Unsuccessful use of anonymous function for time-varying boundary condition

I have asked previously about time varying boundary conditions. Advice offered suggested that I should recast my heat transfer problem to a general PDE equation. I have now done that and am trying to apply an anonymous function approach to a time varying boundary condition as suggested in the MatLab PDE Toolbox User’s Guide. As a simple example, I have defined a problem that is basically transient cryogenic cooling on one surface of a 1D slab with a known time-varying refrigeration temperature. I include the code below. MatLab says that the anonymous function for the boundary condition that I tried to define [bcfuncN] does not exist. What am I doing wrong?

Error using pde.BoundaryCondition (line 93. The value of 'g' is invalid. Function bcfuncN does not exist.

Another issue is that for a transient anonymous boundary condition function, I presume that I should be using state.time for the time variable. To define time limits of interest should I include code something like the following:

state.time= 0:1:100

Thanks

%% Create transient thermal model

thermalmodel = createpde(1);

R1= [3,4,0,4,4,0,0,0,1,1]';
gd= [R1];

sf= 'R1';
ns = char('R1');
ns = ns';
dl = decsg(gd,sf,ns);

%% Create & plot geometry

geometryFromEdges(thermalmodel,dl);
pdegplot(thermalmodel,"EdgeLabels","on","FaceLabels","on")
xlim([-1 5])
ylim([0 1])

% axis equal

%% Generate and plot mesh

generateMesh(thermalmodel)

ans = 
  FEMesh with properties:

             Nodes: [2x737 double]
          Elements: [6x338 double]
    MaxElementSize: 0.1649
    MinElementSize: 0.0825
     MeshGradation: 1.5000
    GeometricOrder: 'quadratic'

figure
pdemesh(thermalmodel)
title("Mesh with Quadratic Triangular Elements")

%% Apply BCs

% Edge 4 is left edge; Edge 2 is right side

hrefrig= 262

hrefrig = 262

f1= 3.843e-8;
f2= -3.482e-5;
f3= 1.179e-2;
f4= -1.95;
f5= 23.69;

bcfuncN = @(location,state)hrefrig*(f1*state.time.^4 + f2*state.time.^3 + f3*state.time.^2 + f4*state.time + f5);      % Anonymous function 


%% Define time limits

%tlist= 0: 1: 100;   
state.time= 0:1:100;

applyBoundaryCondition(thermalmodel,"neumann", ...
    Edge=4,g=@bcfuncN);

Error using pde.BoundaryCondition (line 93)
The value of 'g' is invalid. Function bcfuncN does not exist.

Error in pde.PDEModel/applyBoundaryCondition (line 177)
bc = pde.BoundaryCondition(BCcont,argsToPass{:});

applyBoundaryCondition(thermalmodel, "dirichlet",Edge=[2],u=20);

%% Apply thermal properties [copper]

rho= 8933                                  % 
cp= 385                                      % 
rhocp= rho*cp                         %
k= 401                                         % W/mK
alpha= k/rhocp

%% Define uniform volumetric heat generation rate

Qgen= 0                   % W/m3                   [1e12]

%% Define coefficients for generic Governing Equation to be solved

m= 0
a= 0
d= rhocp
c= [k]
f= [Qgen]

specifyCoefficients(thermalmodel, m=0, d=rhocp, c=k, a=0, f=f);


%% Apply initial condition

setInitialConditions(thermalmodel, 20);


thermalresults= solvepde(thermalmodel, tlist);


% Plot results

% Plot temperature profile along a defined line

plotAlongLine(thermalresults.Mesh.Nodes, thermalresults.NodalSolution(:,100), [0.0,0.5], [1,0.5], 100);

function plotAlongLine(p, u, xy1, xy2, numpts)
x = linspace(xy1(1),xy2(1),numpts);
y = linspace(xy1(2),xy2(2),numpts);
F = TriScatteredInterp(p(1,:)', p(2,:)', u);
uxy = F(x,y);
figure; plot(x, uxy);
end
ylim([20 50])

Answer 1

[Steven Lord]

When you run this line of code (commented out so I can run one line of code later in this answer):

%{
applyBoundaryCondition(thermalmodel,"neumann", ...
Edge=4,g=@bcfuncN);
%}

bcfuncN is a variable that contains a function handle (an anonymous function is a function handle as you can see from the output of whos.)

fh = @(x) x+1;
whos fh

  Name      Size            Bytes  Class              Attributes

  fh        1x1                32  function_handle              

Your code attempts to create a function handle to a function named bcfuncN and pass it into the function. That's not what you want; you want to pass the already existing function handle in like:

%{
applyBoundaryCondition(thermalmodel,"neumann", ...
Edge=4,g=bcfuncN);
%}

[John McGrath]

Thanks Steven

That did the trick