whats wrong with my code?

function ped1
sol =pdepe(m,@pdefun,@pdeic,@pdebc,xmesh,tspan);
u=sol(:,:,1);

function [c,f,s]= pdefun(x,t,u,DuDx)
c = V/D;
f = DuDx;
s=0;
end

ped1

Undefined function or variable 'V'.

Error in pdefun (line 2)

c = V/D;

Error in pdepe (line 246)

[c,f,s] = feval(pde,xi(1),t(1),U,Ux,varargin{:});

Error in ped1 (line 27)

sol =pdepe(m,@pdefun,@pdeic,@pdebc,xmesh,tspan);

[Stephen23]

Before this line:

c = V/D;

Where are V and D defined?

[Shangeetha Mahendran]

I have defined in ped1

function ped1
m=1;
R=2.2e-4;                 %radius of lumen (m)
dm = 13.04e-6;           % TM thickness (m)
r1 =R + dm;               %radius of outer surface of membrane (m)
L=1;                      %height of the membrane (m)
Q =  6.5e-9;                %volumetric flow rate
D=1.76e-9;
RT = 2477.6;
H = 1.62;                   %Henry's law constant Pam^3/mol
u0= 285.1;

xn = 10;                        % grid-steps channel x-axis(radius side)
xmesh = linspace(0,R,xn);
tspan =linspace(0,L,10);            %counter point of length% spatial solution domain (m)
dx = 1/(xn-1);
x = [xmesh];

V = Q/3.14/R^2;

%U_z =zeros(1,xn);
%for ii=1:xn
%U_z(ii) =2*U_a *(1- x(ii)^2/R^2);

%end

sol =pdepe(m,@pdefun,@pdeic,@pdebc,xmesh,tspan);
u=sol(:,:,1);

surf(x,t,u)
xlabel('radi')
ylabel('height')


figure 
plot(x,u(end,:))
xlabel('radi')
ylabel('concentration')
end


function [c,f,s]= pdefun(x,t,u,DuDx)
c = V/D;
f = DuDx;
s=0;
end

function [pl,ql,pr,qr] = pdebc(xl,ul,xr,ur,t)
pl=0;
ql=1;
pr= u0 *(1-0.6*x/R)* H / RT / x / log (r1/R);
qr=1;
end

function u0 = pdeic(x)
u0 =285.1;
end

Answer 1

[Stephen23]

Make pdefun and pdebc nested functions by defining them inside of ped1:

function ped1()
...
V = ...
D = ...
R = ...
...
   function [...]= pdefun(...)
      ...
      V/D
      ...
   end
   function [...] = pdebc(...)
       ...
   end
end

https://www.mathworks.com/help/matlab/math/parameterizing-functions.html

[Shangeetha Mahendran]

Hello stephan, thank you for your answer. but still i am getting error

Error using surf (line 71)

Data dimensions must agree.

Error in ped1 (line 30)

surf(x,t,u)

[Stephen23]

That is a totally different error.

Check the sizes of x, t, and u. Read the surf documentation to see if that size combination is permitted.

[Shangeetha Mahendran]

I found the mistake. I didn't defined the term t.

one more question

in pdefun; is that possible to use array for the term "c" nstead of constant?

[Stephen23]

"in pdefun; is that possible to use array for the term "c" nstead of constant?"

MATLAB does not have any "constant" class, so it is not clear what you mean. Perhaps you mean that c is scalar?

In any case, the pdepe help states the the first output c should be a column vector. Given that both V and D are scalars, it is not clear what you expect c to be. Please show an example.

[Shangeetha Mahendran]

function [c,f,s]= pdefun(x,t,u,DuDx)
c = V/D;
f = DuDx;
s=0;
end

"c" is from this function.

if v is a column vector and t is the raw matrix is that possible to solve with pdepe