0 down vote favorite I am solving the diffusion equation in 1D with derivative boundary conditions. I am pretty new/rusty in mathematica so there may be several problems with the code but I think the main issue is trying to implement the boundary condition that is dependent on the previous timestep solution at x=0. Here is the code:

 Clear[x, y, t]
 ClearAll["Global`*"];
 Ceq =  4.5*10^(-6);
 F = 9*10^(-9);
 L = 10^(-3);
 Dif = 10^(-5);
 pde = D[u[x, t], t] == (Dif)*D[u[x, t], x, x]
 BC = {(D[u[x, t], x] /. 
 x -> L) == (L/Dif)*(c[0, t] - Ceq), (D[u[x, t], x] /. 
 x -> L) == (1/Dif)*F}
 IC = c[x, 0] = Ceq
 sol = NDSolve[{pde, IC, BC}, {u[x, t]}, {t, 0, 30}, {x, 0,L}]; 
 Plot3D[u[t, x] /. sol, {x, 0, 10^(-3)}, {t, 0, 20}]

I get a laundry list of errors as my output:

(1) NDSolve::deqn: Equation or list of equations expected instead of Ceq in 
    the      
    first argument {(u^(0,1))[x,t]==(u^(2,0))[x,t]/100000,Ceq,{(u^(1,0))        
    [1/1000,t]==100 (-Ceq+c[0,t]),(u^(1,0))[1/1000,t]==9/10000}}.

(2) NDSolve::dsvar: 0.00143` cannot be used as a variable.
(3) ReplaceAll::reps: {NDSolve[{(u^(0,1))[7.15*10^-8,0.00143]==(u^(2,0))
    [7.15*10^-8,0.00143]/100000,Ceq,{(u^(1,0))[1/1000,0.00143]==100 
    (Times[<<2>>]+c[<<2>>]),(u^(1,0))[1/1000,0.00143]==9/10000}},
    {u[7.15*10^-8,0.00143]},{0.00143,0,30},{7.15*10^-8,0,1/1000}]} is 
    neither a list of replacement rules nor a valid dispatch table, and so 
    cannot be used for replacing.

I am just trying to use mathmatica to double check a portion of a python solver that I wrote but it is turning out to be a huge hassle. Help on any of these error messages is greatly appreciated.enter code here