Threeq3

Name:	Threeq3 - Multiple steady states in a cooled exothermic CSTR
Source:	Shacham, M., N. Brauner, and M. B. Cutlip, Chem. Eng. Educ, 28(1), 30(1994)
Reference/s	Cutlip, M. B. and Shacham, M, Problem Solving in Chemical
	Engineering with Numerical Methods, Prentice Hall Inc., 1999
Model:	3 implicit equations, indep. variables Ca, T, Tj
	Lower difficulty level
	Constraints: Ca>0
	Discontinuities: Undefined for T=0
	Initial estimates: 1. t=100, x1=0.2, x2=0.8, 2. t=70, x1=0.5, x2=0.5;
	3. t=80, x1=0.2, x2=0.8 4. t=80, x1=0.5, x2=0.5
Solved by	Shacham, M., POLYMATH 5.1, build 19, April 4, 2001
Model Eqs.	Multiple steady states in a cooled exothermic CSTR |POLVER05_1
EXCEL FILE	f(T)=F*(T0-T)/V+30000*k*Ca/rhocp-U*A*(T-Tj)/(rhocp*V) #
TEXT FILE	f(Ca) =F*(Ca0-Ca)/V-k*Ca #
POLYMATH FILE	f(Tj)=Fj*(Tj0-Tj)/3.85+U*A*(T-Tj)/(62.3*1.0*3.85) #
	k=7.08e10*exp(-30000/1.9872/T) #
	rhocp=50*0.75 #
	F=40 #
	T0=530 #
	V=48 #
	U=150 #
	A=250 #
	Ca0=0.55 #
	Fj=49.9 #
	Tj0=530 #
	T(0)=600
	Ca(0)=0.1
	Tj(0)=600
Variable/function values	Variable	Value	f(x)
	T	600	8.6284E+00
	Ca	0.1	2.9130E-01
	Tj	600	-9.0727E+02
	k	0.8370
	rhocp	37.5
	F	40.00
	T0	530.00
	V	48
	U	150
	A	250.00
	Ca0	0.55
	Fj	49.90
	Tj0	530.00
Solution 1	Variable	Value	f(x)
	T	671.27832050250	-5.4001E-13
	Ca	0.0354195308679	-1.0547E-15
	Tj	660.46287831030	1.1369E-11
	k	12.1067966487100
Solution 2	Variable	Value	f(x)
	T	590.34979512380	-1.1653E-12
	Ca	0.3301868979161	-1.3878E-16
	Tj	585.72976766210	1.0118E-11
	k	0.5547693934132
Solution 3	Variable	Value	f(x)
	T	537.85475413080	9.8055E-13
	Ca	0.5213904932394	7.6328E-17
	Tj	537.25344007970	-7.6597E-12
	k	0.0457262952489