Assignment # 7:
Advanced Maple
CENG303
No due date, but must be completed before the last session of your 303 group
Reading Assignment
Chapter 4 : Advanced Maple Topics: 4.1 and 4.2
4.1 Saving and
Including User Written Programs
4.2 Solving
Ordinary Differential Equations
4.4 Use of
Maple to Find Laplace Transforms
4.5 Using
Maple to Transform ODEs
Laboratory Problems
These problems may be completed with help from any user on Owlnet. You may not
copy anyone else's work, but you can get other users to give you suggestions
and point out mistakes that should be corrected.
1) Develop a Maple program or a session in Maple so that you can plot multiple curves on the same plot. Each curve would be specified by two vectors of data giving the independent and the dependent variables. Thus the set of points on the X-axis might vary from one curve to the next.
Use your program or procedure to plot the vapor pressures of water and
ethanol vs temperature.
The water data is stored in the vectors twater and pwater. The
ethanol data is stored in the vectors teth and peth. All four
will be set if you execute the function vapr in MATLAB.
Make sure that your labels on the axes reflect the meaning of this data and the
title describes the curves produced. In this case the temperatures are given in
oC and the pressures are in atmospheres.
2) Use Maple to solve the problem in Felder and Rousseau described in Example
11.3-1.
3) The formula to model radial temperature gradients
in an annular reactor (hollow cylinder reactor) is:
where
r is the cylinder radius, T is the temperature, keff is the
effective thermal conductivity, and Sc is the volume rate of thermal
energy production by the chemical reaction. First convert the variables in the equation
above to the following dimensionless quantities:
and 
using
the dchange function. Next use the
function dsolve to solve the differential equation that comes out. Use the following boundary conditions:
and 
(Note:
Use “D” notation when evaluating the second boundary condition).
Test Problems
You may work these problems with help ONLY from the course instructor and/or
your TA.
1) This problem will look at using Maple for fitting a curve through the experimental vapor pressure data introduced in Lab Problem 1. The MATLAB functions: polyval and polyfit do this job in MATLAB. Fit both a straight line and a quadratic though the water data. Plot both the original data and the data that would be given by the polynomial fit. Then try the same thing but with the natural log of the vapor pressures instead of the vapor pressures. Which fit looks most promising? For the approximation that appears best, repeat with the ethanol data.
2) Use Maple to solve the problem described in Felder and Rousseau as Example 11.3-2.
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Project by: Scott Esterholm and Mark Pond
CENG 402
2005