Time-dependent boundary condition in PDE Toolbox

Hello ! I'm facing some issues with PDE Toolbox in Matlab, indeed I'm trying to solve the heat diffusion equation in a plate of Phase Change Material . So I've got a Temperature-dependent capacity , but I need to solve the equation in a sinusoidal state , I mean with a sin boundary condition. But today, when I specify 'sin(t)' as 'u' condition, it gives me back an error. I don't know very well the PDE toolbox app and I think i did something wrong, could you help me please ? Thanks a lot !

 Error using pde.internal.pde2DBCImpl/getBCMatrices (line 50)
 The "u" parameter of a pde.BoundaryCondition entity has more entries, 1001, than the number of equations,  1.
 This error occurred in the definition of a pde.BoundaryCondition entity on edge 4.

 Error in pde.internal.pde2DBCImpl>@(varargin)self.getBCMatrices(varargin{:}) (line 23)
       fh = @self.getBCMatrices;

 Error in pdeefxpd (line 9)
   [q,g,h,r]=feval(bl,p,e,u,time);

 Error in pdeexpd (line 39)
 [q,g,h,r]=pdeefxpd(p,e,u,time,bl);

 Error in assemb (line 164)
   [q,g,h,r]=pdeexpd(p,e,u,time,bl);

 Error in pdeODEInfo/getMats (line 165)
         [Q,G,H,R]=assemb(self.b,self.p,self.e,u,time);

 Error in pdeODEInfo/checkFuncDepen (line 61)
       [MM0,K0,M0,F0,Q0,G0,H0,R0] = self.getMats(u0, t0);

 Error in pdeParabolicInfo (line 13)
       obj=obj.checkFuncDepen(u0, tlist);

 Error in parabolic (line 109)
   pdeprb=pdeParabolicInfo(u0,tlist,b,p,e,t,c,a,f,d);

 Error in diffusionMCP (line 52)
 u = parabolic(u0, tlist, pdem, c, a, f, d);

Here is the code I wrote !

 %%DIFFUSION DANS UN MCP EN 1D 
 % Ecrit par Alexis CAILLON ### Dernière version : 11/03/2016

 %%CREATION D'UN MODELE de PDE Toolbox
 numberOfPDE = 1;
 pdem = createpde(numberOfPDE);

 %%Geometrie de la plaque / Geometry

 %Definition de la plaque
 hauteur = 0.005;
 largeur = 0.005;
 gdm = [3 4 0 largeur largeur 0 0 0 hauteur hauteur]';
 g = decsg(gdm, 'S1', ('S1')');
 geometryFromEdges(pdem,g);

 %Tracé et affichage / Plot
 figure;
 pdegplot(pdem,'edgeLabels','on');
 axis equal
 title 'Plaque (vue en coupe) avec légende';

 %Maillage de la plaque / Mesh
 hmax = 0.005/10; %taille d'un element fini
 msh=generateMesh(pdem,'Hmax', hmax);
 figure; 
 pdeplot(pdem); 
 axis equal
 title 'Plaque avec maillage triangulaire' 

 %%Conditions aux limites / Boundary coundition
 % 50° sur le bord gauche

 Tgauche = applyBoundaryCondition(pdem,'Edge',4, 'u', sin(350*t).^2);

 %%Définition des coefficients

 d = '500.*(4250 +(15000-4250).*exp(-((22.3-u)./3).^2))'; %capacité calorifique*rho

 c = 0.25; % conductivité thermique

 a = 0;
 f = 0;

 %%Solution en régime transitoire

 tlist = 0:1:1000;
 u0 = 15;
 u = parabolic(u0, tlist, pdem, c, a, f, d);

 getClosestNode = @(p,x,y) min((p(1,:) - x).^2 + (p(2,:) - y).^2);
 % Call this function to get a node near the center of the right edge.
 [~,nid] = getClosestNode( msh.Nodes, 1, 0 );

 h = figure;
 h.Position = [1 1 2 1].*h.Position;

 subplot(1,2,1); 
 axis equal

 pdeplot(pdem, 'xydata', u(:,end), 'contour', 'on', 'colormap', 'hot'); 
 axis equal
 title 'Temperature, Temps final, solution transitoire'

 subplot(1,2,2); 
 axis equal
 plot(tlist, u(nid,:));
 grid on
 title 'Temperature sur le bords droit a t final';
 xlabel 'Temps, secondes'
 ylabel 'Temperature, degrées-Celsius'

Answer 1

[Ravi Kumar]

Hi Alexis,

Replace the BC assignment line:

Tgauche = applyBoundaryCondition(pdem,'Edge',4, 'u', sin(350*t).^2);

with

 mybc = @(region,state) sin(350*state.time).^2;
 Tgauche = applyBoundaryCondition(pdem,'Edge',4, 'u', mybc);

Refer to the following documentation for additional details on specifying non-constant BC: http://www.mathworks.com/help/pde/ug/nonconstant-boundary-object-specification.html

Hope this helps!

Ravi