how to solve diffusion equation using pde toolbox

I have ficks diffusion equation need to solved in pde toolbox and the result of which used in another differential equation to find the resultant parameter can any help on this! Thanks for the attention

Answer 1

[Ravi Kumar]

You can solve diffusion equation in PDE Toolbox. Check this example:

% Create a model.
model = createpde(1);

% Create geometry and assign it to the model
R1 = [3;4;-1;1;1;-1;-1;-1;1;1];
C1 = [1;0;0;0.4];
C1 = [C1;zeros(length(R1) - length(C1),1)];
gd = [R1,C1];
sf = 'R1+C1';
ns = char('R1','C1')';
g = decsg(gd,sf,ns);
geometryFromEdges(model,g);

figure
pdegplot(model,'EdgeLabels','on','FaceLabels','on')

% Specify coefficients, diffusion coefficient as c and source as f
% Assign zero source and a diffusion coefficient, c = 1
specifyCoefficients(model,'Face',1,'m',0,'d',1,'c',1,'a',0,'f',0);
% Assign non-zero source and a different diffusion coefficient c = 2 on inner
% circle 
specifyCoefficients(model,'Face',2,'m',0,'d',1,'c',2,'a',0,'f',1);

% Set initial condition
setInitialConditions(model,0);
setInitialConditions(model,1,'Face',2);

% Generate mesh and solve.
generateMesh(model)
tlist = linspace(0,0.1,20);
result = solvepde(model,tlist)

% Plot results of last time-step.
figure
pdeplot(model,'XYData',result.NodalSolution(:,end))

[SUDALAI MANIKANDAN]

Thanks Ravi I have my model as 3D geometry which was imported from STL file how could i specify the regions of my model

[Ravi Kumar]

Can you post a picture of 3-D geometry you have? How many sub-domains does it have?

[SUDALAI MANIKANDAN]

It is a rectangular geometry with the following specifications i would like to know how to specify the boundary conditions

Nodes: [3×19797 double] Elements: [10×13170 double] MaxElementSize: 0.8718 MinElementSize: 0.4359 MeshGradation: 1.5000 GeometricOrder: 'quadratic'