solving PDE with boundary conditions involving derivative

Hi!

I'm trying to solve a PDE problem with boundary conditions: C(0,t)=Cf & dC(L,t)dz=0

My final goal is to find the C(z,t) and L.

Here is my full code for now:

Da=findDa(d_p,u,epsilon,Rho,eta);%function
constant=findConstant(epsilon, q_max, k_eq);
% z=findz(u, Da,Cf);

z = linspace(0,0.1,50);
t = linspace(0,1,50);

m = 0;
eqn = @(z,t,C,dCdz) setPDE(z,t,C,dCdz,Da,constant,u);
sol = pdepe(m,eqn,@findIC,@setBC,z,t);
C = sol(:,:,1);

function constantVal=findConstant(epsilon, q_max, k_eq)
    constantVal=(1+(1-epsilon)/epsilon*q_max*k_eq);
end 
function Daval=findDa(d_p,u,epsilon,Rho,eta)
    Re=u*d_p*Rho/eta;
    Daval=d_p*u*epsilon/(0.339+0.033*Re^0.48);
end 
function [g,f,s]=setPDE(z,t,C,dCdz,Da,constant,u)
    g=1;
    f=Da/constant*dCdz;
    s=-u/constant*dCdz;
end
function C0=findIC(z)
    C0=0;
end
function [pl,ql,pr,qr]=setBC(zl,Cl,zr,Cr,t)
...
end

Answer 1

[Torsten]

Cf = ...;
bcfcn = @(zl,Cl,zr,Cr,t)setBC(zl,Cl,zr,Cr,t,Cf);
sol = pdepe(m,eqn,@findIC,bcfcn,z,t);

function [pl,ql,pr,qr]=setBC(zl,Cl,zr,Cr,t,Cf)
  pl = Cl - Cf;
  ql = 0.0;
  pr = 0.0;
  qr = 1.0;
end

[YeEn Kim]

thank you!!

but i get this problem now:

Error using pdepe (line 293)

Spatial discretization has failed. Discretization supports only

parabolic and elliptic equations, with flux term involving spatial

derivative.

Error in math (line 23)

sol = pdepe(m,eqn,@findIC,bcfcn,z,t);

m = 0;

eqn = @(z,t,C,dCdz) setPDE(z,t,C,dCdz,Da,constant,u);

bcfcn = @(zl,Cl,zr,Cr,t) setBC(zl,Cl,zr,Cr,t,Cf);

sol = pdepe(m,eqn,@findIC,bcfcn,z,t);

[Torsten]

Check the values of your inputs Da, constant, u and Cf

.

[YeEn Kim]

I cleared it and it worked!!! Thank you so much!

Though, it still doesn't give me anything in the figure, but I guess I will slowly figure that out...

Thank you for your help XD