Pdepe matlab convection diffusion

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Tasneem Na 2015-7-27

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https://ww2.mathworks.cn/matlabcentral/answers/231379-pdepe-matlab-convection-diffusion

评论： Torsten 2015-7-28

I want to solve this pde with initial and boundary conditions given. Tried Matlab's pdepe, but does not work satisfactorily. Maybe the boundary conditions is creating problem for me. I also used this isotherm equation for equilibrium: q = K*Cp^(1/n). This is convection-diffusion equation but i could not find any write ups that addresses solving this type of equation properly.

sol = pdepe(m,@ParticleDiffusionpde,@ParticleDiffusionic,@ParticleDiffusionbc,x,t);
% Extract the first solution component as u.
u = sol(:,:,:); 
function [c,f,s] = ParticleDiffusionpde(x,t,u,DuDx)
global Ds 
c = 1/Ds;
f = DuDx;
s = 0;
function u0 = ParticleDiffusionic(x)
global qo
u0 = qo;
function [pl,ql,pr,qr] = ParticleDiffusionbc(xl,ul,xr,ur,t,x)
global Ds K n
global Amo Gc kf rhop
global uavg
global dr R nr
sum = 0;
for i = 1:1:nr-1
r1 = (i-1)*dr; % radius at i
r2 = i * dr; % radius at i+1
r1 = double(r1); % convert to double precision
r2 = double(r2);
sum = sum + (dr / 2 * (r1*ul+ r2*ur));
end;
uavg = 3/R^3 * sum;
ql = 1;
pl = 0;
qr = 1;
pr = -((kf/(Ds.*rhop)).*(Amo - Gc.*uavg - ((double(ur/K)).^2).^(n/2) ));`
dq(r,t)/dt = Ds( d2q(r,t)/dr2 + (2/r)*dq(r,t)/dr )
q(r, t=0) = 0
dq(r=0, t)/dr = 0
dq(r=dp/2, t)/dr = (kf/Ds*rhop) [C(t) - Cp(at r = dp/2)]
q = solid phase concentration of trace compound in a particle with radius dp/2
C = bulk liquid concentration of trace compound
Cp = trace compound concentration at particle surface

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Walter Roberson 2015-7-27

I moved the text above the code to make the question easier to read.

Torsten 2015-7-28

It's not obvious for me how

pr = -((kf/(Ds.*rhop)).*(Amo - Gc.*uavg - ((double(ur/K)).^2).^(n/2) ));

corresponds with

dq(r=dp/2, t)/dr = (kf/Ds*rhop) [C(t) - Cp(at r = dp/2)]

Further, I don't understand what you try to average in the for-loop. You refer to radii r1 and r2, but you use the values of u at the boundary. Moreover, averaging would be choosing r^2*u instead of r*u in spherical coordinates.

Best wishes

Torsten.

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