Page 220 - Numerical methods for chemical engineering

206 4 Initial value problems

1

ϕ A

2

1 2 1 1 1 1 1 1 2
a
2
1
1
θ
1
12

1
1 2 1 1 1 1 1 1 2
a
Figure 4.17 Nonisothermal CSTR behavior for γ = 1(β =−1,χ = 0,θ c = 1).

1

ϕ A

2

1 2 1 1 1 1 1 1 2
a
2
1
1
θ
1
12
1
1 2 1 1 1 1 1 1 2
a
Figure 4.18 Nonisothermal CSTR behavior for γ = 5(β =−1,χ = 0,θ c = 1).

to decrease Da, we would reach another turning point at which the system jumps back to
the low-temperature steady state (extinction). For Da values between the turning points, the
system has three steady states, but only the upper and lower ones are stable. Clearly, it is best
to design the system to operate safely away from this region of rapid, difficult-to-control,
transitions.