灵鹊做题网谁能用matlab帮我解个微分方程组啊?我是新手啊!
来源：学生作业帮 编辑：灵鹊做题网作业帮 分类：综合作业 时间：2024/05/15 12:33:45
谁能用matlab帮我解个微分方程组啊?我是新手啊!
d(XA)/d(Z)=RA/(G*WAO/MA)
d(T)/d(Z)=(RA*(-DHR)-4*U*(T-TC)/dt)/(G*CPT)
RA=C1*C2*C3*KE*((PE-PS*PH/KP)+PE*(KT+KB))/(1+LEME*PE+LEMS*PS)^2*ROU
其中：Z范围[0,40] XA初值=0,T初值=793.15K
PE=34.1952*(1-XA)/(356.452+37.477*XA)*P
PS=(31.801*XA+0.0208)/(356.452+37.477*XA)*P
PH=38.982*XA/(356.452+37.477*XA)*P
KE=5.7e8*exp(-34420/(R*T))
KT=1.3e3*exp(-18880/(R*T))
KB=9.1e7*exp(-38190/(R*T))
KP=exp(16.12-15350/T)
LEME=3.6e-3*exp(-40780/(R*T))
LEMS=1.5e-3*exp(-16430/(R*T))
C1=((3624.641-61.549*XA)/2265.401*(1-XA)/2.45)^0.25
C2=0.247
C3=0.95
R=1.987
G=9430.217/(250*3.14159/4*0.123^2)
WAO=0.3884
ROU=1100
MA=106
CPT=2.22
U=20.02
TC=923.15
DHR=30850
P=0.155/0.101325
dt=0.123
关键是要解100组啊!
d(XA)/d(Z)=RA/(G*WAO/MA)
d(T)/d(Z)=(RA*(-DHR)-4*U*(T-TC)/dt)/(G*CPT)
RA=C1*C2*C3*KE*((PE-PS*PH/KP)+PE*(KT+KB))/(1+LEME*PE+LEMS*PS)^2*ROU
其中：Z范围[0,40] XA初值=0,T初值=793.15K
PE=34.1952*(1-XA)/(356.452+37.477*XA)*P
PS=(31.801*XA+0.0208)/(356.452+37.477*XA)*P
PH=38.982*XA/(356.452+37.477*XA)*P
KE=5.7e8*exp(-34420/(R*T))
KT=1.3e3*exp(-18880/(R*T))
KB=9.1e7*exp(-38190/(R*T))
KP=exp(16.12-15350/T)
LEME=3.6e-3*exp(-40780/(R*T))
LEMS=1.5e-3*exp(-16430/(R*T))
C1=((3624.641-61.549*XA)/2265.401*(1-XA)/2.45)^0.25
C2=0.247
C3=0.95
R=1.987
G=9430.217/(250*3.14159/4*0.123^2)
WAO=0.3884
ROU=1100
MA=106
CPT=2.22
U=20.02
TC=923.15
DHR=30850
P=0.155/0.101325
dt=0.123
关键是要解100组啊!
终于完成了.
function hahha
%global XA T G WAO MA DHR U TC dt G CPT RA
syms XA T
C2=0.247
C3=0.95
R=1.987
G=9430.217/(250*3.14159/4*0.123^2)
WAO=0.3884
ROU=1100
MA=106
CPT=2.22
U=20.02
TC=923.15
DHR=30850
P=0.155/0.101325
dt=0.123
PE=34.1952*(1-XA)/(356.452+37.477*XA)*P
PS=(31.801*XA+0.0208)/(356.452+37.477*XA)*P
PH=38.982*XA/(356.452+37.477*XA)*P
KE=5.7e8*exp(-34420/(R*T))
KT=1.3e3*exp(-18880/(R*T))
KB=9.1e7*exp(-38190/(R*T))
KP=exp(16.12-15350/T)
LEME=3.6e-3*exp(-40780/(R*T))
LEMS=1.5e-3*exp(-16430/(R*T))
C1=((3624.641-61.549*XA)/2265.401*(1-XA)/2.45)^0.25
RA=C1*C2*C3*KE*((PE-PS*PH/KP)+PE*(KT+KB))/(1+LEME*PE+LEMS*PS)^2*ROU
dXAdZ=RA/(G*WAO/MA)
dTdZ=(RA*(-DHR)-4*U*(T-TC)/dt)/(G*CPT)
[Z,XA_T] = ODE45(@myfun,[0:40],[0,793.15])
plotyy(Z,XA_T(:,1),Z,XA_T(:,2))
function dy=myfun(t,x)
%global XA T G WAO MA DHR U TC dt G CPT RA
XA=x(1);T=x(2);
dXAdZ =82824321519584909721600000/320864126079765233*20^(1/4)*49^(3/4)*((7970669852027257/4981669482150756-4229615073624064/155677171317211125*XA)*(1-XA))^(1/4)*exp(-34420000/1987/T)*(6200/4053*(21372/625-21372/625*XA)/(89113/250+37477/1000*XA)-499489360/5475603*(31801/1000*XA+13/625)/(89113/250+37477/1000*XA)^2*XA/exp(403/25-15350/T)+6200/4053*(21372/625-21372/625*XA)/(89113/250+37477/1000*XA)*(1300*exp(-18880000/1987/T)+91000000*exp(-38190000/1987/T)))/(1+186/33775*exp(-40780000/1987/T)*(21372/625-21372/625*XA)/(89113/250+37477/1000*XA)+31/13510*exp(-16430000/1987/T)*(31801/1000*XA+13/625)/(89113/250+37477/1000*XA))^2;
dTdZ =-998097780812185337856000000/75938290652647843*20^(1/4)*49^(3/4)*((7970669852027257/4981669482150756-4229615073624064/155677171317211125*XA)*(1-XA))^(1/4)*exp(-34420000/1987/T)*(6200/4053*(21372/625-21372/625*XA)/(89113/250+37477/1000*XA)-499489360/5475603*(31801/1000*XA+13/625)/(89113/250+37477/1000*XA)^2*XA/exp(403/25-15350/T)+6200/4053*(21372/625-21372/625*XA)/(89113/250+37477/1000*XA)*(1300*exp(-18880000/1987/T)+91000000*exp(-38190000/1987/T)))/(1+186/33775*exp(-40780000/1987/T)*(21372/625-21372/625*XA)/(89113/250+37477/1000*XA)+31/13510*exp(-16430000/1987/T)*(31801/1000*XA+13/625)/(89113/250+37477/1000*XA))^2-17609778230460416/190620607148483361*T+81282333867247665152/953103035742416805;
dy=[dXAdZ;dTdZ];
结果：
Z =
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
XA_T =
0 793.1500
0.3043 789.9721
0.3892 797.6251
0.4334 806.5600
0.4702 815.0588
0.5040 822.9552
0.5344 830.3187
0.5629 837.1223
0.5887 843.4597
0.6123 849.3483
0.6341 854.7995
0.6529 859.9201
0.6710 864.6180
0.6873 868.9888
0.7019 873.0588
0.7149 876.8467
0.7271 880.3388
0.7378 883.5979
0.7476 886.6092
0.7565 889.4039
0.7642 892.0048
0.7722 894.3671
0.7782 896.6123
0.7847 898.6369
0.7896 900.5655
0.7951 902.2929
0.7993 903.9262
0.8035 905.4203
0.8076 906.7874
0.8110 908.0661
0.8142 909.2369
0.8171 910.3243
0.8194 911.3458
0.8221 912.2550
0.8240 913.1243
0.8263 913.8938
0.8280 914.6293
0.8300 915.2819
0.8312 915.9180
0.8327 916.4820
0.8336 917.0237
function hahha
%global XA T G WAO MA DHR U TC dt G CPT RA
syms XA T
C2=0.247
C3=0.95
R=1.987
G=9430.217/(250*3.14159/4*0.123^2)
WAO=0.3884
ROU=1100
MA=106
CPT=2.22
U=20.02
TC=923.15
DHR=30850
P=0.155/0.101325
dt=0.123
PE=34.1952*(1-XA)/(356.452+37.477*XA)*P
PS=(31.801*XA+0.0208)/(356.452+37.477*XA)*P
PH=38.982*XA/(356.452+37.477*XA)*P
KE=5.7e8*exp(-34420/(R*T))
KT=1.3e3*exp(-18880/(R*T))
KB=9.1e7*exp(-38190/(R*T))
KP=exp(16.12-15350/T)
LEME=3.6e-3*exp(-40780/(R*T))
LEMS=1.5e-3*exp(-16430/(R*T))
C1=((3624.641-61.549*XA)/2265.401*(1-XA)/2.45)^0.25
RA=C1*C2*C3*KE*((PE-PS*PH/KP)+PE*(KT+KB))/(1+LEME*PE+LEMS*PS)^2*ROU
dXAdZ=RA/(G*WAO/MA)
dTdZ=(RA*(-DHR)-4*U*(T-TC)/dt)/(G*CPT)
[Z,XA_T] = ODE45(@myfun,[0:40],[0,793.15])
plotyy(Z,XA_T(:,1),Z,XA_T(:,2))
function dy=myfun(t,x)
%global XA T G WAO MA DHR U TC dt G CPT RA
XA=x(1);T=x(2);
dXAdZ =82824321519584909721600000/320864126079765233*20^(1/4)*49^(3/4)*((7970669852027257/4981669482150756-4229615073624064/155677171317211125*XA)*(1-XA))^(1/4)*exp(-34420000/1987/T)*(6200/4053*(21372/625-21372/625*XA)/(89113/250+37477/1000*XA)-499489360/5475603*(31801/1000*XA+13/625)/(89113/250+37477/1000*XA)^2*XA/exp(403/25-15350/T)+6200/4053*(21372/625-21372/625*XA)/(89113/250+37477/1000*XA)*(1300*exp(-18880000/1987/T)+91000000*exp(-38190000/1987/T)))/(1+186/33775*exp(-40780000/1987/T)*(21372/625-21372/625*XA)/(89113/250+37477/1000*XA)+31/13510*exp(-16430000/1987/T)*(31801/1000*XA+13/625)/(89113/250+37477/1000*XA))^2;
dTdZ =-998097780812185337856000000/75938290652647843*20^(1/4)*49^(3/4)*((7970669852027257/4981669482150756-4229615073624064/155677171317211125*XA)*(1-XA))^(1/4)*exp(-34420000/1987/T)*(6200/4053*(21372/625-21372/625*XA)/(89113/250+37477/1000*XA)-499489360/5475603*(31801/1000*XA+13/625)/(89113/250+37477/1000*XA)^2*XA/exp(403/25-15350/T)+6200/4053*(21372/625-21372/625*XA)/(89113/250+37477/1000*XA)*(1300*exp(-18880000/1987/T)+91000000*exp(-38190000/1987/T)))/(1+186/33775*exp(-40780000/1987/T)*(21372/625-21372/625*XA)/(89113/250+37477/1000*XA)+31/13510*exp(-16430000/1987/T)*(31801/1000*XA+13/625)/(89113/250+37477/1000*XA))^2-17609778230460416/190620607148483361*T+81282333867247665152/953103035742416805;
dy=[dXAdZ;dTdZ];
结果：
Z =
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
XA_T =
0 793.1500
0.3043 789.9721
0.3892 797.6251
0.4334 806.5600
0.4702 815.0588
0.5040 822.9552
0.5344 830.3187
0.5629 837.1223
0.5887 843.4597
0.6123 849.3483
0.6341 854.7995
0.6529 859.9201
0.6710 864.6180
0.6873 868.9888
0.7019 873.0588
0.7149 876.8467
0.7271 880.3388
0.7378 883.5979
0.7476 886.6092
0.7565 889.4039
0.7642 892.0048
0.7722 894.3671
0.7782 896.6123
0.7847 898.6369
0.7896 900.5655
0.7951 902.2929
0.7993 903.9262
0.8035 905.4203
0.8076 906.7874
0.8110 908.0661
0.8142 909.2369
0.8171 910.3243
0.8194 911.3458
0.8221 912.2550
0.8240 913.1243
0.8263 913.8938
0.8280 914.6293
0.8300 915.2819
0.8312 915.9180
0.8327 916.4820
0.8336 917.0237