3D diffusion equation in cylinder

Hi everyone, I am new in Matlab and I need some help. I want know if there is a way to solve the PDE for diffusion in a cylinder with 2 cm radius and 10 cm height.

thanks

Answer 1

[Precise Simulation]

Modelling and simulation of convection and diffusion for a 3D cylindrical (and other) domains is possible with the Matlab Finite Element FEM Toolbox , either by using the built-in GUI or as a m-script file as shown below.

    % Set up 3D cylindric domain.
    fea.sdim = { 'x' 'y' 'z' };
    fea.grid = cylgrid( 4, 3, 20, 0.02, 0.1 );
    % plotgrid( fea )   % Plot mesh.

    % Add covection and diffusion physics mode.
    fea = addphys( fea, @convectiondiffusion, {'C'} );

    % Define diffusion coefficient.
    fea.phys.cd.eqn.coef{2,end} = {'d_coef'};
    fea.expr = { 'c',      {'1.23'} ;
                 'd_coef', {'(1+c)^2/((1+c)^2+1)'} };

    % Set reaction source term to 1e3.
    fea.phys.cd.eqn.coef{6,end} = {1e3};

    % Use C = -1 on side boundaries, and insulation
    % flux boundary conditions on the top and bottom.
    fea.phys.cd.bdr.sel = [ 3 1 1 1 1 3 ];
    [fea.phys.cd.bdr.coef{1,end}{2:5}] = deal(-1);

    % Check, parse, and solve problem with stationary solver.
    fea = parsephys( fea );
    fea = parseprob( fea );

    fea.sol.u = solvestat( fea );

    % Postprocessing.
    postplot( fea, 'sliceexpr', 'C' )
    title( 'Concentration, C' )

[camila guerra]

hola trate de utilizar tu programacion y me aparece un error y discula esta programacion si es para la seguunda ley de fick verdad en 3 dimenciones

[camila guerra]

hi try to use your programming and I get an error and apologize for this programming if it is for the second law of true fick in 3 dimensions

[Precise Simulation]

The script example program above should work without error (what was the error message you got?).

To model Fick's second law of diffusion you typicall replace the expression in d_coef with whatever your diffusion coefficient is.

[태욱 김]

error occured : Untitled (line 3)

FEA.grid = cylgrid( 4, 3, 20, 0.02, 0.1 )

[Rae K.]

@Precise Simulation The cylgrid function doesn't appear to be part of the Matlab Finite Element FEM Toolbox, or appear anywhere in MATLAB Help/Answers other than this post.

[Precise Simulation]

The cylgrid function is available as part of the toolbox installation:

https://github.com/precise-simulation/featool-multiphysics/blob/master/grid/cylgrid.m

Answer 2

[Torsten]

If you have experience with the discretization of partial differential equations, you can write your own MATLAB code.

Otherwise, I'd suggest you use the PDE toolbox.

Best wishes

Torsten.