 a
differential-algebraic system (DAE) need to be solved, in Prob. 12 a partial
differential equation (PDE) is solved using the method of lines, and multiple
linear regression of the data in Prob. 14 with a model that includes a free
parameter yields an ill conditioned regression model while removing the free
parameter provides a statistically valid model. Problems 10 and 13 require
special stiff integration algorithms to find the correct solution. Problems 17
and 18 represent special challenges to the NLE solver algorithms as the values
of some of the variables (mole fractions) are very close to zero at the
solution, however these variables are not allowed to obtain negative values
during the solution process as their logarithm or square root needs to be
computed.
In spite of the
special challenges in terms of the problem size and algorithmic requirements,
the solutions obtained using PolyMathLight on smartphones and tablets matched
the solution obtained by Polymath 6.1 up to seven significant digits for all
the problems included in the test problem set. The solutions were obtained in a
very short time, even for the large scale, complex problems. On the negative
side, the problem input via the touch screen has proven to be very cumbersome
and time consuming.
In the extended
abstract and the presentation the testing of PolyMathLite will be described in
more detail and the potential effects of the availability of numerical problem
solving tools for smartphones and tablets on the CHE education and practice
will be discussed.
References
1.
Cutlip, M., Hwalek, J.J., Nuttall, H.E., Shacham, M.,
Brule, J., Widman, J., Han, T., Finlayson, B., Rosen, E. M. and Taylor, R., ?A
Collection of Ten Numerical Problems in Chemical Engineering Solved by Various
Mathematical Software Packages.? Comput. Appl. Eng. Educ., 6(3),
169-180(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.
Shacham, M., M. B. Cutlip, and N. Brauner, "General
Purpose Software for Equation Solving and Modeling of Data", pp. 73-84 in
Carnahan, B. (Ed), ?Computers in Chemical Engineering Education?, CACHE
Corporation, Austin, TX, 1996.
4.
Shacham, M. and M.B. Cutlip, ?A Comparison of Six
Numerical Software Packages for Educational Use in the Chemical Engineering
Curriculum?, Computers in Education Journal, IX(3), 9-15 (1999)
5.
Shacham, M., N. Brauner and M. B. Cutlip, ?A Web-based
Library for Testing Performance of Numerical Software for Solving Nonlinear
Algebraic Equations?, Computers chem. Engng. 26(4-5), 547-554(2002)
6.
Shacham, M., Cutlip, M. B. and Elly, M., "Live
Problem Solving via Computer in the Classroom to Avoid "Death by
PowerPoint"", Computer Applications in Engineering Education Vol 17,
No. 3, 285-294(2009)
7.
Wingfield, N., "PC Sales Still in a Slump, Despite
New Offerings", The New York Times, April 10, 2013.
Table
1. List of Sample/Test Problems for PolyMathLite
No. |
COURSE |
PROBLEM TITLE |
MATHEMATICAL MODEL |
1 |
Introduction to Ch. E. |
Steady State Material Balances on a Separation Train |
Simultaneous Linear Equations^{1} |
2 |
Introduction to Ch. E. and Thermodynamics |
Molar Volume and Compressibility Factor from Van Der Waals Equation |
Single NLE^{1} |
3 |
Thermodynamics and Separation Processes |
Three Phase Equilibrium - Bubble Point |
NLE System^{2} |
4 |
Fluid Dynamics |
Terminal Velocity of Falling Particles |
Single NLE^{1} |
5 |
Thermodynamics and Reaction Engineering |
Reaction Equilibrium for Multiple Gas Phase Reactions |
NLE System^{1} |
6 |
Mathematical Methods |
Vapor Pressure Data Representation by a Polynomial and Equations |
Polynomial Fitting, Linear and Nonlinear Regression^{1} |
7 |
Heat Transfer |
Unsteady State Heat Exchange in a Series of Agitated Tanks |
ODE's with known initial conditions^{1}. |
8 |
Mass Transfer & Reaction Engineering |
Diffusion with Chemical Reaction in a One Dimensional Slab |
ODE's with split boundary conditions^{1}. |
9 |
Reaction Engineering |
Reversible, Exothermic, Gas Phase Reaction in a Catalytic Reactor |
ODE System^{1} |
10 |
Process Dynamics and Control |
Dynamics of a Heated Tank with PI Temperature Control |
Stiff ODE System^{1} |
11 |
Separation Processes |
Binary Batch Distillation |
Differential-Algebraic System^{1} |
12 |
Heat Transfer |
Unsteady state Heat Conduction in a Slab |
Partial Differential equations^{2} |
13 |
Reaction Engineering |
Rate Data Analysis for a Catalytic Reforming Reaction |
Nonlinear Regression^{2} |
14 |
Mathematical Methods |
Regression of Heat of Hardening Data of Cement |
Multiple Linear Regression^{3} |
15 |
Biotechnology |
Stoichiometric Calculations for Biological Reactors |
Simultaneous Linear Equations^{2} |
16 |
Biotechnology, Reaction Engineering and Mathematical Methods |
Biological Reaction in a Batch Reactor |
Stiff ODE System^{2} |
17 |
Reaction Engineering and Mathematical Methods |
Combustion of Propane in Air |
NLE system where some variables must be positive^{4} |
18 |
Reaction Engineering and Optimization |
Complex Chemical Equilibrium |
NLE system where some variables must be positive^{2} |
^{1}Reference: Cutlip et al., 1998
^{2}Reference: Cutlip and Shacham, 2008
^{3}Reference: Shacham et al., 2009
^{4}Reference: Shacham et al., 2002
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