Temperature-dependent boundary conditions

Hello,

I am having some difficulty developing my code for a heat transfer process using pde toolbox. I got errors as shown below,

Error using sym>tomupad (line 1240)
Unable to convert 'pde.PDEModel' to 'sym'.

Error in sym (line 214)
                S.s = tomupad(x);

Error in solve>getEqns (line 402)
        a = sym(a);

Error in solve (line 226)
[eqns,vars,options] = getEqns(varargin{:});

Error in heat_toy (line 56)
results = solve(model,tspan);

My boundary condition are tempeature-dependent. The coefficients 'g' and 'q' are defined by functions g1 and q1 respecitvely, and are as written as below,

    function value = g1(location,state)
        value = h*Ta./(S(state.u).*D(state.u));
    end
    function value = q1(location,state)
        value = h.*S(SpecificHeat(state.u).*D(state.u));
    end

S and D are functions of temperature, and are written as shown below,

    function value = S(u)
        cp = A3*u.^2 + B3*u + C3;
    end
    function value = D(u)
        rho = A2*u.^2 + B2*u + C2;
    end    

Is it the boundary condititions that are causing me errors? Is there any way to solve it?

Thank you very much!

Best regards,

SS

Answer 1

[Ravi Kumar]

Do you have PDE Toolbox in your installed products list? You can check this by executing 'ver' at the command prompt. If so, did you create the 'model' variable using model=createpde(....)?

Regards,

Ravi

[Shengyue Shan]

Hello Ravi,

Yes I have pde toolbox installed, and it worked for constant boundary conditions.I also created the model with createpde function.

Thank you!

Best, SS

[Ravi Kumar]

Hmm...can you paste the output when you type model at the command prompt, like:

>> model

[Shengyue Shan]

No problem, it is as shown below

ans = 

  FEMesh with properties:

             Nodes: [2×1151 double]
          Elements: [6×542 double]
    MaxElementSize: 0.0894
    MinElementSize: 0.0447
     MeshGradation: 1.5000
    GeometricOrder: 'quadratic'

Thanks!

[Ravi Kumar]

Yes thats it. Somewhere in your workflow you have overwritten the model variable with mesh. You don't have model, which would have looked something like this:

model = 

  ThermalModel with properties:

               AnalysisType: 'transient'
                   Geometry: []
         MaterialProperties: []
                HeatSources: []
    StefanBoltzmannConstant: []
         BoundaryConditions: []
          InitialConditions: []
                       Mesh: []
              SolverOptions: [1×1 pde.PDESolverOptions]

[Shengyue Shan]

Hi,

Thanks for your answer! But I am trying to not use the thermal analysis package, and I am just using the general solver to solve my problem as the package can't meet my need.

Is that the

generateMesh(model)

overwrites the model with mesh? But I thought it is a must-have step for solving the problem.

Thank you!

Best,

SS

[Ravi Kumar]

Can you post the complete code?

I am guessing you are overwriting the model, like:

model = generateMesh(model)

Regards,

Ravi

[Shengyue Shan]

Hi Ravi,

I guess I figured it out. The error was caused by using function solve instead of solvepde. Thanks for your help!

Best regards,

Shengyue Shan