Time dependent external heat flux in PDE Toolbox

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Pascal Kobuß 2019-11-21

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https://ww2.mathworks.cn/matlabcentral/answers/492326-time-dependent-external-heat-flux-in-pde-toolbox

评论： Ravi Kumar 2019-11-25

Dear Community;

i am dealing with an issue with my model of a heat distribution of a cylindrical circular rod. My model is quite similar to https://de.mathworks.com/help/pde/examples/heat-distribution-in-a-circular-cylindrical-rod.html, but i am trying to create a heat flux, which is time-dependent. None of the tutorials or examples is really helpful. Unfortunately i am a beginner with Matlab, so i dont offer much skills in programming.

This is my code for the heatflux at the moment. Right now i am just working with an average heatflux, but i would like to use a time-dependent formula.

y_dach = 600; 
n=2; 
ts=1/8000; %increment
T=4; %T_max
t=0:ts:T; %timelist
heat = y_dach*sin(2*pi*n*t+pi/2); %Formula i want to use
heatflux_percentage = 0.35; 
Positive = heat >0;
heat(~Positive)=0; % only positive values
heatflux = heat/ V_cyl; ,
avg_heatflux=mean(heatflux_percentage*heatflux); 
thermalBC(thermalModelT,'Edge',[7,8],'HeatFlux',avg_heatflux)

This is my solver:

tfinal = 50; %tmax
tlist = 0:2:tfinal; %timeincrements
thermalModelT.SolverOptions.ReportStatistics = 'on';
result = solve(thermalModelT,tlist);
T = result.Temperature;

I know that i somehow have to use a function handle with state.time, but i dont know how to use it.

Many thanks in advance!

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Answer 1

Ravi Kumar 2019-11-21

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在 MATLAB Online 中打开

Hi Pascal,

You are on the right track, refer to the externalHeatFlux in the example:

https://www.mathworks.com/help/pde/ug/heat-conduction-in-multidomain-geometry-with-nonuniform-heat-flux.html

Thought the example is for spatial variaion, you can make your heat flux funciton of time using state.time, state is available to you as second argument.

function Qflux = timeDepHeatFlux(region,state)
    if isnan(state.time)
    Qflux = nan(size(region.x));
    return;
    end
    % Write you time dependent function here....
end

Regards,

Ravi

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Pascal Kobuß 2019-11-22

Hi Ravi,

thank you. So, the problem is the very large time vector. I cant change the vector though, because my analysis lasts such a long period of time. But besides that, is there a possiblity to say, that the heatflux will stop at a certain amount of time, so that my model will cool down after the heating phase?