10.34, Numerical Methods Applied to Chemical Engineering
Professor William H. Green
Lecture #6: Modern Methods for Solving Nonlinear Equations.
1D-Problem
unknown: T of reactor
f(x) = 0
Q
rxn
exp(
-Ea
/
RT
) + h(T – T
a
) + c(T
4
– T
a
4
) = 0
heat of reaction
convection
radiation
(+)
(-)
(-)
Gain heat
Lose heat
Lose heat
f(
T
)
0
T
2 steady state temperatures
Make a plot with MATLAB
*netheat.m*
function qdot = netheat(T)
% computes the net heating rate of a reactor
% qdot = 0 at the steady state
qdot = Q.*exp(-Ea/(R.*T)) + h.*(T-Ta) + c.*(T.^4-Ta.^4);
Figure 2.
Professor Green modified variables Q and c until the plot looked like
the one above. Increased Q and decreased c.
To solve for steady state zeros
f(
T
) = 0
a
Æ
Å
b
Figure 1.
1D problem
Q = -2e-5;
Ea = 5000;
R = 1.987;
h = 3;
Ta = 300;
c = 1e-8;
Tvec = linspace(300,3000)
qdot = netheat(Tvec)
plot(Tvec,qdot)
Figure 3.
Have computer bracket in and find small
range where plot goes from negative to positive.
Cite as: William Green, Jr., course materials for 10.34 Numerical Methods Applied to Chemical
Engineering, Fall 2006. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of
Technology. Downloaded on [DD Month YYYY].

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