I understand that you want to find the heat generated by the circular plate for it to reach 100°C using FEM (Finite Elements Method).
You can define the target temperature and modify the heat generation rate until the current temperature reaches the target temperature. You can use a tolerance value for getting the desired temperature and adjust accordingly to control the accuracy of the result.
I have modified the code as below:
model = createpde;
R1 = [3,4,0,10,10,0,10,10,0,0]';
C1 = [1,5,8,0.2]';
C1 = [C1;zeros(length(R1) - length(C1),1)];
gm = [R1,C1];
sf = 'R1+C1';
% Create the geometry.
ns = char('R1','C1');
ns = ns';
g = decsg(gm,sf,ns);
% Include the geometry in the model and plot it.
thermalModel = createpde("thermal","steadystate");
geometryFromEdges(thermalModel,g);
figure(1);
pdegplot(thermalModel,'FaceLabels','on','EdgeLabels','on')
axis equal
xlim([0,10])
% Generate mesh
mesh = generateMesh(thermalModel,"Hmax",0.25,"Hedge",{[5 6 7 8],0.01});
figure(2)
pdeplot(thermalModel)
% Set thermal properties
thermalProperties(thermalModel,'ThermalConductivity',1,'Face',1);
thermalProperties(thermalModel,'ThermalConductivity',1/6,'Face',2);
% Define the internal heat generation
heatGeneration = 500;
internalHeatSource(thermalModel, heatGeneration, 'Face', 2);
% Set boundary conditions
thermalBC(thermalModel,'Edge',[1,2,3],'Temperature',25);
thermalBC(thermalModel,'Edge',4,'ConvectionCoefficient',7.371,'AmbientTemperature',30);
% Solve the steady-state heat transfer problem
thermalresults = solve(thermalModel);
T = thermalresults.Temperature;
% Plot the temperature distribution
set(gcf,'color','white')
figure(3)
pdeplot(thermalModel,'XYData',T,'Contour','on')
axis equal
title(['\fontsize{16}Steady-State Temperature. Max temp. ',num2str(max(T)),' \fontsize{16}^0C'])
% Find the heat generation required to reach the target temperature
targetTemperature = 100;
tolerance = 0.01;
while abs(max(T) - targetTemperature) > tolerance
% Adjust the heat generation based on the current temperature
heatGeneration = heatGeneration * (targetTemperature / max(T));
% Update the internal heat generation
internalHeatSource(thermalModel, heatGeneration, 'Face', 2);
% Solve the heat transfer problem
thermalresults = solve(thermalModel);
T = thermalresults.Temperature;
end
disp(['Heat generation required to reach ', num2str(targetTemperature), '°C: ', num2str(heatGeneration), ' W/m^3']);
The code has produced the following output:
Heat generation required to reach 100°C: 608.4878 W/m^3
You can try referring to:
Hope this helps!!
