PDE thermal model with internal heat sources as a function of temperature

For the steady state heat transfer model I want to specify internal heat source as a function of local temperature. I tried as:

internalHeatSource(myPde, @(location, state) A*((interpolateTemperature(state.u, [location.x; location.y; location.z]))' - Tb), 'cell', 11);

but when I try to solve the model, I get an error:

Function specifying a heat source must accept two

input arguments and return one output argument.

Perhaps I have to somehow transform state.u to thermalresults form. Can you explain me how to properly do that?

Answer 1

[Tadeu Fagundes]

I have the same issue. It seems like if you only use the location input, it works fine. But anything using the state input gives me the same error.

[Urban Simoncic]

Exactly, you can use location, but not the state. But I found a solution for my problem. I wanted to have an internal heat source LINEARLY proportional to the local temperature and that can be done by solving general PDE in Matlab and setting appropriate terms to 0.

[Diego]

Same issue. I have been looking around, but I can't find an answer for this problem. I have been trying to simulate the steady state of a curing process inside a heated die and I can’t progress because of this problem with a temperature dependent internal heat source.

Answer 2

[Bradley]

I might have something for this... after many hours of trial and error.

For my model, I created an anonymous function as you did. In my model, I have a temperature minimum which will trigger the internal heat generated to switch between 0 and whatever my net heat value is for the system.

Q_int = @(location,state) myInternalHeat(TemperatureMin,HeatParams,state.u);

TemperatureMin is a double, and HeatParams is a structure containing Q_net.

Then, myInternalHeat works like this:

function Q_int = myInternalHeat(TemperatureMin,HeatParams,state)

mean_temp = mean(state);

if mean_temp <= TemperatureMin

Q_int = zeros(size(state));

else

Q_int = zeros(size(state)) + HeatParams.Q_net;

end

end

It was important to keep Q_int the same size as state so it would actually read and return correctly. From there, I assigned my internal heat with the normal internalHeatSource function. From their documentation here it seems that the form of your function must follow the two in, one out format.