S1=a''[t]==-a'[t]+α(-Rnd[t]+Rab[t])+a[t]+Qe[t]π+α(Rab'[t]-Rnd'[t])+Qf'[t]π+a'[t];S2=b'[t]==-((-Ri)b[t]-αa[t]F+παa[t]c[t]);S3=c'[t]==(απa[t]b[t]-8c[t]+2c[t]Ri);S4=d'[t]==-παe[t]a[t]+αa[t]++b[t];S5=e'[t]==-a[t]d[t]+4+c[t];S6=f'[t]==(πa[t]-f[t]-παg[t]a[t]);S7=g'[t]==-a[t]f[t]+4g[t];S8={S1,S2,S3,S4,S5,S6,S7};
Pr
λ
1
2
δ
2
δ
Pr
4
δ
2
δ
λ
1
λ
1
λ
1
2
δ
λ
2
4
δ
2
δ
1
2
2
π
2
δ
d[t]
Le
NA
Le
-πα
2
2
π
e[t]
Le
NA
Le
1
Pm
2
δ
1
Pm
πα
2
2
α
correctListOfEquations={S1,S2,S3,S4,S5,S6,S7,a[0]0.04,b[0]0.04,c[0]0,d[0]0.04,e[0]0.0,f[0]0.04,g[0]0.04,a'[0]0.04}/.Rn0.5/.δ4/.Pr1/.α2/.Ra3600/.NA3.0/.Le200/.1.0/.0.5/.Q5/.Ri1/.F-0.5129942973523781`/.Pm0.4
λ
1
λ
2
[t]-0.0625(256a[t]+2(3600b[t]-0.5d[t])+80πe[t]+144.[t]+2(3600.[t]-0.5[t])+251.327[t]),[t]-1.02599a[t]-15b[t]-2πa[t]c[t],[t](2πa[t]b[t]+2c[t]-8c[t]),[t]-2a[t]-160.015b[t]+-2πa[t]e[t],[t]πa[t]d[t]-40.015c[t]+,[t]2.5(πa[t]-16f[t]-2πa[t]g[t]),[t]-2.5(πa[t]f[t]+16g[t]),a[0]0.04,b[0]0.04,c[0]0,d[0]0.04,e[0]0.,f[0]0.04,g[0]0.04,[0]0.04
′′
a
′
a
′
b
′
d
′
f
′
b
′
c
1
2
2
π
′
d
d[t]
200
′
e
2
π
e[t]
200
′
f
′
g
′
a
solution=NDSolve[correctListOfEquations,{a,b,c,d,e,f,g},{t,0.0,10}]
{{aInterpolatingFunction[{{0.,10.}},<>],bInterpolatingFunction[{{0.,10.}},<>],cInterpolatingFunction[{{0.,10.}},<>],dInterpolatingFunction[{{0.,10.}},<>],eInterpolatingFunction[{{0.,10.}},<>],fInterpolatingFunction[{{0.,10.}},<>],gInterpolatingFunction[{{0.,10.}},<>]}}
{b[0.2]}/.solution
{{-0.111557}}
{c[0.2]}/.solution
{{-0.0179058}}
ContourPlot[-0.11155708971704904`Cos[2x]Sin[πz]-0.01790580044290322`Sin[2πz],{x,0,2.5},{z,0,1.0}]
{b[0.25]}/.solution
{{-0.166933}}
{c[0.25]}/.solution
{{-0.0456366}}
ContourPlot[-0.1669334023013586`Cos[2x]Sin[πz]-0.045636593247283454`Sin[2πz],{x,0,2.1},{z,0,1.0}]
{b[0.3]}/.solution
{{-0.190635}}
{c[0.3]}/.solution
{{-0.0722601}}
ContourPlot[-0.19063533517575743`Cos[2x]Sin[πz]-0.07226010198824859`Sin[2πz],{x,0,2.1},{z,0,1.0}]
