Mathematica about NDsolve PDE set - wolfram-mathematica

Question

I am trying to use NDsolve function to solve a PDE set.
I am pretty new to mathematica and here is the code I put in.
NDSolve[{D[Cm[t, x], t] == Dm*D[Cm[t, x], x, x] + Kg*Cs[t, x] - Ka*Cm[t, x],
D[Cs[t, x], t] == Ds*D[Cs[t, x], x, x] + Ka*Cm[t, x] - Kg*Cs[t, x],
Cm[0, x] == Cm0,
Cs[0, x] == Cs0,
Dm*ND[Cm[t, 0]] == 0.5*FT,
Ds*ND[Cs[t, 0]] == 0.5*FT,
Cm[t, Infinity] == Cm0,
Cs[t, Infinity] == Cs0}
{Cm[t, x], Cs[t, x]}, {t, 0, 1000}, {x, 0, Infinity}];
plot3D[Cs, {t, 0, 1000}, {x, 0, 10000}]
Dm = 9 e - 8;
Ds = 5 e - 9;
Cm0 = 1.276 e + 15;
Cs0 = 1.276 e + 20;
Ka = 1;
Kg = 1 e - 5;
FT = 1 e + 11;
So, basically, we have two PDEs, 2 initial conditions and 4 boundary conditions(two constant B.C. two flux B.C.). We know all the values of parameters. I am not sure if its a formatting problem or boundary choosing problem. The system gives
"Thread::tdlen: Objects of unequal length in "
"NDSolve::argmu: NDSolve called with 1 argument; 3 or more arguments are expected."
Could somebody give some valuable suggestions?
Thanks
Update
Dm = 9*10^-8;
Ds = 5*10^-9;
Cm0 = 1.276*10^+15;
Cs0 = 1.276*10^+20;
Ka = 1;
Kg = 1*10^-5;
FT = 1*10^+11;
NDSolve[{D[Cm[t, x], t] ==
Dm*D[Cm[t, x], x, x] + Kg*Cs[t, x] - Ka*Cm[t, x],
D[Cs[t, x], t] == Ds*D[Cs[t, x], x, x] + Ka*Cm[t, x] - Kg*Cs[t, x],
Cm[0, x] == Cm0,
Cs[0, x] == Cs0,
Dm*(D[Cm[t, x], x] /. x -> 0) == 0.7*FT,
Ds*(D[Cs[t, x], x] /. x -> 0) == 0.3*FT,
Cs[t, 10000] == Cs0,
Cm[t, 10000] == Cm0},
{Cm[t, x], Cs[t, x]}, {t, 0, 1000}, {x, 0, 10001},
PrecisionGoal -> 2];
Animate[Plot[Cs[t, x], {x, 0, 10000},
PlotRange -> {{0, 1000}, {0, 5*10^20}}], {t, 0, 1000}]

Answer 1

The "unequal" error was because you are missing a comma between } and { on your 8th and 9th line.
But that isn't your only problem. This fixes some other, but not all problems.
Dm = 9*10^-8;
Ds = 5 *10^-9;
Cm0 = 1.276*10^+15;
Cs0 = 1.276*10^+20;
Ka = 1;
Kg = 1*10^-5;
FT = 1*10^+11;
NDSolve[{D[Cm[t, x], t] == Dm*D[Cm[t, x], x, x] + Kg*Cs[t, x] - Ka*Cm[t, x],
D[Cs[t, x], t] == Ds*D[Cs[t, x], x, x] + Ka*Cm[t, x] - Kg*Cs[t, x],
Cm[0, x] == Cm0, Cs[0, x] == Cs0, Dm*ND[Cm[t, 0]] == 0.5*FT,
Ds*ND[Cs[t, 0]] == 0.5*FT, Cm[t, Infinity] == Cm0,
Cs[t, Infinity] == Cs0}, {Cm[t, x], Cs[t, x]}, {t, 0, 1000}, {x, 0, Infinity}];
plot3D[Cs, {t, 0, 1000}, {x, 0, 10000}]
Everything (except for the functions you are solving for and the independent variables) inside an NDSolve must be initialized to numeric values before starting the NDSolve, so I moved your assignments up. Mathematica has its' own way of writing exponents.
Now for bigger issues.
You have an ND function that you haven't defined. That is going to have to be defined before the NDSolve starts.
It is possible, maybe even likely that NDSolve is going to be less than cooperative with limits of Infinity for your x variable. It may work, but I wouldn't bet on that. You might try a smaller finite value, maybe 10^4 because that is bigger than your 10^3, and see if that will work if Infinity doesn't.
I don't spot any other big problems at the moment, but without knowing what your ND function is I can't begin to test this and perhaps flush out the next layer or two or three of problems to look for.
But this is actually pretty good if this is your first try at Mathematica.