# 1D time dependent mass transfer and reaction in a very small slab

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Moji on 29 Mar 2018
Reopened: Moji on 12 Apr 2018
I am trying to model a pde including advection-diffusion and reaction terms. i want to see the concentration profil after a long time(2*60*60 sec) in a very tiny slab(5 micrometer). i used method of line(ode15s) to solve this pde but my result is not match with the experimental result. because the outlet concentration gets maximum concetration right away(as can be seen in myplot).does anybody know where is my mistake?
Bill Greene on 31 Mar 2018
I don't see anything wrong with your pdepe code. So I suspect there is something wrong with your constants (values or units). For example, if I make the total time 1e-7 instead of 120, the solution looks more reasonable.

Abraham Boayue on 30 Mar 2018
By carefully defining the parameters of your function in matlab using the pdepe solver, I was able to obtain the image below. Does this look like what you want to see?
function PDEPE_diff
m = 0;
x = linspace(0,1,200);
t = linspace(0,2,100);
sol = pdepe(m,@pdepfun,@icfun,@bcfun,x,t);
u = sol(:,:,1);
plot(x,u(1:100,:,1),'linewidth',1.5)
title('Numerical solution computed with 200 mesh points.')
xlabel('Distance x')
ylabel('Time t')
grid
function [g,f,s] = pdepfun(x,t,c,DcDx)
D = 8.6e-6;
k = 1;
K = 0.24;
ux = 0.5;
g = 1;
f = D*DcDx;
s = -(ux*DcDx + k*K*c);
function c0 = icfun(x)
c0 = 0*x;
function [pl,ql,pr,qr] = bcfun(xl,cl,xr,cr,t)
pl = cl-20;
ql = 0;
pr = cr;
qr = 1;
%
Abraham Boayue on 31 Mar 2018
I understand what you mean. I strongly believe that it depends on the method of coding, you could try other numerical schemes like the finite difference method. Was it mentioned how the results were obtained in the paper that you are reading?