How do I create and place a non-uniform heat flux (Gaussian) on a cylinder with a center hole?

I'm trying to add a non-uniform heat flux to my simple model of a cylinder with a center hole. I know I need to create a function that describes the heat flux (Gaussian) but not sure how to do that in the context of my model. I believe the function can be applied as a thermalBC to Face 2 as shown below.

T_initial = 20;
t_end = 100;

model=createpde('thermal','transient');

geo = multicylcinder([.3,2],.2,'void',[1,0]);
modelGeometry = geo;
pdegplot(model,'FaceLabels',on);
thermalProperties(model,'ThermalConductivity',4,'MassDensity',210,'SpecificHeat',73);
thermalIC(model,T_initial);

% Heat Flux Function
% ------------------
% function Qflux = @nonUniformHeatFlux
%  ???
%  ???
%  ???
% end

thermalBC(model,'Face',1,'Temperature',20);
thermalBC(model,'Face',2,'HeatFlux',@nonUniformHeatFlux)

generateMesh(model)
pdemesh(model)

tlist = 0:10:t_end
modelresults = solve(model, tlist)

end

Answer 1

[Ravi Kumar]

Hi Michael,

Please take look at this example:

https://www.mathworks.com/help/pde/ug/heat-transfer-in-orthotropic-material-plate-due-to-laser-beam.html

Specifically, heatFluxSteady or heatFluxTimeDependent at the end of the example function might help you figure out the details you are looking for.

Regards,

Ravi

[Michael Tilton]

Thanks Ravi,

The example you lead me to had enough detail so that I was able create and apply my particular heat flux function.

Mike