Mathematics taught in chemical engineering. What material should be covered?

1

Mathematics taught in chemical engineering. What material should be covered?

Benito Serrano, Juan José Mejía, Víctor Javier Cruz, Alfonso Talavera, Jesús Moreira.

UNIVERSIDAD AUTONOMA DE ZACATECAS, MEXICO

The AICHE-2008-Philadelphia PA 2

Survey about the contents.

To pass the self seminars. To solve ¨complicated problems¨Is this a risky task?A survey was performed.Several universities of MexicoSeveral universities of USAOne university in Canada.


Common courses and topics.

Differential and integral calculus, with one or several variables,

Linear algebraVectorial calculusStatistics and probabilityDifferential equations of first, second

and n-th order, linear, with constant coefficients, homogeneous and non homogeneous.


Differences among the programs

Differential equations with variable coefficients,

Series of powersSystems of differential equations of

first order.Partial differential equations solved

with the method of variable separations.

This is a non definite frontier.


Basic Area.Basic Professional Area.Professional Area.Complementary Area.

Structure of the Chem. Eng. Programs.


Focuses

mathematical rigorRecipes. The collected documents did not show

the focus.Math in Chem. Eng. Taught by

Mathematicians?, Physics by Physicians?

Is it correct to teach Math just as Formulas?


Math in Chem. Eng.

A combination between the rigor and formulas.

The basic professional and main nucleus of subjects dictate the level of math.

Analytical capacity because good formation in mathematics.

Math is the osseous skeleton of science.


Graduate Courses in Math.

Matrices and eigen - values.Construction of mathematical models.Partial differential equations.Methods of discrete the equations.Numerical methods.Mathematical tools need for the thesis.


Graduate and Undergraduate Courses.

The border is not clear and defined.Common courses: Ordinary diff. eqs. with

variable coefficients, systems of equations, partial differential equations, etc.


Type of problems.

Undergraduate: Convection + Chemical Reaction: Ordinary Differential Equations.

Graduate: Diffusion + convection + chemical reaction: Partial differential equations.

It is necessary to delimit the contents and focus of all the subjects in Chem. Eng.

Certifying institutions request a number of courses and hours.

Math provides a solid basis for graduate studies.


Special Undergraduate Course.

For those undergraduate students interested in learning more about applied math.

Special and optional course.Title: Applied Mathematics in Selected

Topics.General Objective: To encourage the

students to pursue graduated studies.


Contents of the Course.

A model of laminar flow through a lubricated tube.

Slow flow over a solid sphere.Transient flow inside a cylindrical tube.No stationary heat conduction in a bar.Potential flow on a cylindrical tube.Multiple steady states of chemical

reactors.


Transient Flow Equations.

r

ur

rrz

P

t

u zz 1

Rruz at 0 0,0 ratdr

duz

00 tatuzUsing the following dimensionless variables:

2max

R

t

u

u

R

rs

z

z


Transient Flow 1

ss

ss1

1at 0 s 0 along 0

ss

0 s-1- 2 Variable separation

STTsSs ,


Transient Flow Equations 2.

Td

dT 2

01 2

2

Sds

dS

sds

Sd

AeT t 2

sYcsJcsS 0201

0

2

20 2!

1

n

nnx

nxJ .....

23046441

642

xxx 100 J


Transient Equations 3

0,!2

12

ln2 2

1

2222

12

0

22

0

ssm

HsJssY

m

m

mm

m

21,0 s

1

02 11

nmm SJBs

1

1

0 00

n

mmm sdssJsJB

mmm

JB

14

8

1

2

130 exp8

nn

nn

n

J

sJ


Results.


Conclusions.

The undergraduate students in chemical engineering have a big potential, if they are motivated.

Special course to interests students.Equilibrium between formulas and

mathematical rigor.Border between undergraduate and

graduate courses should be indicated by the objectives of the career.

Dominion of mathematics prepare graduate students.


Documents

Mathematics taught in chemical engineering. What material should be covered?